# questions

tags: ['Physics', 'Ray Optics', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P1.db
title:
an-object-is-placed-60-cm-in-front-of-a-convex-mirror-of-focal-length-30-cm-a-plane-mirror-is-now-placed-facing-the-object-in-between-the-object-and-t

slug:
an-object-is-placed-60-cm-in-front-of-a-convex-mirror-of-focal-length-30-cm-a-plane-mirror-is-now-placed-facing-the-object-in-between-the-object-and-t-75761

question:
<div class="question">An object is placed $60 \mathrm{~cm}$ in front of a convex mirror of focal length $30 \mathrm{~cm}$. A plane mirror is now placed facing the object in between the object and the convex mirror such that it covers lower half of the convex mirror. What should be the distance of the plane mirror from the object so that there will be no parallax between the images formed by the two mirrors?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$40 \mathrm{~cm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$30 \mathrm{~cm}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$20 \mathrm{~cm}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$15 \mathrm{~cm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$40 \mathrm{~cm}$</span> </div>

answer:
<div class="solution">Hint: 
<br/>$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
<br/>$\frac{1}{v}-\frac{1}{60}=\frac{1}{30}$
<br/>$\mathrm{v}=\frac{60}{3}=\pm 20 \mathrm{~cm}$
<br/>$\therefore$ Distance between object and image $=60+20=80 \mathrm{~cm}$ $\therefore x=40 \mathrm{~cm}$</div>


tags: ['Physics', 'Ray Optics', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P1.db
title:
an-object-placed-at-a-distance-of-16-cm-from-a-convex-lens-produces-an-image-of-magnification-m-m-1-if-the-object-is-moved-towards-the-lens-by-8-cm-th

slug:
an-object-placed-at-a-distance-of-16-cm-from-a-convex-lens-produces-an-image-of-magnification-m-m-1-if-the-object-is-moved-towards-the-lens-by-8-cm-th-72381

question:
<div class="question">An object placed at a distance of $16 \mathrm{cm}$ from a $\begin{array}{llll}\text { convex lens } &amp; \text { produces } &amp; \text { an image } &amp; \text { of }\end{array}$ magnification $m(m&gt;1)$. If the object is moved towards the lens by $8 \mathrm{cm}$, then again an image of magnification $m$ is obtained. The numerical value of the focal length of the lens is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$12 \mathrm{cm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$14 \mathrm{cm}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$18 \mathrm{cm}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$20 \mathrm{cm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$12 \mathrm{cm}$</span> </div>

answer:
<div class="solution">Linear magnification, $m=\frac{f}{f+u}$
<br/>As given that magnification is same for both cases this is possible if the two different values of $u$ are of opposite sign.
<br/>$i, \theta,+\frac{f}{f-16}=\frac{-f}{f-8}$
<br/>$\Rightarrow \quad 16-f=f-8$
<br/>$\Rightarrow \quad 2 f=24$
<br/>or $\quad f=12 \mathrm{cm}$</div>


tags: ['Physics', 'Ray Optics', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch1_P1.db
title:
an-object-placed-in-front-of-a-concave-mirror-at-a-distance-of-x-cm-from-the-pole-gives-a-3-times-magnified-real-image-if-it-is-moved-to-a-distance-of

slug:
an-object-placed-in-front-of-a-concave-mirror-at-a-distance-of-x-cm-from-the-pole-gives-a-3-times-magnified-real-image-if-it-is-moved-to-a-distance-of-63964

question:
<div class="question">An object placed in front of a concave mirror at a distance of $x$ cm from the pole gives a 3 times magnified real image. If it is moved to a distance of $(x+5) \mathrm{cm},$ the magnification of the image becomes 2 . The focal length of the mirror is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$15 \mathrm{cm}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$20 \mathrm{cm}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$25 \mathrm{cm}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$30 \mathrm{cm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$30 \mathrm{cm}$</span> </div>

answer:
<div class="solution">Given $y_{1}=3 x$ and $v_{2}=2(x+5)$ So here, Ist case
<br/>$$
<br/>\begin{array}{r}
<br/>\frac{1}{-x}+\frac{1}{-3 x}=\frac{1}{f} \\
<br/>\frac{1}{-(x+5)}+\frac{1}{-2(x+5)}=\frac{1}{f}
<br/>\end{array}
<br/>$$
<br/>On solving Eqs. (i) and (ii) we get $f=30 \mathrm{cm}$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch1_P1.db
title:
an-object-weighs-mathrmm1-in-a-liquid-of-density-mathrmd1-and-that-in-liquid-of-density-mathrmd2-is-mathrmm2-the-density-d-of-the-object-is

slug:
an-object-weighs-mathrmm1-in-a-liquid-of-density-mathrmd1-and-that-in-liquid-of-density-mathrmd2-is-mathrmm2-the-density-d-of-the-object-is-29450

question:
<div class="question">An object weighs \(\mathrm{m}_1\) in a liquid of density \(\mathrm{d}_1\) and that in liquid of density \(\mathrm{d}_2\) is \(\mathrm{m}_2\). The density \(d\) of the object is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(\mathrm{d}=\frac{\mathrm{m}_2 \mathrm{~d}_2-\mathrm{m}_1 \mathrm{~d}_1}{\mathrm{~m}_2-\mathrm{m}_1}\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(d=\frac{\mathrm{m}_1 \mathrm{~d}_1-\mathrm{m}_2 \mathrm{~d}_2}{\mathrm{~m}_2-\mathrm{m}_1}\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(\mathrm{d}=\frac{\mathrm{m}_2 \mathrm{~d}_1-\mathrm{m}_1 \mathrm{~d}_2}{\mathrm{~m}_1-\mathrm{m}_2}\)</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">\(\mathrm{d}=\frac{\mathrm{m}_1 \mathrm{~d}_2-\mathrm{m}_2 \mathrm{~d}_1}{\mathrm{~m}_1-\mathrm{m}_2}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\mathrm{d}=\frac{\mathrm{m}_1 \mathrm{~d}_2-\mathrm{m}_2 \mathrm{~d}_1}{\mathrm{~m}_1-\mathrm{m}_2}\)</span> </div>

answer:
<div class="solution">Hints: \(V\left(d-d_1\right) g=m_1 g\)<br/>\(\mathrm{V}\left(\mathrm{d}-\mathrm{d}_2\right) \mathrm{g}=\mathrm{m}_2 \mathrm{~g}\)<br/>\(\frac{\mathrm{d}-\mathrm{d}_1}{\mathrm{~d}-\mathrm{d}_2}=\frac{\mathrm{m}_1}{\mathrm{~m}_2} \quad \therefore \mathrm{d}=\frac{\mathrm{m}_1 \mathrm{~d}_2-\mathrm{m}_2 \mathrm{~d}_1}{\mathrm{~m}_1-\mathrm{m}_2}\)</div>


tags: ['Mathematics', 'Probability', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P1.db
title:
an-objective-type-test-paper-has-5-questions-out-of-these-5-questions-3-questions-have-four-options-each-a-b-c-d-with-one-option-being-the-correct-ans

slug:
an-objective-type-test-paper-has-5-questions-out-of-these-5-questions-3-questions-have-four-options-each-a-b-c-d-with-one-option-being-the-correct-ans-64728

question:
<div class="question">An objective type test paper has 5 questions. Out of these 5 questions, 3 questions have four options each $(a, b, c, d)$ with one option being the correct answer. The other 2 questions have two options each, namely true and false. A candidate randomly ticks the options. Then, the probability that he/she will tick the correct option in atleast four questions, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{5}{32}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{3}{128}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{3}{256}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{3}{64}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{3}{64}$</span> </div>

answer:
<div class="solution">Total sample space, $n(S)=4^{3} \cdot 2^{2}$ and total number of favourable cases
<br/>$$
<br/>n(E)=\left({ }^{3} C_{1} \cdot 3+{ }^{2} C_{1} \cdot 1\right)+1
<br/>$$
<br/>$\therefore$ Required probability $=\frac{n(E)}{n(S)}$
<br/>$$
<br/>=\frac{{ }^{3} \mathrm{C} \cdot 3+{ }^{2} \mathrm{C}_{1} \cdot 1+1}{4^{3} \cdot 2^{2}}=\frac{3 \cdot 3+2+1}{4^{3} \cdot 4}
<br/>$$
<br/>$=\frac{12}{64 \cdot 4}=\frac{3}{64}$</div>


tags: ['Chemistry', 'Hydrocarbons', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P1.db
title:
an-optically-active-compound-having-molecular-formula-c-8-h-16-on-ozonolysis-gives-acetone-as-one-of-the-products-the-structure-of-the-compound-is

slug:
an-optically-active-compound-having-molecular-formula-c-8-h-16-on-ozonolysis-gives-acetone-as-one-of-the-products-the-structure-of-the-compound-is-87748

question:
<div class="question">An optically active compound having molecular formula $\mathrm{C}_{8} \mathrm{H}_{16}$ on ozonolysis gives acetone as one of the products. The structure of the compound is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q23_opta.png"/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q23_optb.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q23_optc.png"/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q23_optd.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q23_optb.png"/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_a23.png"/></div>


title: an-organic-compound-made-of-c-h-and-n-contains-20-nitrogen-its-molecular-weight-is
slug: an-organic-compound-made-of-c-h-and-n-contains-20-nitrogen-its-molecular-weight-is-93189
tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'WBJEE', 'WBJEE 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$70$</span> </div>
source_db: db\MarksBatch1_P1.db
question:
<div class="question">An organic compound made of $\mathrm{C}, \mathrm{H}$ and $\mathrm{N}$ contains $20 \%$ nitrogen. Its molecular weight is :</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$70$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$140$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$100$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$65$</span> </li> </ul>

answer:
<div class="solution">Nitrogen at. wt. $=14$ in a molecule minimum one atom of $\mathrm{N}$ is present<br/>i.e., $\begin{array}{rlr}20 \% &amp; \equiv 14 &amp; \text { Molecular weight }=70 \\ 100 \% &amp; \equiv 14 \times 5=70 &amp; \end{array}$</div>


tags: ['Mathematics', 'Probability', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch1_P1.db
title:
an-urn-contains-8-red-and-5-white-balls-three-balls-are-drawn-at-random-then-the-probability-that-balls-of-both-colours-are-drawn-is

slug:
an-urn-contains-8-red-and-5-white-balls-three-balls-are-drawn-at-random-then-the-probability-that-balls-of-both-colours-are-drawn-is-65115

question:
<div class="question">An urn contains 8 red and 5 white balls. Three balls are drawn at random. Then, the probability that balls of both colours are drawn is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{40}{143}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{70}{143}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{3}{13}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{10}{13}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{10}{13}$</span> </div>

answer:
<div class="solution">Total number of selections of three balls in which balls of both colours are drawn
<br/>$=2$ red balls and 1 white ball +1 red ball and 2 white balls
<br/>$\begin{array}{l}
<br/>={ }^{8} C_{2} \times{ }^{5} C_{1}+{ }^{8} C_{1} \times{ }^{5} C_{2} \\
<br/>=140+80=220
<br/>\end{array}$
<br/>$\therefore$ Required probability
<br/>$=\frac{220} {{ }^{13} C_{3}}=\frac{220 \times 6}{13 \times 12 \times 11}=\frac{10}{13}$</div>


title: angle-between-an-equipotential-surface-and-electric-lines-of-force-is
slug: angle-between-an-equipotential-surface-and-electric-lines-of-force-is-70410
question: <div class="question">Angle between an equipotential surface and electric lines of force is</div>
tags: ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0^{\circ}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$90^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$180^{\circ}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$270^{\circ}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$90^{\circ}$</span> </div>

answer:
<div class="solution">The electric lines of force are always perpendicular to the equpotential surtace
<br/>$$
<br/>\theta=90^{\circ}
<br/>$$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_phy_a30.png"/></div>


title: angle-between-the-planes-x-y-2-z-6-and-2-x-y-z-9-is
slug: angle-between-the-planes-x-y-2-z-6-and-2-x-y-z-9-is-93082
question: <div class="question">Angle between the planes $x+y+2 z=6$ and $2 x-y+z=9$ is</div>
tags: ['Mathematics', 'Three Dimensional Geometry', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\pi}{4}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\pi}{6}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{\pi}{3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\pi}{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\pi}{3}$</span> </div>

answer:
<div class="solution">Equations of planes are
<br/>$x+y+2 z-6=0$
<br/>and $\quad 2 x-y+z-9=0$
<br/>$\cos \theta=\frac{a_{1} a_{2}+b_{1}b_{2}+c
<br/>_{1}c_{2}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}} \sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}$
<br/>$=\frac{1 \times 2+1 \times(-1)+2 \times 1}{\sqrt{1+1+4} \sqrt{4+1+1}}$
<br/>$=\frac{2-1+2}{\sqrt{6} \times \sqrt{6}}=\frac{3}{6}=\frac{1}{2}$
<br/>$\Rightarrow \quad \cos \theta=\cos \left(\frac{\pi}{3}\right)$
<br/>$\therefore \quad \theta=\frac{\pi}{3}$</div>


title: angle-between-y-2-x-and-x-2-y-at-the-origin-is
slug: angle-between-y-2-x-and-x-2-y-at-the-origin-is-67650
tags: ['Mathematics', 'Application of Derivatives', 'WBJEE', 'WBJEE 2009']
source_db: db\MarksBatch1_P1.db
question:
<div class="question">Angle between $\mathrm{y}^2=\mathrm{x}$ and $\mathrm{x}^2=\mathrm{y}$ at the origin is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \tan ^{-1}\left(\frac{3}{4}\right)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\tan ^{-1}\left(\frac{4}{3}\right)$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{\pi}{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\pi}{4}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\pi}{2}$</span> </div>

answer:
<div class="solution">Hins : Angle between axes (since co-ordinate axes are the tangents for the given curve).<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/DwLfBMRAlzqptDvApJjKAssCZyUbAkJ11Pnp5tzfxGs.original.fullsize.png"/><br/></div>


title: anhydrous-ferric-chloride-is-prepared-by-1
slug: anhydrous-ferric-chloride-is-prepared-by-1-17600
question: <div class="question">Anhydrous ferric chloride is prepared by</div>
tags: ['Chemistry', 'd and f Block Elements', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Dissolving \(\mathrm{Fe}(\mathrm{OH})_3\) in concentrated \(\mathrm{HCl}\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Dissolving \(\mathrm{Fe}(\mathrm{OH})_3\) in dilute \(\mathrm{HCl}\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Passing dry \(\mathrm{HCl}\) over heated iron scrap</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Passing dry \(\mathrm{Cl}_2\) gas over heated iron scrap</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Passing dry \(\mathrm{Cl}_2\) gas over heated iron scrap</span> </div>

answer:
<div class="solution">Hints: \(2 \mathrm{Fe}+3 \mathrm{Cl}_2 \stackrel{\Delta}{\longrightarrow} 2 \mathrm{FeCl}_3\)</div>


tags: ['Mathematics', 'Application of Derivatives', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
title:
applying-lagranges-mean-value-theorem-for-a-suitable-function-f-x-in-0-h-we-have-f-h-f-0-h-f-h-0-1-then-for-f-x-cos-x-the-value-of-lim-h-0-is

slug:
applying-lagranges-mean-value-theorem-for-a-suitable-function-f-x-in-0-h-we-have-f-h-f-0-h-f-h-0-1-then-for-f-x-cos-x-the-value-of-lim-h-0-is-84084

question:
<div class="question">Applying Lagrange's Mean Value Theorem for a suitable function $f(x)$ in $[0, h],$ we have $f(h)=f(0)+h f^{\prime}(\theta h), \quad 0    &lt; \theta &lt; 1 . \quad$ Then, for $f(x)=\cos x,$ the value of $\lim _{h \rightarrow 0^{*}} \theta$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">0</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$1 / 2$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1 / 3$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1 / 2$</span> </div>

answer:
<div class="solution">We know that in a Lagrange mean value theorem there exist $c \in(a, b)$ such that
<br/>$$
<br/>f^{\prime}(c)=\frac{f(b)-f(a)}{b-a}
<br/>$$
<br/>$\therefore \quad f^{\prime}(\theta h)=\frac{f(h)-\cos 0}{h-0}$
<br/>$$
<br/>\begin{aligned}
<br/>\Rightarrow \quad-\sin (\theta h)=&amp; \frac{\cos h-\cos 0}{h-0} \\
<br/>&amp;[\because f(x)=\cos x] \\
<br/>=&amp; \frac{\cos h-1}{h}
<br/>\end{aligned}
<br/>$$
<br/>$=\frac{\left(1-\frac{h^{2}}{2 !}\right)-1}{h}$
<br/>[neglecting higher power of $\Rightarrow \quad-\sin (\theta h)=\frac{-\frac{h^{2}}{2}}{h}$
<br/>$\Rightarrow \quad \sin (\theta h)=\frac{\frac{h}{2}}{1}$
<br/>$\Rightarrow \quad \theta h=\sin ^{-1}\left(\frac{h}{2}\right)$
<br/>$\Rightarrow \quad \theta=\frac{\sin ^{-1} \frac{h}{2} \times \frac{1}{2}}{h \times \frac{1}{2}}$
<br/>$\therefore \quad \lim _{h \rightarrow \theta^{+}} \theta=\frac{1}{2} \lim _{h \rightarrow 0^{+}} \frac{\sin ^{-1} \frac{h}{2}}{\frac{h}{2}}$
<br/>$=\frac{1}{2} \times 1=\frac{1}{2}$</div>


tags: ['Chemistry', 'Ionic Equilibrium', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch1_P1.db
title:
aqueous-solution-of-hno-3-koh-ch-3-cooh-and-ch-3-coona-of-identical-concentration-are-provided-the-pair-s-of-solutions-which-form-a-buffer-upon-mixing

slug:
aqueous-solution-of-hno-3-koh-ch-3-cooh-and-ch-3-coona-of-identical-concentration-are-provided-the-pair-s-of-solutions-which-form-a-buffer-upon-mixing-58442

question:
<div class="question">Aqueous solution of $\mathrm{HNO}_{3}, \mathrm{KOH}, \mathrm{CH}_{3} \mathrm{COOH}$ and $\mathrm{CH}_{3} \mathrm{COONa}$ of identical concentration are provided. The pair (s) of solutions which form a buffer upon mixing is (are)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{HNO}_{3}$ and $\mathrm{CH}_{3} \mathrm{COOH}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{KOH}$ and $\mathrm{CH}_{3} \mathrm{COONa}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{HNO}_{3}$ and $\mathrm{CH}_{3} \mathrm{COONa}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{COOH}$ and $\mathrm{CH}_{3} \mathrm{COONa}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">$\mathrm{HNO}_{3}$ and $\mathrm{CH}_{3} \mathrm{COONa}$, $\mathrm{CH}_{3} \mathrm{COOH}$ and $\mathrm{CH}_{3} \mathrm{COONa}$</span> </div>

answer:
<div class="solution">A Weak acid and its salt with a strong base forms a buffer.$\therefore$ (D)
<br/>$\mathrm{HNO}_{3}$ being a strong acid, displaces weaker acid $\mathrm{CH}_{3} \mathrm{COOH}$.
<br/>$\mathrm{HNO}_{3}+\mathrm{CH}_{3}-\mathrm{COO}^{-} \rightleftharpoons \mathrm{CH}_{3}-\mathrm{COOH}+\mathrm{NO}_{3}^{-}$
<br/>If $\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]&gt;\left[\mathrm{HNO}_{3}\right]$, then solution contains weak acid $\left(\mathrm{CH}_{3} \mathrm{COOH}\right)$ and its conjugate base $\left(\mathrm{CH}_{3} \mathrm{COO}^{-}\right) . \quad \therefore(\mathrm{C})$</div>


title: area-in-the-first-quadrant-between-the-ellipses-x-2-2-y-2-a-2-and-2-x-2-y-2-a-2-is
slug: area-in-the-first-quadrant-between-the-ellipses-x-2-2-y-2-a-2-and-2-x-2-y-2-a-2-is-85416
tags: ['Mathematics', 'Ellipse', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P1.db
question:
<div class="question">Area in the first quadrant between the ellipses $x^{2}+2 y^{2}=a^{2}$ and $2 x^{2}+y^{2}=a^{2}$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{a^{2}}{\sqrt{2}} \tan ^{-1} \frac{1}{\sqrt{2}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{3 a^{2}}{4} \tan ^{-1} \frac{1}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{5 a^{2}}{2} \sin ^{-1} \frac{1}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{9 \pi a^{2}}{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{a^{2}}{\sqrt{2}} \tan ^{-1} \frac{1}{\sqrt{2}}$</span> </div>

answer:
<div class="solution">Hint: 
<br/>$A=\left(\frac{a^{2}}{6}+\int_{a / \sqrt{3}}^{a / \sqrt{2}} \sqrt{a^{2}-2 x^{2}} d x\right) \times 2=\frac{a^{2}}{\sqrt{2}} \tan ^{-1}\left(\frac{1}{\sqrt{2}}\right)$</div>


title: area-of-the-figure-bounded-by-the-parabola-y-2-8-x-16-and-y-2-24-x-48-is-1
slug: area-of-the-figure-bounded-by-the-parabola-y-2-8-x-16-and-y-2-24-x-48-is-1-13714
tags: ['Mathematics', 'Area Under Curves', 'JEE Main']
source_db: db\MarksBatch1_P1.db
question:
<div class="question">Area of the figure bounded by the parabola $y^2+8 x=16$ and $y^2-24 x=48$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{11}{9}$ sq. unit</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{32}{3} \sqrt{6}$ sq. unit</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{16}{3}$ sq. unit</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{24}{5}$ sq. unit</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{32}{3} \sqrt{6}$ sq. unit</span> </div>

answer:
<div class="solution">$$<br/>\begin{gathered}<br/>y^2=-8(x-2) \\<br/>y^2=24(x+2) \cdots(2)<br/>\end{gathered}<br/>$$<br/>Solving (1) and $(2) \Rightarrow x=-1$<br/>Area $=2\left[\int_{-2}^{-1} 2 \sqrt{6} \sqrt{x+2} \mathrm{dx}+\int_{-1}^2 2 \sqrt{2} \sqrt{2-x} \mathrm{dx}\right]=\frac{32}{3} \sqrt{6}$ sq. unit<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/XbnA7qORB_ifSCmYsFQsd1pGSu1T5AZKUk51DWfKh3U.original.fullsize.png"/></div>


title: area-of-the-region-bounded-by-y-x-and-y-x-2-is
slug: area-of-the-region-bounded-by-y-x-and-y-x-2-is-54716
question: <div class="question">Area of the region bounded by $y=|x|$ and $y=-|x|+2$ is</div>
tags: ['Mathematics', 'Area Under Curves', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$4 \mathrm{sq}$ units</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3 \mathrm{sq}$ units</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$2 \mathrm{sq}$ units</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1 sq unit</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \mathrm{sq}$ units</span> </div>

answer:
<div class="solution">In figure, $B=(0,2) \Rightarrow O B=2$
<br/>and $O A B C$ is a square.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_mat_a125.png"/> <br/>So, side of length $=\sqrt{2}$ units
<br/>$\therefore$ Area of $O A B C=2$ aq units</div>


tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P1.db
title:
arrange-the-following-in-order-of-increasing-mass-i-1-mole-of-mathrmn2-ii-05-mathrmmole2-of-mathrmo3-iii-3011-times-1023-mathrmmolecules-of-mathrmo2-i

slug:
arrange-the-following-in-order-of-increasing-mass-i-1-mole-of-mathrmn2-ii-05-mathrmmole2-of-mathrmo3-iii-3011-times-1023-mathrmmolecules-of-mathrmo2-i-14656

question:
<div class="question">Arrange the following in order of increasing mass<br/>I. 1 mole of \(\mathrm{N}_2\)<br/>II. \(0.5 \mathrm{~mole}^2\) of \(\mathrm{O}_3\)<br/>III. \(3.011 \times 10^{23} \mathrm{molecules}\) of \(\mathrm{O}_2\)<br/>IV. 0.5 gram atom of \(\mathrm{O}_2\)</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">IV \(  &lt; \) III \( &lt; \) II \( &lt; \) I</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">IV \(  &lt; \) I \( &lt; \) III \( &lt; \) II</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">III \(  &lt; \) II \( &lt; \) IV \( &lt; \) I</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">I \(  &lt; \) III \( &lt; \) II \( &lt; \) IV</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">IV \(  &lt; \) III \( &lt; \) II \( &lt; \) I</span> </div>

answer:
<div class="solution">Hint : 1 mole \(\mathrm{N}_2=28 \mathrm{~g}\)<br/>\(0.5 \mathrm{~mole} \mathrm{O}_3=24 \mathrm{~g}\)<br/>\(3.011 \times 10^{23}\) molecules of \(\mathrm{O}_2=1 / 2\) mole \(\mathrm{O}_2=1\) mole \(\mathrm{O}=16 \mathrm{~g}\)<br/>\(0.5 \mathrm{~g}\) atom \(\mathrm{O}_2=1 / 2\) mole of atoms of \(\mathrm{O}=8 \mathrm{~g}\)</div>


tags: ['Chemistry', 'Structure of Atom', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
title:
as-per-debroglies-formula-a-macroscopic-particle-of-mass-100-g-and-moving-at-a-velocity-of-100-cm-s-1-will-have-a-wavelength-of

slug:
as-per-debroglies-formula-a-macroscopic-particle-of-mass-100-g-and-moving-at-a-velocity-of-100-cm-s-1-will-have-a-wavelength-of-71130

question:
<div class="question">As per de-Broglie's formula a macroscopic particle of mass $100 \mathrm{g}$ and moving at a velocity of $100 \mathrm{cm} \mathrm{s}^{-1}$ will have a wavelength of</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$6.6 \times 10^{-29} \mathrm{cm}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$6.6 \times 10^{-30} \mathrm{cm}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$6.6 \times 10^{-31} \mathrm{cm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$6.6 \times 10^{-32} \mathrm{cm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$6.6 \times 10^{-31} \mathrm{cm}$</span> </div>

answer:
<div class="solution">According to de-Broglie. wavelength, $\lambda=\frac{h}{m v}$
<br/>Given, $\quad m=100 \mathrm{g}, v=100 \mathrm{cm} \mathrm{s}^{-1}$
<br/>and
<br/>$$
<br/>\begin{aligned}
<br/>h &amp;=6.6 \times 10^{-34} \mathrm{J}-\mathrm{s} \\
<br/>&amp;=6.6 \times 10^{-27} \mathrm{erg}-\mathrm{s}
<br/>\end{aligned}
<br/>$$
<br/>On substituting values, we get
<br/>$$
<br/>\lambda=\frac{6.6 \times 10^{-27}}{100 \times 100}=6.6 \times 10^{-31} \mathrm{cm}
<br/>$$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch1_P1.db
title:
as-shown-in-figure-a-rectangular-loop-of-length-a-and-width-b-and-made-of-a-conducting-material-of-uniform-crosssection-is-kept-in-a-horizontal-plane-

slug:
as-shown-in-figure-a-rectangular-loop-of-length-a-and-width-b-and-made-of-a-conducting-material-of-uniform-crosssection-is-kept-in-a-horizontal-plane-28237

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/Ytr1YnWZlcM2HA2wCXAwqFWq6C97W7_hvBiM4428wds.original.fullsize.png"/><br/><br/>As shown in figure, a rectangular loop of length ' a' and width ' $b$ ' and made of a conducting material of uniform crosssection is kept in a horizontal plane where a uniform magnetic field of intensity $B$ is acting vertically downward. Resistance per unit length of the loop is $\lambda \Omega / \mathrm{m}$. If the loop is pulled with uniform velocity ' $v$ ' in horizontal direction, which of the following statement is / are true?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Current in the loop $\mathrm{I}=\frac{\mathrm{Bbv}}{\lambda(2 \mathrm{~b}+2 \mathrm{a})}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Current will be in clockwise direction, looking from the top.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$V_P-V_S=V_Q-V_R$, where $V$ is the potential</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">There cannot be any induction in part SR.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">Current in the loop $\mathrm{I}=\frac{\mathrm{Bbv}}{\lambda(2 \mathrm{~b}+2 \mathrm{a})}$, There cannot be any induction in part SR.</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/JCdulhuX8EBN-1VmSqN3A3w1vZCXhB1Zp5z8e9ar9Lo.original.fullsize.png"/><br/>$\varepsilon=B \times b \times v$<br/>$\mathrm{i}=\frac{\varepsilon}{\mathrm{R}_{\text {total }}}=\frac{\varepsilon}{\lambda(2 \mathrm{~b}+2 \mathrm{a})}$<br/>Current is anticlockwise<br/>$$<br/>V_P-V_S \neq V_Q-V_R<br/>$$<br/>Also SR, $\vec{\ell} \| \vec{v} ;$ So $\varepsilon=0$</div>


tags: ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">zero</span> </div>
source_db: db\MarksBatch1_P1.db
title:
as-shown-in-figure-below-a-charge-2-c-is-situated-at-the-origin-o-and-another-charge-5-c-is-on-the-x-axis-at-the-point-a-the-later-charge-from-the-poi

slug:
as-shown-in-figure-below-a-charge-2-c-is-situated-at-the-origin-o-and-another-charge-5-c-is-on-the-x-axis-at-the-point-a-the-later-charge-from-the-poi-47687

question:
<div class="question">As shown in figure below, a charge $+2 \mathrm{C}$ is situated at the origin $O$ and another charge $+5 \mathrm{C}$ is on the $x$ -axis at the point $A .$ The later charge from the point $A$ is then brought to a point $B$ on the $y$ -axis. The work done is $\left(\right.$ given $\left.\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \mathrm{m} / \mathrm{F}\right)$ <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_phy_q25.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$45 \times 10^{9} \mathrm{J}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$90 \times 10^{9} \mathrm{J}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-45 \times 10^{9} \mathrm{J}$</span> </li> </ul>

answer:
<div class="solution">Work done $=U_{f}-U_{i}$
<br/>$$
<br/>=\frac{1}{4 \pi \varepsilon_{0}} \times 2 \times 5 \times\left(\frac{1}{2}-\frac{1}{2}\right)=0
<br/>$$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P1.db
title:
as-shown-in-the-figure-a-pump-is-designed-as-horizontal-cylinder-with-a-piston-having-area-a-and-an-outlet-orifice-having-an-area-a-the-piston-moves-w

slug:
as-shown-in-the-figure-a-pump-is-designed-as-horizontal-cylinder-with-a-piston-having-area-a-and-an-outlet-orifice-having-an-area-a-the-piston-moves-w-98715

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/9_O24JAJd1ip2Qh1laVaKNTOp61j9voKw_F4pmB0Znw.original.fullsize.png"/><br/><br/>As shown in the figure, a pump is designed as horizontal cylinder with a piston having area A and an outlet orifice having an area ' \(a\) '. The piston moves with a constant velocity under the action of force \(F\). If the density of the liquid is \(\rho\), then the speed of the liquid emerging from the orifice is, (assume \(A &gt;  &gt; a\) )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(\sqrt{\frac{F}{\rho A}}\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(\frac{a}{A} \sqrt{\frac{F}{\rho A}}\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(\sqrt{\frac{2 F}{\rho A}}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(\frac{A}{a} \sqrt{\frac{2 F}{\rho A}}\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\sqrt{\frac{2 F}{\rho A}}\)</span> </div>

answer:
<div class="solution">Hint: by principle of continuity<br/>\(\mathrm{AV}=\mathrm{av}\)<br/>by Bernoulis principle<br/>\(\begin{aligned} &amp; P+\frac{1}{2} \rho V^2=P_0+\frac{1}{2} \rho v^2 \\ &amp; {\left[\frac{F}{A}+P_0\right]+\frac{1}{2} \rho V^2=P_0+\frac{1}{2} \rho v^2} \\ &amp; \frac{F}{A}+\frac{1}{2} \rho\left[\frac{a v}{A}\right]^2=\frac{1}{2} \rho v^2 \\ &amp; \frac{F}{A}=\frac{1}{2} \rho v^2\left[1-\frac{a^2}{A^2}\right]\end{aligned}\)<br/>\(\begin{aligned} &amp; v=\sqrt{\frac{2 F}{\rho A\left[1-\frac{a^2}{A^2}\right]}} \\ &amp; a^2 \ll A^2 \\ &amp; v=\sqrt{\frac{2 F}{\rho A}}\end{aligned}\)</div>


tags: ['Physics', 'Electromagnetic Induction', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch1_P1.db
title:
as-shown-in-the-figure-a-rectangular-loop-of-a-conducting-wire-is-moving-away-with-a-constant-velocity-v-in-a-perpendiculat-direction-from-a-very-long

slug:
as-shown-in-the-figure-a-rectangular-loop-of-a-conducting-wire-is-moving-away-with-a-constant-velocity-v-in-a-perpendiculat-direction-from-a-very-long-25584

question:
<div class="question">As shown in the figure, a rectangular loop of a conducting wire is moving away with a constant velocity $v$ in a perpendiculat direction from a very long straight conductor carrying a steady current $l$. When the
<br/>breadth of the rectangular loop is very small compared to its distance from the straight conductor, how does the emf. $E$ induced in the loop vary with time $t ?$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_q32.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$E \propto \frac{1}{t^{2}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$E \propto \frac{1}{t}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$E \alpha-\ln (t)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$E \propto \frac{1}{t^{3}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$E \propto \frac{1}{t^{2}}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_a32.png"/> <br/> <br/>$\therefore$ Motional emf in the loop.
<br/>$$
<br/>\begin{aligned}
<br/>E &amp;=E_{1}-E_{2}=vl l\left(B_{1}-B_{2}\right) \\
<br/>&amp;=v\left(\frac{\mu_{0}}{2 \pi} \cdot \frac{I}{y}-\frac{\mu_{0} I}{2 \pi(y+b)}\right] \\
<br/>&amp;=\frac{\mu_{0}}{2 \pi} \cdot I \cdot v l\left[\frac{y+b-y}{y(y+b)}\right]=\frac{\mu_{0}}{2 \pi} \cdot \frac{v I l}{y(y+b)} b
<br/>\end{aligned}
<br/>$$
<br/>$\because \quad b&lt; &lt; y$
<br/>$\therefore \quad E=\frac{\mu_{0}}{2 \pi} \cdot \frac{v l I}{y^{2}} b$
<br/>$\because v=$ constant
<br/>$$
<br/>$$
<br/>Thus, $\quad E=\frac{\mu_{0}}{2 \pi} \cdot \frac{v l l}{v^{2} t^{2}} b$
<br/>Hence, $\quad E \propto \frac{1}{t^{2}}$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Main']
source_db: db\MarksBatch1_P1.db
title:
as-shown-in-the-figure-a-single-conducting-wire-is-bent-to-form-a-loop-in-the-form-of-a-circle-of-radius-r-concentrically-inside-a-square-of-side-a-wh-1

slug:
as-shown-in-the-figure-a-single-conducting-wire-is-bent-to-form-a-loop-in-the-form-of-a-circle-of-radius-r-concentrically-inside-a-square-of-side-a-wh-1-10240

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/eYATWnakr-kiQU5ty-yDqhjJxpu06zyQ253A1841j0Y.original.fullsize.png"/><br/> <br/>As shown in the figure, a single conducting wire is bent to form a loop in the form of a circle of radius 'r' concentrically inside a square of side ' $a$ ', where $a: r=8: \pi$. A battery B drives a current through the wire. If the battery B and the gap G are of negligible sizes, determine the strength of magnetic field at the common centre $O$.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\cdot \frac{\mu_{0} \mid}{2 \pi a} \sqrt{2}(\sqrt{2}-1)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\mu_{0} I}{2 \pi a}(\sqrt{2}+1)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mu_{0} I}{\pi a} 2 \sqrt{2}(\sqrt{2}+1)$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{\mu_{0} I}{\pi \mathrm{a}} 2 \sqrt{2}(\sqrt{2}-1)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mu_{0} I}{\pi \mathrm{a}} 2 \sqrt{2}(\sqrt{2}-1)$</span> </div>

answer:
<div class="solution">Hint: 
<br/>$\frac{a}{r}=\frac{8}{\pi}, r=\frac{\pi a}{8}$
<br/>$B=\frac{\mu_{0} \mid}{2 r}-\frac{4 \mu_{0} I}{4 \pi a / 2} \times \sqrt{2}=\frac{\mu_{0} I}{2 r}-\frac{2 \sqrt{2} \mu_{0} I}{\pi a}=\frac{\mu_{0} \mid \times 8}{2 \pi a}-\frac{2 \sqrt{2} \mu_{0} I}{\pi a}$
<br/>$=\frac{\mu_{0} \mid}{\pi a}(4-2 \sqrt{2})=\frac{\mu_{0} I}{\pi a} 2 \sqrt{2}(\sqrt{2}-1)$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/6sZgeMv7PyO9Y2zg3WIF_qA2-MAilswkDN4W6eSKAHc.original.fullsize.png"/></div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P1.db
title:
as-shown-in-the-figure-a-single-conducting-wire-is-bent-to-form-a-loop-in-the-form-of-a-circle-of-radius-r-concentrically-inside-a-square-of-side-a-wh

slug:
as-shown-in-the-figure-a-single-conducting-wire-is-bent-to-form-a-loop-in-the-form-of-a-circle-of-radius-r-concentrically-inside-a-square-of-side-a-wh-59413

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/eYATWnakr-kiQU5ty-yDqhjJxpu06zyQ253A1841j0Y.original.fullsize.png"/><br/> <br/>As shown in the figure, a single conducting wire is bent to form a loop in the form of a circle of radius 'r' concentrically inside a square of side ' $a$ ', where $a: r=8: \pi$. A battery B drives a current through the wire. If the battery B and the gap G are of negligible sizes, determine the strength of magnetic field at the common centre $O$.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\cdot \frac{\mu_{0} \mid}{2 \pi a} \sqrt{2}(\sqrt{2}-1)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\mu_{0} I}{2 \pi a}(\sqrt{2}+1)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mu_{0} I}{\pi a} 2 \sqrt{2}(\sqrt{2}+1)$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{\mu_{0} I}{\pi \mathrm{a}} 2 \sqrt{2}(\sqrt{2}-1)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mu_{0} I}{\pi \mathrm{a}} 2 \sqrt{2}(\sqrt{2}-1)$</span> </div>

answer:
<div class="solution">Hint: 
<br/>$\frac{a}{r}=\frac{8}{\pi}, r=\frac{\pi a}{8}$
<br/>$B=\frac{\mu_{0} \mid}{2 r}-\frac{4 \mu_{0} I}{4 \pi a / 2} \times \sqrt{2}=\frac{\mu_{0} I}{2 r}-\frac{2 \sqrt{2} \mu_{0} I}{\pi a}=\frac{\mu_{0} \mid \times 8}{2 \pi a}-\frac{2 \sqrt{2} \mu_{0} I}{\pi a}$
<br/>$=\frac{\mu_{0} \mid}{\pi a}(4-2 \sqrt{2})=\frac{\mu_{0} I}{\pi a} 2 \sqrt{2}(\sqrt{2}-1)$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/6sZgeMv7PyO9Y2zg3WIF_qA2-MAilswkDN4W6eSKAHc.original.fullsize.png"/></div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2020']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: db\MarksBatch1_P1.db
title:
as-shown-in-the-figure-a-wire-is-bent-to-form-a-dshaped-loop-carrying-current-i-where-the-curved-part-is-semicircle-of-radius-r-the-loop-is-placed-in-

slug:
as-shown-in-the-figure-a-wire-is-bent-to-form-a-dshaped-loop-carrying-current-i-where-the-curved-part-is-semicircle-of-radius-r-the-loop-is-placed-in-81145

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/QaSSLYvGptmwn8NACiQlF7K4GhRMcPXMxPWuZWwVglo.original.fullsize.png"/><br/> <br/>As shown in the figure, a wire is bent to form a D-shaped loop, carrying current I, where the curved part is semi-circle of radius $\mathrm{R}$. the loop is placed in a uniform magnetic field $\overrightarrow{\mathrm{B}}$, which is directed into the plane of the paper. The magnetic force left by the closed loop is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">0</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">IRB</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2 IRB</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{2} \operatorname{IRB}$</span> </li> </ul>

answer:
<div class="solution">Hint: 
<br/>Zero (Net magnetic force on a closed current loop in a uniform $\overrightarrow{\mathrm{B}}$ is zero)</div>


tags: ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P1.db
title:
as-shwon-in-the-figure-a-point-charge-q-1-1-1-0-8-c-is-placed-at-the-origin-in-x-y-plane-and-another-point-charge-q-2-3-1-0-6-c-is-placed-at-the-coord

slug:
as-shwon-in-the-figure-a-point-charge-q-1-1-1-0-8-c-is-placed-at-the-origin-in-x-y-plane-and-another-point-charge-q-2-3-1-0-6-c-is-placed-at-the-coord-91237

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/_wnGwyqTYHlxphYE4ikxK-KzHLxBdKNMVvKFa0q3cuQ.original.fullsize.png"/><br/> <br/>As shwon in the figure, a point charge $q_{1}=+1 \times 10^{-8} C$ is placed at the origin in $x$ -y plane and another point charge $\mathrm{q}_{2}=+3 \times 10^{-6} \mathrm{C}$ is placed at the co-ordinate $(10,0)$. In that case, which of the following graph(s) shows most correctly the electric field vector in $\mathrm{E}_{x}$ in $\mathrm{x}$ -direction?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/8lbRPEwfjZtWJFUqskgHpDOcMYnjhlsCcr4XCn2aTrI.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/elzwU7aFggPHZkRdD14X-wAutQj6Vo_EPTmsoBpa8pg.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/NBVSZcoriECsVvde2SE_X5huOKStMLZlHs07he-eH8Q.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/xKCAgnLVV8ySObi2B_6arT9unhyTsP8Zru4Hb5nGQL0.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/8lbRPEwfjZtWJFUqskgHpDOcMYnjhlsCcr4XCn2aTrI.original.fullsize.png"/></span> </div>

answer:
<div class="solution">Hint:
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/OksTpCMiyfzyHATdLc7kotZ8rlvUa2YkU3LAL-6DL2U.original.fullsize.png"/></div>


title: aspirin-is
slug: aspirin-is-51049
question: <div class="question">Aspirin is</div>
tags: ['Chemistry', 'Chemistry in Everyday Life', 'WBJEE', 'WBJEE 2010']
source_db: db\MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Acetyl salicylic acid</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Benzoyl salicylic acid</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Chloro benzoic acid</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Anthranilic acid</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Acetyl salicylic acid</span> </div>

answer:
<div class="solution">Hints: <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/sbG4SP28mARUh9itPSDuM54X27PtgZtGicqGLxNfdw8.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Semiconductors', 'JEE Main']
source_db: db\MarksBatch1_P1.db
title:
assume-that-each-diode-as-shown-in-the-tgure-has-a-forvard-bias-resistance-of-50-and-an-infinite-reverse-bias-resistance-the-current-through-the-resis-1

slug:
assume-that-each-diode-as-shown-in-the-tgure-has-a-forvard-bias-resistance-of-50-and-an-infinite-reverse-bias-resistance-the-current-through-the-resis-1-97996

question:
<div class="question">Assume that each diode as shown in the tá»gure has a forvard bias resistance of $50 \Omega$ and an infinite reverse bias resistance. The current through the resistance $150 \Omega$ is
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_q11.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.66 \mathrm{A}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.05 \mathrm{A}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">zero</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$0.04 \mathrm{A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.04 \mathrm{A}$</span> </div>

answer:
<div class="solution">The circuit is 
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_a11.png"/> <br/> <br/>As the lower diode attached to $100 \Omega$ resistance is in reversed biased so, $1 t$ is non-conducting
<br/>Now, the circuit can be redrawn as,<img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_a11a.png"/> <br/> <br/>$\therefore$ Current through the circuit, $I=\frac{V}{R}$
<br/>$$
<br/>=\frac{10}{250}=0.04 \mathrm{A}
<br/>$$</div>


tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch1_P1.db
title:
assume-that-each-diode-as-shown-in-the-tgure-has-a-forvard-bias-resistance-of-50-and-an-infinite-reverse-bias-resistance-the-current-through-the-resis

slug:
assume-that-each-diode-as-shown-in-the-tgure-has-a-forvard-bias-resistance-of-50-and-an-infinite-reverse-bias-resistance-the-current-through-the-resis-22912

question:
<div class="question">Assume that each diode as shown in the tá»gure has a forvard bias resistance of $50 \Omega$ and an infinite reverse bias resistance. The current through the resistance $150 \Omega$ is
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_q11.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.66 \mathrm{A}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.05 \mathrm{A}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">zero</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$0.04 \mathrm{A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.04 \mathrm{A}$</span> </div>

answer:
<div class="solution">The circuit is 
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_a11.png"/> <br/> <br/>As the lower diode attached to $100 \Omega$ resistance is in reversed biased so, $1 t$ is non-conducting
<br/>Now, the circuit can be redrawn as,<img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_a11a.png"/> <br/> <br/>$\therefore$ Current through the circuit, $I=\frac{V}{R}$
<br/>$$
<br/>=\frac{10}{250}=0.04 \mathrm{A}
<br/>$$</div>


tags: ['Physics', 'Gravitation', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch1_P1.db
title:
assume-that-the-earth-moves-around-the-sun-in-a-circular-orbit-of-radius-r-and-there-exists-a-planet-which-also-move-around-the-sun-in-a-circular-orbi

slug:
assume-that-the-earth-moves-around-the-sun-in-a-circular-orbit-of-radius-r-and-there-exists-a-planet-which-also-move-around-the-sun-in-a-circular-orbi-14946

question:
<div class="question">Assume that the earth moves around the sun in a circular orbit of radius $R$ and there exists a planet which also move around the sun in a circular orbit with an angular speed twice as large as that of the earth. The radius of the orbit of the planet is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$2^{-2 / 3} R$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2^{2 / 3} R$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$ 2^{-1 / 3} R$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{R}{\sqrt{2}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2^{-2 / 3} R$</span> </div>

answer:
<div class="solution">According to the Kepler's third law
<br/>$$
<br/>T^{2} \propto r^{3}
<br/>$$
<br/>where, $T=$ time period of revolution
<br/>$r=$ radius 
<br/>Now, $\left(\frac{T_{E}}{T_{P}}\right)^{2}=\left(\frac{r_{E}}{r_{P}}\right)^{3}=\frac{r_{E}}{r_{P}}=\left(\frac{T_{E}}{T_{P}}\right)^{2 / 3}$
<br/>$$
<br/>\frac{r_{E}}{r_{P}}=\left(\frac{2 \pi / \omega_{E}}{2 \pi / \omega_{P}}\right)^{2 / 3} \quad\left[\because T=\frac{2 \pi}{\omega}\right]
<br/>$$
<br/>$$
<br/>\frac{r_{E}}{r_{P}}=\left(\frac{\omega_{P}}{\omega_{E}}\right)^{2 / 3}
<br/>$$
<br/>According to the question, $\omega_{P}=2 \omega_{E}$ and $r_{E}=R$
<br/>$\Rightarrow \quad \frac{R}{r_{P}}=\left(\frac{2 \omega_{E}}{\omega_{E}}\right)^{2 / 3}$
<br/>$$
<br/>\begin{array}{l}
<br/>\frac{R}{r_{P}}=(2)^{2 / 3} \\
<br/>r_{P}=\frac{R}{(2)^{2 / 3}}=R(2)^{-2 / 3}
<br/>\end{array}
<br/>$$</div>


tags: ['Chemistry', 'Solutions', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch1_P1.db
title:
assuming-the-compounds-to-be-completely-dissociated-in-aqueous-solution-identify-the-pair-of-the-solutions-that-can-be-expected-to-be-isotonic-at-the-

slug:
assuming-the-compounds-to-be-completely-dissociated-in-aqueous-solution-identify-the-pair-of-the-solutions-that-can-be-expected-to-be-isotonic-at-the-70086

question:
<div class="question">Assuming the compounds to be completely dissociated in aqueous solution, identify the pair of the solutions that can be expected to be isotonic at the same temperature.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.01 \mathrm{M}$ urea and $0.01 \mathrm{M} \mathrm{NaCl}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.02 \mathrm{M} \mathrm{NaCl}$ and $0.01 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">0.03 M $\mathrm{NaCl}$ and $0.02 \mathrm{M} \mathrm{MgCl}_{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.01 \mathrm{M}$ sucrose and $0.02 \mathrm{M}$ glucose</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">0.03 M $\mathrm{NaCl}$ and $0.02 \mathrm{M} \mathrm{MgCl}_{2}$</span> </div>

answer:
<div class="solution">$\because$ For Isotonic solution
<br/>$$
<br/>\pi_{1}=\pi_{2} \text { i.e. } i_{1} C_{1} R T=i f_{2} R T
<br/>$$
<br/>For option $(c)$
<br/>$$
<br/>\begin{array}{l}
<br/>i_{1}=2, i_{2}=3 \\
<br/>C_{1}=0.03 \\
<br/>C_{2}=0.02
<br/>\end{array}
<br/>$$
<br/>Thus, $\quad i_{1} \times C_{1}=i_{2} \times C_{2}$
<br/>Hence, are isotonic, i.e.
<br/>$$
<br/>0.06=0.06
<br/>$$
<br/>In all other options, $i_{1} \times C_{1} \neq i_{2} \times C_{2}$ Thus, are not isotonic.</div>


title: at-2-5-c-ph-of-a-1-0-8-m-aqueous-koh-solution-will-be
slug: at-2-5-c-ph-of-a-1-0-8-m-aqueous-koh-solution-will-be-56023
tags: ['Chemistry', 'Ionic Equilibrium', 'WBJEE', 'WBJEE 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7.02</span> </div>
source_db: db\MarksBatch1_P1.db
question:
<div class="question">At $25^{\circ} \mathrm{C}, \mathrm{pH}$ of a $10^{-8} \mathrm{M}$ aqueous $\mathrm{KOH}$
<br/>solution will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">6</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">7.02</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">8.02</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">9.02</span> </li> </ul>

answer:
<div class="solution">$\mathrm{NaOH} \longrightarrow \mathrm{Na}^{+}+\mathrm{OH}^{-} \quad\left[\mathrm{OH}^{-}\right]=10^{-8} \mathrm{M}$
<br/>$\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}^{+}+\mathrm{OH}^{-}$ $\left[\mathrm{OH}^{-}\right]=10^{-7} \mathrm{M}$
<br/>$$
<br/>\begin{aligned}
<br/>\therefore\left[\mathrm{OH}^{-}\right]_{\text {total }} &amp;=\left(10^{-8}+10^{-7}\right) \mathrm{M} \\
<br/>&amp;=10^{-7}(1.1) \\
<br/>&amp;=1.1 \times 10^{-7} \\
<br/>\therefore \quad \mathrm{pOH} &amp;=\log 1.1 \times 10^{-7}=6.98 \\
<br/>\therefore \quad \mathrm{pH} &amp;=14-6.98 \\
<br/>&amp;=7.02
<br/>\end{aligned}
<br/>$$</div>


tags: ['Chemistry', 'Electrochemistry', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
title:
at-2-5-c-the-molar-conductance-of-0007-m-hydrofluoric-acid-is-150-mho-cm-2-mol-1-and-its-m-500-mho-c-m-2-m-o-l-1-the-value-of-the-dissociation-constan

slug:
at-2-5-c-the-molar-conductance-of-0007-m-hydrofluoric-acid-is-150-mho-cm-2-mol-1-and-its-m-500-mho-c-m-2-m-o-l-1-the-value-of-the-dissociation-constan-19810

question:
<div class="question">At $25^{\circ} \mathrm{C}$, the molar conductance of $0.007 \mathrm{M}$ hydrofluoric acid is 150 mho $\mathrm{cm}^{2} \mathrm{mol}^{-1}$ and its $\Lambda_{m}^{\circ}=500$mho$cm^2$$mol^{-1}$ The value of the dissociation constant of the acid at the given concentration  at $25^{\circ} \mathrm{C}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$7 \times 10^{-4} \mathrm{M}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$7 \times 10^{-5} \mathrm{M}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$9 \times 10^{-3} \mathrm{M}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$9 \times 10^{-4} \mathrm{M}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$9 \times 10^{-4} \mathrm{M}$</span> </div>

answer:
<div class="solution">Degree of dissociation, $\alpha=\frac{\lambda^{\circ} c}{\lambda^{\circ}m}=\frac{150}{500}=0.3$
<br/>Given, $C=0.007 \mathrm{M}$
<br/>Hydrofluoric acid dissociates in the following manner
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_a50.png"/> <br/>Dissociation constant,
<br/>$$
<br/>K_{a}=\frac{\left[H^{+}\right]\left[F^{-}\right]}{[H F]}=\frac{C \alpha \cdot C \alpha}{C(1-\alpha)}=\frac{C \alpha^{2}}{(1-\alpha)}
<br/>$$
<br/>On substituting values, we get
<br/>$$
<br/>\begin{aligned}
<br/>K_{a}=\frac{0.007 \times(0.3)^{2}}{(1-0.3)} &amp;=\frac{63 \times 10^{-3} \times 10^{-2}}{0.7} \\
<br/>&amp;=9 \times 10^{-4} \mathrm{M}
<br/>\end{aligned}
<br/>$$</div>


tags: ['Chemistry', 'Ionic Equilibrium', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P1.db
title:
at-2-5-c-the-solubility-produet-of-salt-of-mx-2-type-is-32-1-0-8-in-water-the-solubility-in-mol-l-of-m-x-2-in-water-at-the-sume-temperature-will-be

slug:
at-2-5-c-the-solubility-produet-of-salt-of-mx-2-type-is-32-1-0-8-in-water-the-solubility-in-mol-l-of-m-x-2-in-water-at-the-sume-temperature-will-be-12459

question:
<div class="question">At $25^{\circ} \mathrm{C}$, the solubility produet of salt of $\mathrm{MX}_{2}$ type is $3.2 \times 10^{-8}$ in water. The solubility (in $\mathrm{mol} / \mathrm{L})$ of $M X_{2}$ in water at the sume temperature will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1.2 \times 10^{-3}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$2 \times 10^{-3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3.2 \times 10^{-3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1.75 \times 10^{-3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \times 10^{-3}$</span> </div>

answer:
<div class="solution">For $M X_{2}$ type salt,
<br/>Solubility product, $K_{\mathrm{sp}}=4 s^{3} ; 3.2 \times 10^{-8}=4 \mathrm{s}^{3}$
<br/>or $s=\sqrt[3]{\frac{3.2 \times 10^{-8}}{4}}=2 \times 10^{-3} \mathrm{mol} / \mathrm{L}$</div>


title: at-273-k-temperature-and-76-cm-hg-pressure-the-density-of-a-gas-is-1964-g-l-1-the-gas-is
slug: at-273-k-temperature-and-76-cm-hg-pressure-the-density-of-a-gas-is-1964-g-l-1-the-gas-is-85737
tags: ['Chemistry', 'States of Matter', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P1.db
question:
<div class="question">At $273 \mathrm{~K}$ temperature and $76 \mathrm{~cm~} \mathrm{Hg}$ pressure, the density of a gas is $1.964 \mathrm{~g} \mathrm{~L}^{-1} .$ The gas is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{CH}_{4}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{CO}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{He}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{CO}_{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{CO}_{2}$</span> </div>

answer:
<div class="solution">Hint:
<br/>Molar mass of gas $(\mathrm{M})=\frac{\mathrm{dRT}}{\mathrm{P}}=\frac{1.964 \times 0.0821 \times 273}{1}$
<br/>$=44 \mathrm{~g}$
<br/>Hence, the gas is $\mathrm{CO}_{2}$</div>


tags: ['Physics', 'Magnetic Properties of Matter', 'WBJEE', 'WBJEE 2009']
source_db: db\MarksBatch1_P2.db
title:
at-a-certain-place-the-horizontal-component-of-earths-magnetic-field-is-3-times-the-vertical-component-the-angle-of-dip-at-that-place-is

slug:
at-a-certain-place-the-horizontal-component-of-earths-magnetic-field-is-3-times-the-vertical-component-the-angle-of-dip-at-that-place-is-34049

question:
<div class="question">At a certain place, the horizontal component of earth's magnetic field is $\sqrt{3}$ times the vertical component. The angle of dip at that place is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$30^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$60^{\circ}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$45^{\circ}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$90^{\circ}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$30^{\circ}$</span> </div>

answer:
<div class="solution">$\tan \theta=\frac{V}{H}=\frac{1}{\sqrt{3}} \Rightarrow \theta=30^{\circ}$</div>


tags: ['Chemistry', 'States of Matter', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P2.db
title:
at-a-certain-temperature-the-time-required-for-the-complete-diffusion-of-200-ml-of-h-2-gas-is-30-min-the-time-required-for-the-complete-diffusion-of-5

slug:
at-a-certain-temperature-the-time-required-for-the-complete-diffusion-of-200-ml-of-h-2-gas-is-30-min-the-time-required-for-the-complete-diffusion-of-5-28824

question:
<div class="question">At a certain temperature the time required for the complete diffusion of $200 \mathrm{mL}$ of $\mathrm{H}_{2}$ gas is 30 min. The time required for the complete diffusion of $50 \mathrm{mL}$ of $\mathrm{O}_{2}$ gas at the same temperature will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$60 \mathrm{min}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$30 \mathrm{min}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$45 \mathrm{min}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$15 \mathrm{min}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$30 \mathrm{min}$</span> </div>

answer:
<div class="solution">According to Graham's law of diffusion.
<br/>Rate of diffusion, $r \propto \frac{1}{\sqrt{M}}=\frac{V}{t}$
<br/>Here, $M=$ molecular mass, $V=$ volume and $t=$ timel Thus, for $\mathrm{H}_{2}$ gas,
<br/>$$
<br/>\frac{200}{30}=\frac{1}{\sqrt{2}}
<br/>$$
<br/>for $O_{2}$ gas,
<br/>$$
<br/>\frac{50}{t}=\frac{1}{\sqrt{32}}
<br/>$$
<br/>Eqs. (i) and (ii), we get From
<br/>$$
<br/>\begin{aligned}
<br/>\frac{200 \times t}{30 \times 50} &amp;=\frac{\sqrt{32}}{\sqrt{2}} \\
<br/>t &amp;=\frac{\sqrt{16} \times 30 \times 50}{200} \\
<br/>&amp;=\frac{4 \times 30}{4}=30 \mathrm{min}
<br/>\end{aligned}
<br/>$$</div>


tags: ['Chemistry', 'Solutions', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch1_P2.db
title:
at-a-certain-temperature-the-value-of-the-slope-of-the-plot-of-osmotic-pressure-against-concentration-c-in-mol-l-1-of-a-certain-polymer-solution-is-29

slug:
at-a-certain-temperature-the-value-of-the-slope-of-the-plot-of-osmotic-pressure-against-concentration-c-in-mol-l-1-of-a-certain-polymer-solution-is-29-93229

question:
<div class="question">At a certain temperature, the value of the slope of the plot of osmotic pressure $(\pi)$ against concentration $\left(C\right.$ in $\mathrm{mol} \mathrm{L}^{-1}$ ) of a certain polymer solution is $291 \mathrm{R.}$ The temperature at which osmotic pressure is measured, is $(R$ is gas constant)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$271 ^\circ \mathrm{C}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$18 ^\circ \mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$564 \mathrm{k}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$18 \mathrm{K}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$18 ^\circ \mathrm{C}$</span> </div>

answer:
<div class="solution">$$
<br/>\begin{array}{l}
<br/>\text { Slope. } R T=291 R \text { or } T=291 \mathrm{K} \\
<br/>\therefore \text { Temperature }=291-273=18^{\circ} \mathrm{C}
<br/>\end{array}
<br/>$$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_che_a51.png"/></div>


tags: ['Physics', 'Motion In One Dimension', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch1_P2.db
title:
at-a-particular-height-the-velocity-of-an-ascending-body-is-u-the-velocity-at-the-same-height-while-the-body-falls-freely-is

slug:
at-a-particular-height-the-velocity-of-an-ascending-body-is-u-the-velocity-at-the-same-height-while-the-body-falls-freely-is-69076

question:
<div class="question">At a particular height, the velocity of an ascending body is $\mathbf{u}$. The velocity at the same height while the body falls freely is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \mathbf{u}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$-\mathbf{u}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathbf{u}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-2 \mathbf{u}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-\mathbf{u}$</span> </div>

answer:
<div class="solution">Given that velocity of ascending body = u
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_phy_a12.png"/> <br/>Let there is no air resistance when body falls freely in downward direction, the direction of falling body will opposite to the ascending body.
<br/>$\therefore$ The velocily at the same height while the body falls freely $=-u$</div>


tags: ['Chemistry', 'Electrochemistry', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch1_P2.db
title:
at-a-particular-temperature-the-ratio-of-equivalent-conductance-to-specific-conductance-of-a-001-n-nacl-solution-is

slug:
at-a-particular-temperature-the-ratio-of-equivalent-conductance-to-specific-conductance-of-a-001-n-nacl-solution-is-17123

question:
<div class="question">At a particular temperature. the ratio of equivalent conductance to specific conductance of a 0.01 N NaCl solution is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$10^{5} \mathrm{cm}^{3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$10^{3} \mathrm{cm}^{3}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$10 \mathrm{cm}^{3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$10^{5} \mathrm{cm}^{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$10^{5} \mathrm{cm}^{3}$</span> </div>

answer:
<div class="solution">As we know that,
<br/>Equivalent conductance, ( $\lambda$ )
<br/>$=\frac{\text { Specific conductance }(K) \times 1000}{\text { Concentration }}$
<br/>or. $\quad \frac{\lambda}{K}=\frac{1000}{\text { conc. }}$
<br/>Or. $\frac{\lambda}{K}=\frac{1000 \Omega^{-1} \mathrm{cm}^{2} \mathrm{eq}^{-1}}{0.01 \Omega^{-1} \mathrm{cm}^{-1}}$
<br/>$\frac{\lambda}{K}=10^{5} \mathrm{cm}^{3} \mathrm{eq}^{-1}$
<br/>(Given, conc. $=0.01 \mathrm{N}$ )
<br/>Or,$\frac{\lambda}{K}=10^{5} \mathrm{cm}^{3} \mathrm{eq}^{-1}$</div>


title: at-constant-pressure-the-heat-of-formation-of-a-compound-is-not-dependent-on-temperature-when
slug: at-constant-pressure-the-heat-of-formation-of-a-compound-is-not-dependent-on-temperature-when-38022
tags: ['Chemistry', 'Thermodynamics (C)', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch1_P2.db
question:
<div class="question">At constant pressure, the heat of formation of a compound is not dependent on temperature, when</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\Delta C_{p}=0$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\Delta C_{v}=0$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\Delta C_{p}&gt;0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\Delta C_{p}    &lt; 0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\Delta C_{p}=0$</span> </div>

answer:
<div class="solution">Key Point According to Kirchhoff sequation
<br/>$$
<br/>\Delta H_{(f)}=\Delta H_{(i)}+C_{P}(\Delta T)
<br/>$$
<br/>At constant pressure
<br/>$$
<br/>\Delta C_{p}=O
<br/>$$
<br/>Therefore, heat of formation $\left(\Delta H_{f}\right)$ does not depend on temperature and value of $\Delta C_{p}$ i.e. when $\Delta C_{p}=0$
<br/>Hence, option (a) is the correct answer.</div>


tags: ['Chemistry', 'States of Matter', 'WBJEE', 'WBJEE 2010']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: db\MarksBatch1_P2.db
title:
at-identical-temperature-and-pressure-the-rate-of-diffusion-of-hydrogen-gas-is-3-3-times-that-o-f-ah-y-d-roc-a-r-b-o-nha-v-in-g-m-o-l-ec-u-l-a-r-f-or-

slug:
at-identical-temperature-and-pressure-the-rate-of-diffusion-of-hydrogen-gas-is-3-3-times-that-o-f-ah-y-d-roc-a-r-b-o-nha-v-in-g-m-o-l-ec-u-l-a-r-f-or-16034

question:
<div class="question">$$<br/>\text { At identical temperature and pressure, the rate of diffusion of hydrogen gas is } 3 \sqrt{3} \text { times that }<br/>$$<br/>of a hydrocarbon having molecular formula $\mathrm{C}_{\mathrm{n}} \mathrm{H}_{2 \mathrm{n}-2}$. What is the value of ' $n$ '?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">4</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">3</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">8</span> </li> </ul>

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>&amp; \text { Hints : } \frac{r_{H_2}}{r_{C_n H_{2 n-2}}}=\sqrt{\frac{M_{\mathrm{C}_{\mathrm{n}} \mathrm{H}_{2 \mathrm{n}-2}}}{\mathbf{M}_{\mathrm{H}_2}}}=\sqrt{\frac{\mathbf{M}_{\mathrm{C}_{\mathrm{n}} \mathrm{H}_{2 \mathrm{n}-2}}}{2}} \\<br/>&amp; \because \sqrt{\frac{\mathrm{M}_{\mathrm{C}_{\mathrm{n}} \mathrm{H}_{2 \mathrm{n}-2}}}{2}}=3 \sqrt{3}=\sqrt{27} \\<br/>&amp; \Rightarrow \mathbf{M}_{\mathrm{C}_{\mathrm{n}} \mathrm{H}_{2 \mathrm{n}-2}}=27 \times 2=54<br/>\end{aligned}<br/>$$<br/>Hence, $12 n+(2 n-2) \times 1=54 \Rightarrow 14 n=56 \Rightarrow n=4$ Thus Hydrocarbon is $\mathrm{C}_4 \mathrm{H}_6$</div>


title: at-room-temperature-the-reaction-between-water-and-fluorine-produces
slug: at-room-temperature-the-reaction-between-water-and-fluorine-produces-66981
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch1_P2.db
question:
<div class="question">At room temperature, the reaction between
<br/>water and fluorine produces</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{HF}$ and $\mathrm{H}_{2} \mathrm{O}_{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{HF}, \mathrm{O}_{2}$ and $\mathrm{F}_{2} \mathrm{O}_{2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$F^{-}, O_{2}$ and $H^{+}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">HOF and HF</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$F^{-}, O_{2}$ and $H^{+}$</span> </div>

answer:
<div class="solution">At room temperature, the reaction between water and fluorine produces $\mathrm{F}^{-}, \mathrm{O}_{2}$ and $\mathrm{H}^{+}$ Fluorine, being non-polar molecule, readily dissolves with water and forms mixture of oxygen and ozone as shown below
<br/>$$
<br/>\begin{array}{l}
<br/>2 \mathrm{F}_{2}+2 \mathrm{H}_{2} \mathrm{O} \longrightarrow 4 \mathrm{HF}+\mathrm{O}_{2} \\
<br/>3 \mathrm{F}_{2}+3 \mathrm{H}_{2} \mathrm{O} \longrightarrow 6 \mathrm{HF}+\mathrm{O}_{3}
<br/>\end{array}
<br/>$$
<br/>HF exist as $\mathrm{H}^{+}$ and $\mathrm{F}^{-}$ in a solution.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P2.db
title:
at-stp-the-dissociation-reaction-of-water-is-mathrmh2-mathrmo-rightleftharpoons-mathrmhaq-mathrmohaq-and-the-mathrmph-of-water-is-70-the-change-of-sta

slug:
at-stp-the-dissociation-reaction-of-water-is-mathrmh2-mathrmo-rightleftharpoons-mathrmhaq-mathrmohaq-and-the-mathrmph-of-water-is-70-the-change-of-sta-59711

question:
<div class="question">At STP, the dissociation reaction of water is \(\mathrm{H}_2 \mathrm{O} \rightleftharpoons \mathrm{H}^{+}\)(aq.) \(+\mathrm{OH}^{-}\)(aq.), and the \(\mathrm{pH}\) of water is 7.0. The change of standard free energy \(\left(\Delta \mathrm{G}^{\circ}\right)\) for the above dissociation process is given by</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(20301 \mathrm{~cal} / \mathrm{mol}\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(19091 \mathrm{~cal} / \mathrm{mol}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(20096 \mathrm{~cal} / \mathrm{mol}\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(21301 \mathrm{~cal} / \mathrm{mol}\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(19091 \mathrm{~cal} / \mathrm{mol}\)</span> </div>

answer:
<div class="solution">\(\begin{aligned}<br/>&amp; \text {Hint : } \Delta G^{\circ}=-2.303 R T \log \mathrm{K}_{\mathrm{w}} \\<br/>&amp; =-2.303 \times 1.987 \times 298 \log 10^{-14} \\<br/>&amp; =+2.303 \times 1.987 \times 298 \times 14 \mathrm{~cal} / \mathrm{mol} \quad \quad\left[\mathrm{K}_{\mathrm{w}}=\left[\mathrm{H}^{+}\right][\mathrm{OH}]=10^{-7} \times 10^{-7}=10^{-14} \mathrm{~as~} \mathrm{pH}=7\right] \\<br/>&amp; =19091.3 \mathrm{cal} / \mathrm{mol}=19091 \mathrm{cal} / \mathrm{mol}<br/>\end{aligned}\)</div>


title: at-stp-the-volume-of-75-g-of-a-gas-is-56-l-the-gas-is
slug: at-stp-the-volume-of-75-g-of-a-gas-is-56-l-the-gas-is-10668
tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'WBJEE', 'WBJEE 2019']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">NO</span> </div>
source_db: db\MarksBatch1_P2.db
question:
<div class="question">At S.T.P. the volume of $7.5 \mathrm{g}$ of a gas is $5.6 \mathrm{L}$. The gas is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">NO</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{N}_{2} \mathrm{O}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">CO</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{CO}_{2}$</span> </li> </ul>

answer:
<div class="solution">Given, mass of gas $(W)=7.5 \mathrm{g}$
<br/>Volume of gas at $\operatorname{STP}(V)=56 \mathrm{L}$
<br/>$\because$ Moles of gas at $\mathrm{STP}=\frac{V(\mathrm{L})}{22.4(\mathrm{L})}=\frac{W}{M}$
<br/>Where $M=$ molar mass of gas.
<br/>$\therefore \quad M=\frac{W \times 22.4}{V}$
<br/>$$
<br/>=\frac{7.5 \times 22.4}{5.6}=30.00 \mathrm{g} \mathrm{mol}^{-1}
<br/>$$
<br/>Among the given options Molar mass $(M)$ of
<br/>$\mathrm{NO}=14+16=30.00 \mathrm{g} \mathrm{mol}^{-1}$
<br/>(b) $\mathrm{N}_{2} \mathrm{O}=28+16=44.00 \mathrm{g} \mathrm{mol}^{-1}$
<br/>(c) $\mathrm{CO}=12+16=28.00 \mathrm{g} \mathrm{mol}^{-1}$
<br/>(d) $\mathrm{CO}_{2}=12+32=44.00 \mathrm{g} \mathrm{mol}^{-1}$
<br/>$\because$ Molar mass of $\mathrm{NO}=30 \mathrm{g} \mathrm{mol}^{-1}$
<br/>Thus, the given gas is NO. Hence, is the correct option.</div>


tags: ['Chemistry', 'Electrochemistry', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch1_P2.db
title:
at-temperature-of-298-k-the-emf-of-the-following-electrochemical-cell-ag-s-ag-01-m-zn-2-01-m-zn-s-will-be-given-e-call-1562-v

slug:
at-temperature-of-298-k-the-emf-of-the-following-electrochemical-cell-ag-s-ag-01-m-zn-2-01-m-zn-s-will-be-given-e-call-1562-v-12546

question:
<div class="question">At temperature of $298 \mathrm{K}$, the emf of the following electrochemical cell. $\mathrm{Ag}(\mathrm{s})\left|\mathrm{Ag}^{+*}(0.1 \mathrm{M}) \| \mathrm{Zn}^{2 +}(0.1 \mathrm{M})\right| \mathrm{Zn}(\mathrm{s})$ will be (Given, $E^{\prime \prime}$ call $=-1.562 \mathrm{V}$ )</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$-1.532 \mathrm{V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$-1.503 V$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1.532 \mathrm{V}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-3.06 V$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-1.532 \mathrm{V}$</span> </div>

answer:
<div class="solution">From the given cell, the cell reaction is
<br/>$2 \mathrm{Ag}(s)+Z \mathrm{n}^{2+}(01 \mathrm{M}) \longrightarrow$ $2 \mathrm{Ag}^{+}(0.1 \mathrm{M})+\mathrm{Zn}(s)$
<br/>The Nemst equation is,
<br/>$E_{\text {cel }}=E_{\text {cel }}^{\circ}-\frac{0.0591}{n} \log \frac{\left[\mathrm{Ag}^{+}\right]^{2}}{\left.\mid \mathrm{Zn}^{2+}\right]}$
<br/>or, $E_{\text {cal }}=(-1.562)-\frac{(0.0591)}{2} \log \frac{(0.1)^{2}}{(0.1)}$
<br/>$\begin{aligned} \text { Or, } E_{\text {cel }} &amp;=(-1.562)-\frac{0.0591}{2} \log 10^{-1} \\ &amp;=-1.562+\frac{0.0591}{2} \\ &amp;=-1.562+0.02955 \\ &amp;=-1.532 \mathrm{V} \end{aligned}$</div>


tags: ['Physics', 'Magnetic Properties of Matter', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P2.db
title:
at-two-different-places-the-angles-of-dip-are-respectively-3-0-and-4-5-at-these-two-places-the-ratio-of-horizontal-component-of-earths-magnetic-field-

slug:
at-two-different-places-the-angles-of-dip-are-respectively-3-0-and-4-5-at-these-two-places-the-ratio-of-horizontal-component-of-earths-magnetic-field-44411

question:
<div class="question">At two different places, the angles of dip are respectively $30^{\circ}$ and $45^{\circ} .$ At these two places the ratio of horizontal component of earth's magnetic field is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\sqrt{3}: \sqrt{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1: \sqrt{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1: 2</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1: \sqrt{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\sqrt{3}: \sqrt{2}$</span> </div>

answer:
<div class="solution">The horizontal component of earth's magnetic field is given by, $H=R \cos \delta$
<br/>where, $\delta$ is the angle of dip so $H_{1}=R \cos 30^{\circ}$ and $\mathrm{H}_{2}=\mathrm{Rcos} 45^{\circ}$
<br/>$\therefore \quad \frac{H_{1}}{H_{2}}=\frac{R \cos 30^{\circ}}{R \cos 45^{\circ}}=\frac{\sqrt{3} / 2}{1 / \sqrt{2}}=\frac{\sqrt{3}}{\sqrt{2}}$</div>


title: atoms-in-a-p-4-molecule-of-white-phosphorus-are-arranged-regularly-in-the-following-way
slug: atoms-in-a-p-4-molecule-of-white-phosphorus-are-arranged-regularly-in-the-following-way-80899
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'WBJEE', 'WBJEE 2009']
source_db: db\MarksBatch1_P2.db
question:
<div class="question">Atoms in a $\mathrm{P}_4$ molecule of white phosphorus are arranged regularly in the following way:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">at the corners of a cube</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">at the corners of a octahedron</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">at the corners of a tetrahedron</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">at the centre and corners of a tetrahedron</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">at the corners of a tetrahedron</span> </div>

answer:
<div class="solution">Hints: <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/szwqxyspC_VE0xpvDQcJn6SCNUaeGtV2hDXPKUU0Bqg.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Gravitation', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch1_P2.db
title:
average-distance-of-the-earth-from-the-sun-is-l-1-if-one-year-of-the-earth-d-days-one-year-of-another-planet-whose-average-distance-from-the-sun-is-l-

slug:
average-distance-of-the-earth-from-the-sun-is-l-1-if-one-year-of-the-earth-d-days-one-year-of-another-planet-whose-average-distance-from-the-sun-is-l-47477

question:
<div class="question">Average distance of the Earth from the Sun is $L_{1}$ : If one year of the Earth $=D$ days, one year of another planet whose average distance from the Sun is $L_{2}$ will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$D\left(\frac{L_{2}}{L_{1}}\right)^{\frac{1}{2}}$ days</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$D\left(\frac{L_{2}}{L_{1}}\right)^{\frac{3}{2}}$ days</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$D\left(\frac{L_{2}}{L_{1}}\right)^{\frac{2}{3}}$ days</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$D\left(\frac{L_{2}}{L_{1}}\right)$ days</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$D\left(\frac{L_{2}}{L_{1}}\right)^{\frac{3}{2}}$ days</span> </div>

answer:
<div class="solution">By Keplar's law,
<br/>$$
<br/>\begin{array}{l}
<br/>T^{2} \propto R^{3} \\
<br/>T=D\left(\frac{L_{2}}{L_{1}}\right)^{3 / 2}
<br/>\end{array}
<br/>$$</div>


title: avogadros-law-is-valid-for
slug: avogadros-law-is-valid-for-20992
question: <div class="question">Avogadro's law is valid for</div>
tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'WBJEE', 'WBJEE 2022']
answer: <div class="solution">Fact</div>
source_db: db\MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">all gases</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">ideal gas</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Van der Waals gas</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">real gas</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">ideal gas</span> </div>


tags: ['Mathematics', 'Ellipse', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch1_P2.db
title:
b-is-an-extremity-of-the-minor-axis-of-an-ellipse-whose-foci-are-s-and-s-if-sb-s-is-a-right-angle-then-the-eccentricity-of-the-ellipse-is

slug:
b-is-an-extremity-of-the-minor-axis-of-an-ellipse-whose-foci-are-s-and-s-if-sb-s-is-a-right-angle-then-the-eccentricity-of-the-ellipse-is-93163

question:
<div class="question">$B$ is an extremity of the minor axis of an ellipse whose foci are $S$ and $S^{\prime} .$ If $\angle S B S^{\prime}$ is a right angle, then the eccentricity of the ellipse is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{1}{\sqrt{2}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{2}{3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{\sqrt{2}}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_mat_a22.png"/> <br/> <br/>Slope of $S B, m_{1}=\frac{b-0}{0-a e}=-\frac{b}{a e}$
<br/>and slope of $S^{\prime} B, m_{2}=\frac{b-0}{0-(-a e)}=\frac{b}{a e}$
<br/>since, $\angle S B S^{\prime}$ is a right angle.
<br/>$\therefore$ $$m_{1} m_{2}=-1$$
<br/>$\Rightarrow \quad \frac{-b}{a e} \times \frac{b}{a e}=-1$
<br/>$\Rightarrow \quad b^{2}=a^{2} e^{2}$
<br/>$\Rightarrow \quad \frac{b^{2}}{a^{2}}=e^{2}$
<br/>$\Rightarrow \quad 1-e^{2}=e^{2}$
<br/>$\Rightarrow \quad 2 e^{2}=1$
<br/>$\Rightarrow \quad e^{2}=\frac{1}{2}$
<br/>$\Rightarrow \quad e=\pm \frac{1}{\sqrt{2}}$
<br/>$\Rightarrow \quad e=\frac{1}{\sqrt{2}}$ or $e=-\frac{1}{\sqrt{2}}$</div>


title: baeyers-reagent-is-1
slug: baeyers-reagent-is-1-45983
question: <div class="question">Baeyer's reagent is</div>
tags: ['Chemistry', 'd and f Block Elements', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">alkaline potassium permanganate</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">acidified potassium permanganate</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">neutral potassium permanganate</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">alkaline potassium manganate</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">alkaline potassium permanganate</span> </div>

answer:
<div class="solution">Baeyer's reagent is $1 \%$ cold dilute alkaline potassium permanganate. It is used to identify unsaturation. All unsaturated compounds lose its purple colour.</div>


title: best-reagent-for-nuclear-iodination-of-aromatic-compounds-is-1
slug: best-reagent-for-nuclear-iodination-of-aromatic-compounds-is-1-78315
question: <div class="question">Best reagent for nuclear iodination of aromatic compounds is</div>
tags: ['Chemistry', 'Hydrocarbons', 'JEE Main']
source_db: db\MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{KI} / \mathrm{CH}_{3} \mathrm{COCH}_{3}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$I_{2} / C H_{3} C N$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{KI} / \mathrm{CH}_{3} \mathrm{COOH}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{I}_{2} / \mathrm{HNO}_{3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{I}_{2} / \mathrm{HNO}_{3}$</span> </div>

answer:
<div class="solution">Best reagent for nuclear iodination of aromatic compounds is $\mathrm{I}_{2} / \mathrm{HNO}_{3}$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_che_a68.png"/></div>


title: blackened-oil-painting-can-be-restored-into-original-form-by-the-action-of
slug: blackened-oil-painting-can-be-restored-into-original-form-by-the-action-of-67878
tags: ['Chemistry', 'Hydrogen', 'WBJEE', 'WBJEE 2009']
source_db: db\MarksBatch1_P2.db
question:
<div class="question">Blackened oil painting can be restored into original form by the action of :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Chlorine</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{BaO}_2$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{H}_2 \mathrm{O}_2$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{MnO}_2$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{H}_2 \mathrm{O}_2$</span> </div>

answer:
<div class="solution">Blackening of oil painting is due to $\mathrm{PbS}$ which is oxidised by $\mathrm{H}_2 \mathrm{O}_2$ to form white $\mathrm{PbSO}_4$<br/>$\underset{\text { (Black) }}{\mathrm{PbS}+\mathrm{H}_2 \mathrm{O}_2} \rightarrow \underset{\text { (white) }}{\mathrm{PbSO}_4}+\mathrm{H}_2 \mathrm{O}$</div>


tags: ['Physics', 'Laws of Motion', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch1_P2.db
title:
block-b-lying-on-a-table-weighs-w-the-coefficient-of-static-friction-between-the-block-and-the-table-is-assume-that-the-cord-between-b-and-the-knot-is

slug:
block-b-lying-on-a-table-weighs-w-the-coefficient-of-static-friction-between-the-block-and-the-table-is-assume-that-the-cord-between-b-and-the-knot-is-41721

question:
<div class="question">Block $B$ lying on a table weighs W. The coefficient of static friction between the block and the table is $\mu$. Assume that the cord between $B$ and the knot is horizontal. The maximum weight of the block $A$ for which the system will be stationary is
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_q24.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{W \tan \theta}{\mu}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mu W tan \theta$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mu W \sqrt{1+\tan ^{2} \theta}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mu W \sin \theta$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mu W tan \theta$</span> </div>

answer:
<div class="solution">Let weight of $A$ is $W^{\prime}$. From the free body diagram. For equilibrium of the system,
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_a24.png"/> <br/> <br/>$$
<br/>\begin{aligned}
<br/>T \cos \theta &amp;=\mu N=\mu W \\
<br/>T \sin \theta &amp;=W^{\prime}
<br/>\end{aligned}
<br/>$$
<br/>where $T=$ tension in the thread lying between knot and the support.
<br/>On divindg, we get $\frac{T \sin \theta}{T \cos \theta}=\frac{W^{\prime}}{\mu W}$
<br/>$\Rightarrow \quad \tan \theta=\frac{W^{\prime}}{\mu W}$
<br/>$\Rightarrow W^{\prime}=\mu W \tan \theta$</div>


title: boiling-water-reacts-with-c-6-h-5-n-2-cl-to-give
slug: boiling-water-reacts-with-c-6-h-5-n-2-cl-to-give-50349
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'WBJEE', 'WBJEE 2010']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">phenol</span> </div>
source_db: db\MarksBatch1_P2.db
question:
<div class="question">Boiling water reacts with $\mathrm{C}_6 \mathrm{H}_5 \mathrm{~N}_2{ }^{+} \mathrm{Cl}^{-}$to give</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">aniline</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">benzylamine</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">phenol</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">benzaldehyde</span> </li> </ul>

answer:
<div class="solution">$$<br/>\text { Hints : } \mathrm{C}_6 \mathrm{H}_5 \mathrm{~N}_2^{+} \mathrm{Cl}^{-} \underset{(\text { Boil })}{\stackrel{\mathrm{H}_2 \mathrm{O}}{\longrightarrow}} \mathrm{C}_6 \mathrm{H}_5 \mathrm{OH}\left(\mathrm{S}_{\mathrm{N}} \mathrm{Ar}\right)<br/>$$</div>


title: bond-order-of-he-2-he-2-and-he-2-2-are-respectively
slug: bond-order-of-he-2-he-2-and-he-2-2-are-respectively-26955
tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P2.db
question:
<div class="question">Bond order of $\mathrm{He}_{2}, \mathrm{He}_{2}^{+}$ and $\mathrm{He}_{2}^{2+}$ are respectively:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1, \frac{1}{2}, 0$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$0, \frac{1}{2}, 1$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{2}, 1,0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1,0, \frac{1}{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0, \frac{1}{2}, 1$</span> </div>

answer:
<div class="solution">Hint: 
<br/>$\mathrm{He}_{2}\left(4 \mathrm{e}^{-}\right)=\sigma(1 \mathrm{~s})^{2}, \sigma^{*}(1 \mathrm{~s})^{2} ; \mathrm{B} . \mathrm{O}=\frac{2-2}{2}=0$
<br/>$\mathrm{He}_{2}^{+}\left(3 \mathrm{e}^{-}\right)=\sigma(1 \mathrm{~s})^{2} \sigma^{*}(1 \mathrm{~s})^{1} ; \mathrm{B} . \mathrm{O}=\frac{2-1}{2}=\frac{1}{2}$
<br/>$\mathrm{He}_{2}^{+2}\left(2 \mathrm{e}^{-}\right)=\sigma(\mathrm{1s})^{2} ; \quad$ B.O. $=\frac{2-0}{2}=1$</div>


title: bromination-of-phcome-in-acetic-medium-produces-mainly
slug: bromination-of-phcome-in-acetic-medium-produces-mainly-85347
question: <div class="question">Bromination of PhCOMe in acetic medium produces mainly</div>
tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q51_opta.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q51_optb.png"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q51_optc.png"/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q51_optd.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q51_optd.png"/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_a51.png"/></div>


tags: ['Chemistry', 'Hydrocarbons', 'JEE Main']
source_db: db\MarksBatch1_P2.db
title:
by-passing-excess-cl-2-g-in-boiling-toluene-which-one-of-the-following-compounds-is-exclusively-formed-1

slug:
by-passing-excess-cl-2-g-in-boiling-toluene-which-one-of-the-following-compounds-is-exclusively-formed-1-80637

question:
<div class="question">By passing excess $\mathrm{Cl}_{2}(\mathrm{g})$ in boiling toluene, which one of the following compounds is exclusively formed?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_q34_opta.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_q34_optb.png"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_q34_optc.png"/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_q34_optd.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_q34_optd.png"/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_a34.png"/></div>


tags: ['Chemistry', 'Hydrocarbons', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch1_P2.db
title:
by-passing-excess-cl-2-g-in-boiling-toluene-which-one-of-the-following-compounds-is-exclusively-formed

slug:
by-passing-excess-cl-2-g-in-boiling-toluene-which-one-of-the-following-compounds-is-exclusively-formed-60264

question:
<div class="question">By passing excess $\mathrm{Cl}_{2}(\mathrm{g})$ in boiling toluene, which one of the following compounds is exclusively formed?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_q34_opta.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_q34_optb.png"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_q34_optc.png"/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_q34_optd.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_q34_optd.png"/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_a34.png"/></div>


tags: ['Chemistry', 'Chemical Kinetics', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch1_P2.db
title:
c-6-h-5-f-18-is-a-f-18-radioisotope-labelled-organic-compound-f-18-decays-by-positron-emission-the-product-resulting-on-decay-is

slug:
c-6-h-5-f-18-is-a-f-18-radioisotope-labelled-organic-compound-f-18-decays-by-positron-emission-the-product-resulting-on-decay-is-52470

question:
<div class="question">$\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{F}^{18}$ is a $\mathrm{F}^{18}$ radio-isotope labelled organic compound. $\mathrm{F}^{18}$ decays by positron emission. The product resulting on decay is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}^{18}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Ar}^{10}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{B}^{12} \mathrm{C}_{5} \mathrm{H}_{5} \mathrm{F}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}^{16}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}^{18}$</span> </div>

answer:
<div class="solution">${ }_{9} \mathrm{F}^{18} \longrightarrow{ }_{x} \mathrm{E}^{y}+{ }_{+1} e^{0}$
<br/>$$
<br/>x=8, y=18
<br/>$$
<br/>$\therefore \quad \mathrm{E}^{y}={ }_{8} \mathrm{O}^{18}$
<br/>$\because$ Position has one unit of the charge and
<br/>zero mass. Thus, $\mathrm{F}^{18}$ changes to $\mathrm{O}^{18}$ therefore resulting decay product is $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}^{18}$</div>


tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch1_P2.db
title:
c-6-h-6-liq-2-15-o-2-g-6-co-2-g-3-h-2-o-liq-benzene-burns-in-oxygen-according-to-the-above-equation-what-is-the-volume-of-oxygen-at-stp-needed-for-com

slug:
c-6-h-6-liq-2-15-o-2-g-6-co-2-g-3-h-2-o-liq-benzene-burns-in-oxygen-according-to-the-above-equation-what-is-the-volume-of-oxygen-at-stp-needed-for-com-93183

question:
<div class="question">$\mathrm{C}_6 \mathrm{H}_6(\mathrm{liq})+\frac{15}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow 6 \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{liq})$<br/>Benzene burns in oxygen according to the above equation. What is the volume of oxygen (at STP) needed for complete combustion of 39 gram of liquid benzene?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$11.2$ litre</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$22.4$ litre</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">84 litre</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">168 litre</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">84 litre</span> </div>

answer:
<div class="solution">$\mathrm{n}_{\mathrm{C}_6 \mathrm{H}_6}=\frac{39}{78}=\frac{1}{2}$ mole<br/>From Balanced equation,<br/>$\begin{aligned}<br/>&amp;\mathrm{n}_{\mathrm{C}_6 \mathrm{H}_{\mathrm{G}}}=\frac{2}{15} \mathrm{n}_{\mathrm{O}_2} \\<br/>&amp;\frac{1}{2}=\frac{2}{15} \times \frac{\mathrm{xL}}{22.4 \mathrm{~L}} \\<br/>&amp;\therefore \mathrm{x}=84 \mathrm{~L}<br/>\end{aligned}$</div>


title: calculate-k-c-for-the-reversible-process-given-below-if-k-p-167-and-t-80-0-c-caco-3-s-cao-s-co-2-g
tags: ['Chemistry', 'Chemical Equilibrium', 'WBJEE', 'WBJEE 2010']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1.89</span> </div>
source_db: db\MarksBatch1_P2.db
slug:
calculate-k-c-for-the-reversible-process-given-below-if-k-p-167-and-t-80-0-c-caco-3-s-cao-s-co-2-g-61977

question:
<div class="question">Calculate $\mathrm{K}_{\mathrm{C}}$ for the reversible process given below if $\mathrm{K}_{\mathrm{P}}=167$ and $\mathrm{T}=800^{\circ} \mathrm{C}$<br/>$\mathrm{CaCO}_3(\mathrm{~s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_2(\mathrm{~g})$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1.95</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1.85</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">1.89</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1.60</span> </li> </ul>

answer:
<div class="solution">Hints: $K_p=K_C(R T)^{\Delta n}$<br/>for $\mathrm{eq}^{\mathrm{n}} \quad \mathrm{CaCO}_3(\mathrm{~s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_2(\mathrm{~g}), \Delta \mathrm{n}=1$<br/>$\mathrm{K}_{\mathrm{C}}=\frac{\mathrm{K}_{\mathrm{P}}}{(\mathrm{RT})^{\Delta \mathrm{n}}}=\frac{167}{(0.0821 \times 1073)^1}=1.89$</div>


tags: ['Mathematics', 'Probability', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P2.db
title:
cards-are-drawn-onebyone-without-replacement-from-a-well-shuffled-pack-of-52-cards-then-the-probability-that-a-face-card-jack-queen-or-king-will-appea

slug:
cards-are-drawn-onebyone-without-replacement-from-a-well-shuffled-pack-of-52-cards-then-the-probability-that-a-face-card-jack-queen-or-king-will-appea-30669

question:
<div class="question">Cards are drawn one-by-one without replacement from a well shuffled pack of 52 cards. Then, the probability that a face card (jack, queen or king) will appear for the first time on the third turn is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{300}{2197}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{36}{85}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{12}{85}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{4}{51}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{12}{85}$</span> </div>

answer:
<div class="solution">Ist turn Total number of face card $=12$
<br/>Total number of elements in sample space, $n(s)=52$
<br/>$\therefore P_{1}$ (no face card in first turn) $=\frac{52-12}{52}=\frac{40}{52}$
<br/>IInd turn $P_{2}$ (no face card in second turn)
<br/>$$
<br/>=\frac{(52-13)}{(52-1)}=\frac{39}{51}
<br/>$$
<br/>IIIrd turn $P_{3}$ (face card in third turn)
<br/>$$
<br/>=\frac{(52-40)}{(51-1)}=\frac{12}{50}
<br/>$$
<br/>$\therefore$ Required $P$ (face card on third turn)
<br/>$$
<br/>\begin{array}{l}
<br/>=P_{1} \times P_{2} \times P_{3} \\
<br/>=\frac{40}{52} \times \frac{39}{51} \times \frac{12}{50}=\frac{12}{85}
<br/>\end{array}
<br/>$$</div>


tags: ['Chemistry', 'States of Matter', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P2.db
title:
case-1-an-ideal-gas-of-molecular-weight-m-at-temperature-t-case-2-another-ideal-gas-of-molecular-weight-2-mathrmm-at-temperature-mathrmt-2-identify-th

slug:
case-1-an-ideal-gas-of-molecular-weight-m-at-temperature-t-case-2-another-ideal-gas-of-molecular-weight-2-mathrmm-at-temperature-mathrmt-2-identify-th-29287

question:
<div class="question">Case \(-1:\) An ideal gas of molecular weight \(M\) at temperature \(T\).<br/>Case \(-2:\) Another ideal gas of molecular weight \(2 \mathrm{M}\) at temperature \(\mathrm{T} / 2\)<br/>Identify the correct statement in context of above two cases.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Average kinetic energy and avereage speed will be the same in the two cases</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Both the averages are halved</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Both the averages are doubled</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Only average speed is halved in the second case</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both the averages are halved</span> </div>

answer:
<div class="solution">Hint : As temperature is halved, average \(K E\) is halved.<br/>Average speed \((C) \propto \sqrt{\frac{T}{M}}\)<br/>In case \(-I,(C) \propto \sqrt{\frac{T}{M}}\)<br/>\(\text { In case }-II ~(C) \propto \sqrt{\frac{T}{2 \times 2 M}}=\frac{1}{2} \sqrt{\frac{T}{M}}\)<br/>So average speed is also halved.</div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch1_P2.db
title:
centre-of-mass-cm-of-three-particles-of-masses-1-kg-2-kg-and-3-kg-lies-at-the-point-1-2-3-and-cm-of-another-system-of-particles-of-3-kg-and-2-kg-lies-

slug:
centre-of-mass-cm-of-three-particles-of-masses-1-kg-2-kg-and-3-kg-lies-at-the-point-1-2-3-and-cm-of-another-system-of-particles-of-3-kg-and-2-kg-lies-92797

question:
<div class="question">Centre of mass (C.M.) of three particles of masses $1 \mathrm{~kg}, 2 \mathrm{~kg}$ and $3 \mathrm{~kg}$ lies at the point $(1,2,3)$ and C.M. of another system of particles of $3 \mathrm{~kg}$ and $2 \mathrm{~kg}$ lies at the point $(-1,3,-2)$. Where should we put a particle of mass $5 \mathrm{~kg}$ so that the C.M. of entire system lies at the C.M. of the first system ?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$(3,1,8)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(0,0,0)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(1,3,2)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$(-1,2,3)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(3,1,8)$</span> </div>

answer:
<div class="solution">$\left.\begin{array}{l}6 \mathrm{~kg}[1,2,3] \\ 5 \mathrm{~kg}[-1,3,-2] \\ 5 \mathrm{~kg}[\mathrm{x}, \mathrm{y}, \mathrm{z}]\end{array}\right) \rightarrow(\overline{\mathrm{x}}, \overline{\mathrm{y}}, \overline{\mathrm{z}})=(1,2,3)$
<br/>$\bar{x}=\frac{m_{1} x_{1}+m_{2} x_{2}}{m_{1}+m_{2}}$
<br/>$1=\frac{5(-1)+5 \times x}{10}$
<br/>$-5+5 x=10 \Rightarrow x=3$
<br/>$\bar{y}=2=\frac{5 \times 3+5 y}{10}, 15+5 y=20, y=1$
<br/>$\bar{z}=3=\frac{5(-2)+5 . z}{10},-10+5 z=30, z=8$</div>


tags: ['Physics', 'Thermodynamics', 'WBJEE', 'WBJEE 2022']
answer: <div class="solution">$v_p \propto \sqrt{T}$</div>
source_db: db\MarksBatch1_P2.db
title:
certain-amount-of-an-ideal-gas-is-taken-from-its-initial-state-1-to-final-state-4-through-the-paths-1-2-3-4-as-shown-in-figure-a-b-c-d-ef-are-all-isot

slug:
certain-amount-of-an-ideal-gas-is-taken-from-its-initial-state-1-to-final-state-4-through-the-paths-1-2-3-4-as-shown-in-figure-a-b-c-d-ef-are-all-isot-61010

question:
<div class="question">Certain amount of an ideal gas is taken from its initial state 1 to final state 4 through the paths $1 \rightarrow 2 \rightarrow 3 \rightarrow 4$ as shown in figure. $A B, C D, E F$ are all isotherms. If $v_p$ is the most probable speed of the molecules, then<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/cFRUZS9Cwo5djp44kzUztwJ7sRD3TEcmAQjSAgA2cQw.original.fullsize.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$v_p$ at $3=v_p$ at $4&gt;v_p$ at $2&gt;v_p$ at 1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$v_p$ at $3&gt;v_p$ at $1&gt;v_p$ at $2&gt;v_p$ at 4</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$v_p$ at $3&gt;v_p$ at $2&gt;v_p$ at $4&gt;v_p$ at 1</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$v_p$ at $2=v_p$ at $3&gt;v_p$ at $1&gt;v_p$ at 4</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$v_p$ at $3=v_p$ at $4&gt;v_p$ at $2&gt;v_p$ at 1</span> </div>


title: ch-3-c-c-mgbr-can-be-prepared-by-the-reaction-of
slug: ch-3-c-c-mgbr-can-be-prepared-by-the-reaction-of-76146
tags: ['Chemistry', 'Hydrocarbons', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch1_P2.db
question:
<div class="question">$\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{C} \mathrm{MgBr}$ can be prepared by the
<br/>reaction of</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{CH}_{3}-\mathrm{C}=\mathrm{C}-\mathrm{Br}$ with $\mathrm{MgBr}_{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{CH}$ with $\mathrm{MgBr}_{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{CH}$ with $\mathrm{KBr}$ and $\mathrm{Mg}$ metal</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{CH}$ with $\mathrm{CH}_{3} \mathrm{MgBr}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{CH}$ with $\mathrm{CH}_{3} \mathrm{MgBr}$</span> </div>

answer:
<div class="solution">$\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{CMg}$ Br can be prepared by the reaction of $\mathrm{CH}_{3}-\mathrm{C}=\mathrm{CH}$ with $\mathrm{CH}_{3} \mathrm{MgBr}$. This
<br/>method is used in preparation of higher alkynes from lower alkynes. The chemical equation for the formation of $\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{CMgBr}$ is given below
<br/>$$
<br/>\begin{array}{r}
<br/>\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{CH}+\mathrm{CH}_{3} \mathrm{MgBr} \longrightarrow \\
<br/>\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{CMg} X
<br/>\end{array}
<br/>$$</div>


title: chlorine-gas-reacts-with-red-hot-calcium-oxide-to-give
slug: chlorine-gas-reacts-with-red-hot-calcium-oxide-to-give-15055
question: <div class="question">Chlorine gas reacts with red hot calcium oxide to give</div>
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">bleaching powder and dichlorine monoxide</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">bleaching powder and water</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">calcium chioride and chiorine dioxide</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">calcium chioride and oxygen</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">calcium chioride and oxygen</span> </div>

answer:
<div class="solution">$2 \mathrm{CaO}+\mathrm{Cl}_{2} \stackrel{\text { Red hot }}{\longrightarrow} \mathrm{CaCl}_{2}+\mathrm{O}_{2} \uparrow$</div>


title: choose-the-correct-statement-for-the-ni-cn-4-2-complex-ion-atomic-no-of-ni-28
slug: choose-the-correct-statement-for-the-ni-cn-4-2-complex-ion-atomic-no-of-ni-28-91220
tags: ['Chemistry', 'Coordination Compounds', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch1_P2.db
question:
<div class="question">Choose the correct statement for the $\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$ complex ion (Atomic no. of $\mathrm{Ni}=28$ )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The complex is square planar and paramagnetic</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The complex is tetrahedral and diamagnetic</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">The complex is square planar and diamagnetic</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">The complex is tetrahedral and paramagnetic</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The complex is square planar and diamagnetic</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2AnVoTK_V0OevqkjRANqVqHLtBmVzrhWJJ-fn08lkvI.original.fullsize.png"/></div>


title: choose-the-correct-statements-among-the-following
slug: choose-the-correct-statements-among-the-following-33124
question: <div class="question">Choose the correct statement(s) among the following.</div>
tags: ['Chemistry', 'General Organic Chemistry', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_che_q36_opta.png"/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CHO}$ on reaction with HCN gives racemic mixture</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_che_q36_optc.png"/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{NOH}$ shows geometrical isomerism</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">$\mathrm{CH}_{3} \mathrm{CHO}$ on reaction with HCN gives racemic mixture, $\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{NOH}$ shows geometrical isomerism</span> </div>

answer:
<div class="solution">These are cis and trans isomers not enantiomers (Thus, false).
<br/>(b) $CH_{3}CHO$ on reaction with HCN gives racemic mixture of cyanohydrin (Thus, true).
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_che_a36.png"/></div>


title: chords-of-an-ellipse-are-drawn-through-the-positive-end-of-the-minor-axis-their-midpoint-lies-on
tags: ['Mathematics', 'Ellipse', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch1_P2.db
slug:
chords-of-an-ellipse-are-drawn-through-the-positive-end-of-the-minor-axis-their-midpoint-lies-on-35409

question:
<div class="question">Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">a circle</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">a parabola</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">an ellipse</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">a hyperbola</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">an ellipse</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/iH-NFAg0AXSnvXF4lnFhS01JsDCFY_Pk-rQgEaXMB_c.original.fullsize.png"/><br/><br/>$\begin{array}{ll}<br/>\frac{x_1+0}{2}=h &amp; \frac{y_1+b}{2}=k \\<br/>\Rightarrow x_1=2 h &amp; \Rightarrow y_1=2 k-b<br/>\end{array}$<br/>$\frac{x_1^2}{a^2}+\frac{y_1^2}{b^2}=1 \Rightarrow \frac{4 h^2}{a^2}+\frac{(2 k-b)^2}{b^2}=1 \Rightarrow \frac{h^2}{a^2 / 4}+\frac{\left(k-\frac{b}{2}\right)^2}{b^2 / 4}=1$<br/>$\therefore \frac{x^2}{a^2 / 4}+\frac{\left(y-\frac{b}{2}\right)^2}{b^2 / 4}=1 \rightarrow$ Locus of midpoint which is an ellipse</div>


title: cl-2-o-7-is-the-anhydride-of
slug: cl-2-o-7-is-the-anhydride-of-65920
question: <div class="question">$\mathrm{Cl}_{2} \mathrm{O}_{7}$ is the anhydride of</div>
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{HOCl}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{HClO}_{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{HClO}_{3}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{HClO}_{4}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{HClO}_{4}$</span> </div>

answer:
<div class="solution">$\mathrm{Cl}_{2} \mathrm{O}_{7}$ is the anhydride of $\mathrm{HClO}_{4}$. It reacts with water slowly to give perchloric acid.
<br/>$\mathrm{Cl}_{2} \mathrm{O}_{7}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \underset{\text { Perchloric acid }}{2 \mathrm{HClO}_{4}}$
<br/>Its structure is as follows:
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_che_a41.png"/> <br/> <br/>It is less reactive than other oxides of chlorine and does not react with $P, S,$ coal or paper at room temperature.</div>


title: co-is-practically-nonpolar-since
slug: co-is-practically-nonpolar-since-65780
question: <div class="question">CO is practically non-polar since</div>
tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">the $\sigma$ -electron drift from $C$ to $O$ is almost nullified by the $\pi$ -electron drift from $\mathrm{O}$ to $\mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">the $\sigma$-clectron drift from O to C is almost nullified by the $\pi$ -electron drift from $\mathrm{C}$ to $\mathrm{O}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">the bond moment is low</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">there is a triple bond berween $\mathrm{C}$ and $\mathrm{O}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">the $\sigma$ -electron drift from $C$ to $O$ is almost nullified by the $\pi$ -electron drift from $\mathrm{O}$ to $\mathrm{C}$</span> </div>

answer:
<div class="solution">$\mathrm{C} \frac{\pi}{\sigma} \mathrm{O}$
<br/>In $\mathrm{CO}$ molecule, $\mathrm{C}-\mathrm{O} \sigma$ moment and $\mathrm{O}-\mathrm{C}$ $\pi$ -moment cancels each other. So that it is non-polar.</div>


title: cold-ferrous-sulphate-solution-on-absorptive-of-no-develops-brown-colour-due-to-the-formation-of
tags: ['Chemistry', 'Coordination Compounds', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch1_P2.db
slug:
cold-ferrous-sulphate-solution-on-absorptive-of-no-develops-brown-colour-due-to-the-formation-of-34307

question:
<div class="question">Cold ferrous sulphate solution on absorptive of NO develops brown colour due to the formation of</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">paramagnetic $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}(\mathrm{NO})\right] \mathrm{SO}_{4}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">diamagnetic $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}\left(\mathrm{N}_{3}\right)\right] \mathrm{SO}_{4}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">paramagnetic $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}\left(\mathrm{NO}_{3}\right)\right]\left[\mathrm{SO}_{4} \mathrm{l}_{2}\right.$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">diamagnetic $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{SO}_{4}\right)\right] \mathrm{NO}_{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">paramagnetic $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}(\mathrm{NO})\right] \mathrm{SO}_{4}$</span> </div>

answer:
<div class="solution">Cold FeSO, solution on absorption of NO develops brown colour due to the formation of $[Fe(H_{2}O)_{5}(NO)]SO_4$
<br/>$\mathrm{FeSO}_{4}+\mathrm{NO}+5 \mathrm{H}_{2} \mathrm{O} \rightarrow [Fe(H_{2}O)_{5}(NO)]SO_4$
<br/>This complex has 3.89 BM magnetic moment shows that it has 3 unpaired electrons</div>


title: commercial-sample-of-h-2-o-2-is-labeled-as-10-v-its-strength-is-nearly
slug: commercial-sample-of-h-2-o-2-is-labeled-as-10-v-its-strength-is-nearly-23539
tags: ['Chemistry', 'Hydrogen', 'WBJEE', 'WBJEE 2014']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: db\MarksBatch1_P2.db
question:
<div class="question">Commercial sample of $\mathrm{H}_{2} \mathrm{O}_{2}$ is labeled as $10 \mathrm{V}$. Its % strength is nearly</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">3</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">6</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">9</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">12</span> </li> </ul>

answer:
<div class="solution">10 V $\mathrm{H}_{2} \mathrm{O}_{2}$  means $1 \mathrm{L}$ of this solution will produce $10 \mathrm{LO}_{2}$ at STP.
<br/>$$
<br/>\begin{array}{c}
<br/>2 \mathrm{H}_{2} \mathrm{O}_{2} \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}+\quad \mathrm{O}_{2} \\
<br/>68 \mathrm{g} \quad \quad \quad \quad 22.4 \text{L at STP}
<br/>\end{array}
<br/>$$
<br/>$\therefore 22.4 \mathrm{L}$ of $\mathrm{O}_{2}$ is obtained from $\mathrm{H}_{2} \mathrm{O}_{2}=68 \mathrm{g}$
<br/>10 L of $O_2$ will be obtained from
<br/>$$
<br/>\mathrm{H}_{2} \mathrm{O}_{2}=\frac{68}{22.4} \times 10=30.36 \mathrm{g}
<br/>$$
<br/>$1000 \mathrm{mL}$ of the given solution contains $30.36 \mathrm{g}$ $\mathrm{H}_{2} \mathrm{O}_{2}$ and $100 \mathrm{mL}$ of the given solution contains
<br/>$$
<br/>\frac{30.36 \times 100}{1000}=3.03 \mathrm{g} \mathrm{H}_{2} \mathrm{O}_{2}
<br/>$$
<br/>Thus, $\%$ strength of $\mathrm{H}_{2} \mathrm{O}_{2}$ is $3.03(\approx 3)$</div>


tags: ['Chemistry', 'Practical Chemistry', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch1_P2.db
title:
compound-x-is-tested-and-the-results-are-shown-in-the-table-test-aqueous-sodium-hydroxide-is-added-then-heated-gently-dilute-hydrochioric-acid-is-adde

slug:
compound-x-is-tested-and-the-results-are-shown-in-the-table-test-aqueous-sodium-hydroxide-is-added-then-heated-gently-dilute-hydrochioric-acid-is-adde-16290

question:
<div class="question">Compound $X$ is tested and the results are shown in the table. <br/>$\begin{array}{l|l}\hline \text{ Test } &amp; \text{ Result } \\\hline \text{ Aqueous sodium } &amp; \text{ Gas given off which turns }\\\text{ hydroxide is added, }&amp; \text{ damp red litmus paper }\\\text{ then heated gently. }&amp; \text{ blue. }\\\text{ Dilute hydrochioric }&amp; \text{ Effervescence, gas given }\\\text{ acid is added. }&amp; \text{ off which turns lime water }\\&amp; \text{ milky and acidified }\\&amp; \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} \text{ paper green. }\\\hline\end{array}$<br/>Which ions are present in compound $X ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Ammonium ions and sulphite ions</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Ammonium ions and carbonate ions</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Sodium ions and carbonate ions</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Ammonium ions and sulphate ions</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Ammonium ions and sulphate ions</span> </div>

answer:
<div class="solution">It is a test for ammonia
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_che_a32.png"/> <br/> <br/>(ii) it is a test for $\mathrm{SO}_{4}^{2-}$ ions (Orange)<img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_che_a32a.png"/></div>


title: compounds-with-spinonly-magnetic-moment-equivalent-to-five-unpaired-electrons-are
slug: compounds-with-spinonly-magnetic-moment-equivalent-to-five-unpaired-electrons-are-63692
tags: ['Chemistry', 'Coordination Compounds', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch1_P2.db
question:
<div class="question">Compounds with spin-only magnetic moment equivalent to five unpaired electrons are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{K}_{4}\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Cl}_{3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{K}_{3}\left[\mathrm{FeF}_{6}\right]$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{K}_{4}\left[\mathrm{MnF}_{6}\right]$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">$\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Cl}_{3}$, $\mathrm{K}_{3}\left[\mathrm{FeF}_{6}\right]$, $\mathrm{K}_{4}\left[\mathrm{MnF}_{6}\right]$</span> </div>

answer:
<div class="solution">Among the given species
<br/>$\mathrm{H}_{2} \mathrm{O}$ and $\mathrm{F}$ are weak field ligands and do not cause pairing of electrons in the central metal atom. As CN is a strong field ligand, it causes pairing of electrons in the central metal atom.
<br/>Now,
<br/>Oxidation state of :
<br/>(b) Fe in $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Cl}_{3}=(+) 3$ and electronic
<br/>configuration of $\mathrm{Fe}^{3 +}$ ions is $\mathrm{3d}^{5} 4 \mathrm{s}^{0}$ 
<br/>i.e. have 5 unpaired electrons
<br/>(c) Fe in $\mathrm{K}_{3}\left[\mathrm{FeF}_{6}\right]$
<br/>Oxidation no. of $\mathrm{Fe}=(+) 3$ electronic configuration of $\mathrm{Fe}^{3}$ is $\mathrm{3d}^{4} 4 \mathrm{s}^{0}$
<br/>i.e. have 5 unpaired electrons.
<br/>(d) Oxidation state of $\mathrm{Mn}$ in $\mathrm{K}_{4}\left[\mathrm{MnF}_{6}\right]=(+) 2$ and electronic configuration of $\mathrm{Mn}^{2}+$ is $\mathrm{3d}^{5} 4 \mathrm{s}^{0}$ 
<br/>i.e., have 5 unpaired electrons. Hence, options (b) (c) and (d) are the correct options.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2019_che_a78.png"/></div>


tags: ['Physics', 'Thermal Properties of Matter', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P2.db
title:
consider-a-black-body-radiation-in-a-cubical-box-at-absolute-temperature-t-if-the-length-of-each-side-of-the-box-is-doubled-and-the-temperature-of-the

slug:
consider-a-black-body-radiation-in-a-cubical-box-at-absolute-temperature-t-if-the-length-of-each-side-of-the-box-is-doubled-and-the-temperature-of-the-17724

question:
<div class="question">Consider a black body radiation in a cubical box at absolute temperature $T$. If the length of each side of the box is doubled and the temperature of the walls of the box and that of the radiation is halved, then the total energy</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">halves</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">doubles</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">quadruples</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">remains the same</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">remains the same</span> </div>

answer:
<div class="solution">Assuming temperature of the body and cubica box is same initially, i.e., $T$ and finally it becomes $T / 2$ Because, temperature of body and surrounding remains same.
<br/>Hence, no net loss of radiation occur through the body. This total energy remains constant.</div>


tags: ['Physics', 'Electromagnetic Induction', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P2.db
title:
consider-a-conducting-wire-of-length-l-bent-in-the-form-of-a-circle-of-radius-r-and-another-conductor-of-length-a-a-r-is-bent-in-the-form-of-a-square-

slug:
consider-a-conducting-wire-of-length-l-bent-in-the-form-of-a-circle-of-radius-r-and-another-conductor-of-length-a-a-r-is-bent-in-the-form-of-a-square-18675

question:
<div class="question">Consider a conducting wire of length $\mathrm{L}$ bent in the form of a circle of radius $\mathrm{R}$ and another conductor of length 'a' (a &lt; &lt; R) is bent in the form of a square. The two loops are then placed in same plane such that the square loop is exactly at the centre of the circular loop. What will be the mutual inductance between the two loops?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mu_{0} \frac{\pi a^{2}}{L}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mu_{0} \frac{\pi \mathrm{a}^{2}}{16 \mathrm{~L}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mu_{0} \frac{\pi a^{2}}{4 L}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mu_{0} \frac{\mathrm{a}^{2}}{4 \pi \mathrm{L}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mu_{0} \frac{\pi \mathrm{a}^{2}}{16 \mathrm{~L}}$</span> </div>

answer:
<div class="solution">Hint:
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/CsA8KA24eSJ2dY0y9E7428EHaGgUoD0lPxRCYMMljh0.original.fullsize.png"/><br/> <br/>$2 \pi R=L_{\cdots} \ldots \ldots \ldots .(1)$
<br/>$4 s=a \ldots \ldots \ldots . .(2)$
<br/>$\frac{\mu_{0} I \times S^{2}}{2 R}=\phi, M=\frac{\mu_{0} S^{2}}{2 R}$
<br/>$=\frac{\mu_{0}}{2} \times \frac{a^{2} \times 2 \pi}{16 \times L}=\frac{\mu_{0} a^{2} \pi}{16 L}$</div>


tags: ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P2.db
title:
consider-a-positively-charged-infinite-cylinder-with-uniform-volume-charge-density-r-0-an-electric-dipole-consisting-of-q-and-q-charges-attached-to-op

slug:
consider-a-positively-charged-infinite-cylinder-with-uniform-volume-charge-density-r-0-an-electric-dipole-consisting-of-q-and-q-charges-attached-to-op-52534

question:
<div class="question">Consider a positively charged infinite cylinder with uniform volume charge density \(r &gt; 0\). An electric dipole consisting of \(+Q\) and \(-Q\) charges attached to opposite ends of a massless rod is oriented as shown in the figure. At the instant as shown in the figure, the dipole will experience,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2r2chTkubN0ggXOrd9QFlDYVURIOQhqtPLH_TXV_UWE.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">a force to the left and no torque</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">a force to the right and a clockwise torque</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">a force to the right and a counter clockwise torque</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">non froce but only a clockwise torque</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">a force to the right and a clockwise torque</span> </div>

answer:
<div class="solution">Hint : <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/MBJobX-BnMKxnly2-haCOTuTxPx5vUGSge3oJ_CBLGg.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/pKIfdy_FHPYi5XygKb79MzYNYKjTMlLg1p8f3tgJmVo.original.fullsize.png"/><br/><br/>\(E \propto \frac{1}{r}\)<br/>\(\begin{aligned} &amp; \mathrm{F}_1 &gt; \mathrm{F}_2 \\ &amp; \therefore \quad \mathrm{F}_{\text {net }} \text { towards right } \tau_{\text {net }} \text { clockwise. }\end{aligned}\)</div>


title: consider-a-pure-inductive-ac-circuit-as-shown-in-the-figure-if-the-average-powr-consumed-is-p-then
tags: ['Physics', 'Alternating Current', 'WBJEE', 'WBJEE 2021']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$P=0$</span> </div>
source_db: db\MarksBatch1_P2.db
slug:
consider-a-pure-inductive-ac-circuit-as-shown-in-the-figure-if-the-average-powr-consumed-is-p-then-38426

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/TGCon55JStaHs4VZoG2HcYRVCvx9IOzQ7Z5FSe47mbA.original.fullsize.png"/><br/> <br/>Consider a pure inductive A.C. circuit as shown in the figure. If the average powr consumed is $P$, then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$P&gt;0$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\quad P     &lt; 0$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$P=0$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{P}$ is infinite</span> </li> </ul>

answer:
<div class="solution">Pure inductor consumer no power as I and $\mathrm{V}$ are in $90^{\circ}$ phase difference.</div>


tags: ['Mathematics', 'Sequences and Series', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P2.db
title:
consider-a-quadratic-equation-a-x22-b-xc0-where-a-b-c-are-positive-real-numbers-if-the-equation-has-no-real-root-then-which-of-the-following-is-true

slug:
consider-a-quadratic-equation-a-x22-b-xc0-where-a-b-c-are-positive-real-numbers-if-the-equation-has-no-real-root-then-which-of-the-following-is-true-71052

question:
<div class="question">Consider a quadratic equation \(a x^2+2 b x+c=0\) where \(a, b, c\) are positive real numbers. If the equation has no real root, then which of the following is true?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">a, b, c cannot be in A.P. or H.P. but can be in G.P.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">a, b, c cannot be in G.P. or H.P. but can be in A.P.</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(a, b, c\) cannot be in A.P. or G.P. but can be in H.P.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">a, b, c cannot be in A.P., G.P. or H.P.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(a, b, c\) cannot be in A.P. or G.P. but can be in H.P.</span> </div>

answer:
<div class="solution">Hint : For no real root<br/>\(\begin{aligned}<br/>&amp; (2 b)^2-4 a c  &lt; 0 \\<br/>&amp; b^2 &lt; a c \\<br/>&amp; b &lt; \sqrt{a c} \because a, b, c &gt; 0<br/>\end{aligned}\)<br/>If in \(A P\), then \(a+c=2 b\)<br/>i.e., \(\mathrm{x}=-1\) a solution<br/>\(\begin{aligned}<br/>&amp; \therefore a, b, c \text { not in AP } \\<br/>&amp; \because b^2 &lt; a c<br/>\end{aligned}\)<br/>\(\therefore a, b, c\) not in GP<br/>For HP \(\quad b=\frac{2 a c}{a+c}=\frac{2 \sqrt{a c}}{\sqrt{\frac{a}{c}}+\sqrt{\frac{c}{a}}}\)<br/>\(\sqrt{\frac{a}{c}}+\sqrt{\frac{c}{a}} \geq 2\)<br/>\(\therefore \frac{2 \sqrt{a c}}{\sqrt{\frac{a}{c}}+\sqrt{\frac{c}{a}}} \leq 2 \therefore a, b, c\) in HP is possible</div>


tags: ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch1_P2.db
title:
consider-a-region-in-free-space-bounded-by-the-surfaces-of-an-imaginary-cube-having-sides-of-length-a-as-shown-in-the-figure-a-charge-q-is-placed-at-t

slug:
consider-a-region-in-free-space-bounded-by-the-surfaces-of-an-imaginary-cube-having-sides-of-length-a-as-shown-in-the-figure-a-charge-q-is-placed-at-t-92784

question:
<div class="question">Consider a region in free space bounded by the surfaces of an imaginary cube having sides of length $a$ as shown in the figure. A charge $+Q$ is placed at the centre $O$ of the cube. $P$ is such a point out side the cube that the line $O P$ perpendicularly intersects the surface $A B C D$ at $R$ and also $O R=R P=a / 2$. A charge $+Q$ is placed at point $P$ also. What is the total electric flux through the five faces of the cube other than $A B C D ?$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_q24.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{Q}{\varepsilon_{0}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{5 Q}{6 \varepsilon_{0}}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{10 Q}{6 \varepsilon_{0}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">zero</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{Q}{\varepsilon_{0}}$</span> </div>

answer:
<div class="solution">For surface $A B C D$ clectric flux is zero. Because at surface $A B C D$ net electric field is zero. Using Gauss's law,
<br/>$$
<br/>\oint \mathbf{E} \cdot d \mathbf{S}=\frac{Q_{\mathrm{in}}}{\varepsilon_{0}}
<br/>$$
<br/>Electric flux through the five faces of the cube,
<br/>$$
<br/>\phi_{E}=\frac{Q}{\varepsilon_{0}}
<br/>$$</div>


tags: ['Mathematics', 'Ellipse', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P2.db
title:
consider-a-tangent-to-the-ellipse-2-x-2-1-y-2-1-at-any-point-the-locus-of-the-midpoint-of-the-portion-intercepted-between-the-axes-is

slug:
consider-a-tangent-to-the-ellipse-2-x-2-1-y-2-1-at-any-point-the-locus-of-the-midpoint-of-the-portion-intercepted-between-the-axes-is-83893

question:
<div class="question">Consider a tangent to the ellipse $\frac{x^{2}}{2}+\frac{y^{2}}{1}=1$ at any point. The locus of the midpoint of the portion intercepted between the axes is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{x^{2}}{2}+\frac{y^{2}}{4}=1$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{x^{2}}{4}+\frac{y^{2}}{2}=1$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{3 x^{2}}+\frac{1}{4 y^{2}}=1$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{1}{2 x^{2}}+\frac{1}{4 y^{2}}=1$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">$\frac{1}{2 x^{2}}+\frac{1}{4 y^{2}}=1$</span> </div>

answer:
<div class="solution">Hint: 
<br/>Tangent at $\mathrm{P}\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)$
<br/>$\frac{x x_{1}}{2}+\frac{y y_{1}}{1}=1$
<br/>Let mid point of intercept be $\mathrm{P}(\mathrm{h}, \mathrm{k})$
<br/>$\mathrm{h}=\frac{1}{\mathrm{x}_{1}}, \mathrm{k}=\frac{1}{2 \mathrm{y}_{1}}$ or $\mathrm{x}_{1}=\frac{1}{\mathrm{~h}}, \mathrm{y}_{1}=\frac{1}{2 \mathrm{k}}$
<br/>locus is $\frac{1}{2 x^{2}}+\frac{1}{4 y^{2}}=1$</div>


tags: ['Physics', 'Thermodynamics', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch1_P2.db
title:
consider-a-thermodynamic-process-where-internal-energy-u-a-p-2-v-a-constant-if-the-process-is-performed-adiabatically-then

slug:
consider-a-thermodynamic-process-where-internal-energy-u-a-p-2-v-a-constant-if-the-process-is-performed-adiabatically-then-36593

question:
<div class="question">Consider a thermodynamic process where internal energy $U=A P^2 \mathrm{~V}(\mathrm{~A}=$ constant). If the process is performed adiabatically, then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$A P^2(V+1)=$ constant</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$(\mathrm{AP}+1)^2 \mathrm{~V}=\mathrm{constant}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(\mathrm{AP}+1) \mathrm{V}^2=$ constant</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{V}{(A P+1)^2}=$ constant</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(\mathrm{AP}+1)^2 \mathrm{~V}=\mathrm{constant}$</span> </div>

answer:
<div class="solution">$U=A P^2 V$<br/>$\frac{d U}{d V}=A P^2+2 P A V \frac{d P}{d V}$ [For adiabatic process $\left.d Q=0, d U=-d w=-P d V\right]$<br/>$-\frac{P d V}{d V}=A P^2+2 P A V \frac{d P}{d V}$<br/>$-1=A P+2 A V \frac{d P}{d V} \Rightarrow-1-A P=2 A V \frac{d P}{d V}$<br/>$-\int \frac{d V}{V}=\int \frac{2 A d P}{A P+1}$<br/>$-\ell n V+C=\frac{2 A}{A} \ln (A P+1)$<br/>$C=\ell n(A P+1)^2+\ell n V \Rightarrow C=(A P+1)^2 V$</div>


tags: ['Physics', 'Thermal Properties of Matter', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P2.db
title:
consider-an-engine-that-absorbs-130-cal-of-heat-from-a-hot-reservoir-and-delivers-30-cal-heat-to-a-cold-reservoir-in-each-cycle-the-engine-also-consum

slug:
consider-an-engine-that-absorbs-130-cal-of-heat-from-a-hot-reservoir-and-delivers-30-cal-heat-to-a-cold-reservoir-in-each-cycle-the-engine-also-consum-26560

question:
<div class="question">Consider an engine that absorbs 130 cal of heat from a hot reservoir and delivers 30 cal heat to a cold reservoir in each cycle. The engine also consumes 2 J energy in each cycle to overcome friction. If the engine works at 90 cycles per minute, what will be the maximum power delivered to the load? [Assume the thermal equivalent of heat is $4.2 \mathrm{~J} / \mathrm{cal}]$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$816 \mathrm{~W}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$819 \mathrm{~W}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$627 \mathrm{~W}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$630 \mathrm{~W}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$627 \mathrm{~W}$</span> </div>

answer:
<div class="solution">Hint: 
<br/>work done per cycle $=100 \times 4.2-2=418 \mathrm{~J}$
<br/>Total work done $=418 \times 90$
<br/>Power $=\frac{418 \times 90}{60}=627 \mathrm{~W}$</div>


title: consider-the-circuit-given-here-the-potential-difference-v-bc-between-the-points-b-and-c-is
slug: consider-the-circuit-given-here-the-potential-difference-v-bc-between-the-points-b-and-c-is-66021
tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch1_P2.db
question:
<div class="question">Consider the circuit given here. The potential difference $V_{B C}$ between the points $B$ and $C$ is <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/Tts8UzgA9LlggUUNY4a0hiYk67GdFx1pil_NbWaYQsw.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 \mathrm{V}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$0.5 \mathrm{V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0 \mathrm{V}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-1 \mathrm{V}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.5 \mathrm{V}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_phy_a35.png"/> <br/> <br/>From circuit the current,
<br/>$$
<br/>I=\frac{E}{R}
<br/>$$
<br/>The equivalent resistance of above circuit
<br/>$$
<br/>\begin{array}{l}
<br/>=3+2+1 \\
<br/>=6 \mathrm{k} \Omega \\
<br/>=6 \times 10^{3} \Omega \\
<br/>E=3 \text { volt }
<br/>\end{array}
<br/>$$
<br/>$$
<br/>\begin{aligned}
<br/>I &amp;=\frac{3}{6 \times 10^{3}} \\
<br/>&amp;=0.5 \times 10^{-3} \mathrm{A}
<br/>\end{aligned}
<br/>$$
<br/>Porential, $\begin{aligned} V_{A D} &amp;=i R=0.5 \times 10^{-3} \times 3 \times 10^{3} \\ &amp;=1.5 \mathrm{V} \end{aligned}$
<br/>Charge,
<br/>$$
<br/>\begin{array}{l}
<br/>\frac{1}{C}=\frac{1}{1}+\frac{1}{2}=\frac{3}{2} \\
<br/>C=\frac{2}{3} \\
<br/>Q=C \cdot V_{A D} \\
<br/>=\frac{2}{3} \times 1 \cdot 5 \\
<br/>=1 \mu \mathrm{C}
<br/>\end{array}
<br/>$$
<br/>Applying KVL (Kirchhoffs Voltage Law) from $B$ to $C$
<br/>$$
<br/>\begin{array}{c}
<br/>v_{s}-0 \cdot 5 \times 10^{-3} \times 2 \times 10^{3}+\frac{1}{2}=V_{c} \\
<br/>V_{n}-V_{c}=1-\frac{1}{2}=0.5 \mathrm{V}
<br/>\end{array}
<br/>$$</div>


tags: ['Physics', 'Alternating Current', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P2.db
title:
consider-the-circuit-shown-if-all-the-cells-have-negligible-internal-resistance-what-will-be-the-current-through-the-2-resistor-when-steady-state-is-r

slug:
consider-the-circuit-shown-if-all-the-cells-have-negligible-internal-resistance-what-will-be-the-current-through-the-2-resistor-when-steady-state-is-r-74560

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/4F-qXB0BL4ksrmaI40EgCAPbJmrAhUxOvKSQRZvurlU.original.fullsize.png"/><br/> <br/>Consider the circuit shown. If all the cells have negligible internal resistance, what will be the current through the $2 \Omega$ resistor when steady state is reached?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.66 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.29 \mathrm{~A}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$0 \mathrm{~A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.14 \mathrm{~A}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0 \mathrm{~A}$</span> </div>

answer:
<div class="solution">Hint:
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/eZRZqXy0Sc7xJIS4Uefq37IoiH2CnNxyOaM1yJhDJbc.original.fullsize.png"/><br/> <br/>$2-8 I-8 I-2=0$
<br/>$-8 I=0$
<br/>$I=0$</div>


tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch1_P2.db
title:
consider-the-circuit-shown-in-the-figure-the-value-of-the-resistance-x-for-which-the-thermal-power-generated-in-it-is-independent-of-small-variation-o

slug:
consider-the-circuit-shown-in-the-figure-the-value-of-the-resistance-x-for-which-the-thermal-power-generated-in-it-is-independent-of-small-variation-o-54252

question:
<div class="question">Consider the circuit shown in the figure.
<br/>The value of the resistance $X$ for which the thermal power generated in it is independent of small variation of its resistance is
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_phy_q16.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$X=R$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$X=\frac{R}{3}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$X=\frac{R}{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$X=2 R$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$X=\frac{R}{2}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_phy_a16.png"/> <br/> <br/>For above circuit
<br/>$$
<br/>\begin{array}{l}
<br/>\frac{1}{R^{\prime}}=\frac{1}{R}+\frac{1}{X}=\frac{R+X}{R X} \\
<br/>R^{\prime}=\frac{R X}{R+X}
<br/>\end{array}
<br/>$$
<br/>The current in the circuit $i=\frac{E}{R+R^{\prime}}=\frac{E}{\left(R+\frac{R X}{R+X}\right)}$
<br/>$V_{k=}=\frac{E \cdot \frac{R X}{R+X}}{\left(R+\frac{R X}{R+X}\right)}=\frac{E X}{R+2 X}$
<br/>Power dissipated in the circuit
<br/>$\begin{aligned} P_{x} &amp;=\frac{V_{B X}^{2}}{X}=\frac{E^{2} \cdot X^{2}}{X(R+2 X)^{2}} \\ &amp;=\frac{E^{2} X}{(R+2 X)^{2}} \\ \frac{d P_{X}}{d X} &amp;=E^{2} \frac{(R-2 X)}{(R+2 X)^{3}} \\ d P_{X} &amp;=\frac{E^{2}(R-2 X)}{(R+2 X)^{3}} \cdot d X \end{aligned}$
<br/>$\left(d P_{x}\right)$ will be zero for all $(d X)$ if $X=\frac{R}{2} \quad\left[d P_{x}=\frac{E^{2}\left(R-2 \times \frac{R}{2}\right)}{\left(R+2 \times \frac{R}{2}\right)^{3}}\right]$
<br/>$$
<br/>=0</div>


tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch1_P2.db
title:
consider-the-circuit-shown-in-the-figure-where-all-the-resistances-are-of-magnitude-1-k-if-the-current-in-the-extreme-right-resistance-x-is-1-ma-the-p

slug:
consider-the-circuit-shown-in-the-figure-where-all-the-resistances-are-of-magnitude-1-k-if-the-current-in-the-extreme-right-resistance-x-is-1-ma-the-p-54246

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_phy_q17.png"/>Consider the circuit shown in the figure where all the resistances are of magnitude $1 \mathrm{k} \Omega$. If the current in the extreme right resistance $X$ is $1 \mathrm{mA},$ the potential difference between $A$ and $B$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$34 \mathrm{V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$21 \mathrm{V}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$68 \mathrm{V}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$55 \mathrm{V}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$34 \mathrm{V}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_phy_a17.png"/> <br/> <br/>The potential between points $A$ and $B$ $V_{N}=34$ volt</div>


tags: ['Mathematics', 'Ellipse', 'WBJEE', 'WBJEE 2020']
answer: <div class="solution">Hint: <br/>Property</div>
source_db: db\MarksBatch1_P2.db
title:
consider-the-curve-a-2-x-2-b-2-y-2-1-the-portion-of-the-tangent-at-any-point-of-the-curve-intercepted-between-the-point-of-contact-and-the-directrix-s

slug:
consider-the-curve-a-2-x-2-b-2-y-2-1-the-portion-of-the-tangent-at-any-point-of-the-curve-intercepted-between-the-point-of-contact-and-the-directrix-s-98511

question:
<div class="question">Consider the curve $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$. The portion of the tangent at any point of the curve intercepted between the point of contact and the directrix subtends at the corresponding focus an angle of</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\pi}{4}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\pi}{3}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{\pi}{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\pi}{6}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\pi}{2}$</span> </div>


title: consider-the-curve-y-be-a-x-where-a-and-b-are-nonzero-real-numbers-then
slug: consider-the-curve-y-be-a-x-where-a-and-b-are-nonzero-real-numbers-then-72969
tags: ['Mathematics', 'Application of Derivatives', 'WBJEE', 'WBJEE 2020']
answer: <div class="solution">Hint: <br/>$y-b=-\frac{b}{a}(x) \Rightarrow \frac{x}{a}+\frac{y}{b}=1$</div>
source_db: db\MarksBatch1_P2.db
question:
<div class="question">Consider the curve $y=$ be $^{-\frac{x}{ \text { a }}}$ where $a$ and $b$ are non-zero real numbers. Then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{x}{a}+\frac{y}{b}=1$ is tangent to the curve at $(0,0)$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{x}{a}+\frac{y}{b}=1$ is tangent to the curve where the curve crosses the axis of $y$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{x}{a}+\frac{Y}{b}=1$ is tangent to the curve at $(a, 0)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{x}{a}+\frac{y}{b}=1$ is tangent to the curve at $(2 a, 0)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{x}{a}+\frac{y}{b}=1$ is tangent to the curve where the curve crosses the axis of $y$</span> </div>


tags: ['Mathematics', 'Straight Lines', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch1_P2.db
title:
consider-the-equation-y-y-1-m-x-x-1-if-m-and-x-1-are-fixed-and-different-lines-are-drawn-for-different-values-of-y-1-then

slug:
consider-the-equation-y-y-1-m-x-x-1-if-m-and-x-1-are-fixed-and-different-lines-are-drawn-for-different-values-of-y-1-then-53718

question:
<div class="question">Consider the equation $y-y_1=m\left(x-x_1\right)$. If $m$ and $x_1$ are fixed and different lines are drawn for different values of $y_1$, then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">the lines will pass through a fixed point</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">there will be a set of parallel lines</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">all lines intersect the line $x=x_1$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">all lines will be parallel to the line $y=x_1$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">there will be a set of parallel lines, all lines intersect the line $x=x_1$</span> </div>

answer:
<div class="solution">$m$ and $x_1$ are fixed and $y_1$ is variable<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/umfn99eiwmUs9zxNM9WlNe3xTM20vIUPn_bju72m7OA.original.fullsize.png"/><br/><br/>Hence, (B) There will be a set of parallel lines<br/>(C) All lines intersect the line $x=x_1$</div>


tags: ['Chemistry', 'Chemical Kinetics', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P2.db
title:
consider-the-following-reaction-for-2-no-2-g-f-2-g-2-no-2-f-g-the-expression-for-the-rate-of-reaction-in-terms-of-the-rate-of-change-of-partial-pressu

slug:
consider-the-following-reaction-for-2-no-2-g-f-2-g-2-no-2-f-g-the-expression-for-the-rate-of-reaction-in-terms-of-the-rate-of-change-of-partial-pressu-54108

question:
<div class="question">Consider the following reaction for $2 \mathrm{NO}_{2}(g)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2} \mathrm{F}(g) . \quad$ The expression for the rate of reaction in terms of the rate of change of partial pressure of reactant and product is/are</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">rate $=-\frac{1}{2}\left[\frac{d p\left(\mathrm{NO}_{2}\right)}{d t}\right]$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">rate $=\frac{1}{2}\left[\frac{d p\left(\mathrm{NO}_{2}\right)}{d t}\right]$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">rate $=-\frac{1}{2}\left[\frac{d p\left(\mathrm{NO}_{2} F\right)}{d t}\right]$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">rate $=\frac{1}{2}\left[\frac{d p\left(\mathrm{NO}_{2} \mathrm{F}\right)}{\mathrm{dt}}\right]$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">rate $=-\frac{1}{2}\left[\frac{d p\left(\mathrm{NO}_{2}\right)}{d t}\right]$, rate $=\frac{1}{2}\left[\frac{d p\left(\mathrm{NO}_{2} \mathrm{F}\right)}{\mathrm{dt}}\right]$</span> </div>

answer:
<div class="solution">$2 \mathrm{NO}_{2}(g)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2} \mathrm{F}(g)$
<br/>$$
<br/>\begin{aligned}
<br/>\text { Rate of reaction } &amp;=-\frac{1}{2}\left[\frac{d p\left(\mathrm{NO}_{2}\right)}{d t}\right] \\
<br/>&amp;=-\left[\frac{d p\left(F_{2}\right)}{d t}\right] \\
<br/>&amp;=+\frac{1}{2}\left[\frac{d p\left(\mathrm{NO}_{2} F\right)}{d t}\right]
<br/>\end{aligned}
<br/>$$</div>


tags: ['Chemistry', 'Practical Chemistry', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch1_P2.db
title:
consider-the-following-salts-nacl-hgcl-2-hg-2-cl-2-cucl-2-cucl-and-agcl-identify-the-correct-set-of-insoluble-salts-in-water

slug:
consider-the-following-salts-nacl-hgcl-2-hg-2-cl-2-cucl-2-cucl-and-agcl-identify-the-correct-set-of-insoluble-salts-in-water-81345

question:
<div class="question">Consider the following salts: $\mathrm{NaCl}, \mathrm{HgCl}_{2}, \mathrm{Hg}_{2} \mathrm{Cl}_{2}, \mathrm{CuCl}_{2}, \mathrm{CuCl}$ and $\mathrm{AgCl}$. Identify the correct set of insoluble salts in water.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{Hg}_{2} \mathrm{Cl}_{2}, \mathrm{CuCl}, \mathrm{AgCl}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{Hg} \mathrm{Cl}_{2}, \mathrm{CuCl}, \mathrm{AgCl}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Hg}_{2} \mathrm{Cl}_{2}, \mathrm{CuCl}_{2}, \mathrm{AgCl}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Hg}_{2} \mathrm{Cl}_{2}, \mathrm{CuCl}, \mathrm{NaCl}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Hg}_{2} \mathrm{Cl}_{2}, \mathrm{CuCl}, \mathrm{AgCl}$</span> </div>

answer:
<div class="solution">Salts such as $\mathrm{NaCl}, \mathrm{HgCl}_{2}, \mathrm{CuCl}_{2}$ are soluble in water while salts such as $\mathrm{Hg}_{2} \mathrm{Cl}_{2}, \mathrm{CuCl}$ and $\mathrm{AgCl}$ are insoluble in water.</div>


tags: ['Chemistry', 'Chemical Kinetics', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch1_P2.db
title:
consider-the-following-two-first-order-reactions-occurring-at-298-k-with-same-initial-concentration-of-a-1-a-b-rate-constant-k-0693-min-1-2-a-c-halfli

slug:
consider-the-following-two-first-order-reactions-occurring-at-298-k-with-same-initial-concentration-of-a-1-a-b-rate-constant-k-0693-min-1-2-a-c-halfli-44138

question:
<div class="question">Consider the following two first order reactions occurring at 298 K with same initial concentration of $A$ :(1) $A \rightarrow B ;$ rate constant, $k=0.693 \mathrm{min}^{-1}$ (2) $A \rightarrow C$; half-life, $l_{1 / 2}=0.693$ min Choose the correct option.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Reaction (1) is faster than reaction (2).</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Reaction (1) is slower than reaction (2).</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Both reactions proceed at the same rate.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Since two different products are formed, rates cannot be compared.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Reaction (1) is slower than reaction (2).</span> </div>

answer:
<div class="solution">Given, for two first order reactions.
<br/>$$
<br/>A \rightarrow B k=0.693 \mathrm{min}^{-1}...(1)
<br/>$$
<br/>and
<br/>$$
<br/>A \rightarrow C, t_{1 / 2}=0.693 \mathrm{min}...(2)
<br/>$$
<br/>For first order reaction
<br/>$$
<br/>t_{1 / 2}=\frac{0.693}{k}
<br/>$$
<br/>Thus, for the reaction $A \rightarrow B$
<br/>$$
<br/>t_{1 / 2}=\frac{0.693}{k}=\frac{0.693}{0.693}=1.0 \mathrm{min}
<br/>$$
<br/>Also, for first order reaction, lower the $t_{1 / 2}$ value, faster is the reaction.
<br/>$$
<br/>t_{1 / 2} \propto \frac{1}{k}
<br/>$$
<br/>and $k$ for $A \rightarrow C$ is $\frac{0.693}{0.693}=1 \mathrm{min}^{-1}$
<br/>Thus, reaction (2) is faster than reaction
<br/>(1) or reaction (1) is slower than reaction (2) Hence, option (b) is the correct answer.</div>


title: consider-the-function-f-x-4-x-3-sin-x-3
slug: consider-the-function-f-x-4-x-3-sin-x-3-35326
question: <div class="question">Consider the function $f(x)=\frac{x^{3}}{4}-\sin \pi x+3$</div>
tags: ['Mathematics', 'Differentiation', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$f(x)$ does not attain value within the interval [-2,2]</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$f(x)$ takes on the value $2 \frac{1}{3}$ in the interval [-2,2]</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$f(x)$ takes on the value $3 \frac{1}{4}$ in the interval [-2,2]</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$f(x)$ takes no value $\rho, 1    &lt; p &lt; 5$ in the interval [-2,2]</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">$f(x)$ takes on the value $2 \frac{1}{3}$ in the interval [-2,2], $f(x)$ takes on the value $3 \frac{1}{4}$ in the interval [-2,2]</span> </div>

answer:
<div class="solution">\(f(-2)=1\) and \(f(2)=5\) and \(f\) is continuous also.
<br/>So intermediate value theorem, function \(f(x)\) takes all values between 1 to 5 .
<br/>\(\Rightarrow \quad 2 \frac{1}{3}\) and \(3 \frac{1}{4}\) lies in 1 to 5 so option \(B, C\) are correct</div>


title: consider-the-function-f-x-cos-x-2-then
slug: consider-the-function-f-x-cos-x-2-then-70023
question: <div class="question">Consider the function $f(x)=\cos x^{2}$. Then,</div>
tags: ['Mathematics', 'Functions', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$f$ is of period $2 \pi$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$f$ is of period $\sqrt{2 \pi}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$f$ is not periodic</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$f$ is of period $\pi$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$f$ is not periodic</span> </div>

answer:
<div class="solution">We have,
<br/>$$
<br/>f(x)=\cos x^{2}
<br/>$$
<br/>Let $T$ be the period of $f(x)$. Then
<br/>$$
<br/>\begin{aligned}
<br/>&amp; &amp; f(x+T) &amp;=f(x) \\
<br/>\Rightarrow &amp; &amp; \cos (x+T)^{2} &amp;=\cos x^{2}
<br/>\end{aligned}
<br/>$$
<br/>But there is no value of $T$ for which
<br/>$$
<br/>\cos (x+T)^{2}=\cos x^{2}
<br/>$$
<br/>$\therefore f(x)$ is not periodic</div>


title: consider-the-function-y-lo-g-a-x-x-2-1-a-0-a-1-the-inverse-of-the-function
slug: consider-the-function-y-lo-g-a-x-x-2-1-a-0-a-1-the-inverse-of-the-function-79077
tags: ['Mathematics', 'Functions', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch1_P2.db
question:
<div class="question">Consider the function $y=\log _{a}\left(x+\sqrt{\left.x^{2}+1\right)}\right.$ $a&gt;0, a \neq 1 .$ The inverse of the function</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">does not exist</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">is $x=\log _{1 / a}\left(y+\sqrt{y^{2}+1}\right)$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">is $x=\sinh (y$ loga)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">is $x=\cosh \left(-y \log \frac{1}{a}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">is $x=\sinh (y$ loga)</span> </div>

answer:
<div class="solution">Given, $y=\log _{a}\left(x+\sqrt{x^{2}+1}\right), a&gt;0, a \neq 1$
<br/>$\Rightarrow \quad a^{y}=\left(x+\sqrt{x^{2}+1}\right)$
<br/>$\Rightarrow \begin{aligned} a^{-y} &amp;=\frac{1}{x+\sqrt{x^{2}+1}} \\ &amp;=\sqrt{x^{2}+1}-x \end{aligned}$
<br/>$\Rightarrow \quad a^{y}-a^{-y}=2 x \Rightarrow x=\frac{a^{y}-a^{-y}}{2}$
<br/>$\Rightarrow \quad f^{-1}(y)=\frac{e^{y \log a}-e^{-y \log a}}{2}$
<br/>$\Rightarrow f^{-1}(y)=\sinh (y \log a)$$\quad\left(\because \frac{e^{x}-e^{-x}}{2}=\sinh (x)\right)$</div>


title: consider-the-functions-f-1-x-x-f-2-x-2-lo-g-e-x-x-0-the-graphs-of-the-functions-intersect
slug: consider-the-functions-f-1-x-x-f-2-x-2-lo-g-e-x-x-0-the-graphs-of-the-functions-intersect-27574
tags: ['Mathematics', 'Functions', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch1_P2.db
question:
<div class="question">Consider the functions $f_{1}(x)=x, f_{2}(x)=2+\log _{e} x, x&gt;0$. The graphs of the functions intersect.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">once in $(0,1)$ but never in $(1, \infty)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">once in $(0,1)$ and once in $\left(e^{2}, \infty\right)$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">once in $(0,1)$ and once in $\left(e, e^{2}\right)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">more than twice in $(0, \infty)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">once in $(0,1)$ and once in $\left(e, e^{2}\right)$</span> </div>

answer:
<div class="solution">$\mathrm{f}_{1}(\mathrm{x})=\mathrm{x}, \mathrm{f}_{2}(\mathrm{x})=2+\log _{\mathrm{e}} \mathrm{x}$
<br/>Let $g(x)=f_{2}(x)-f_{1}(x)=2+\log _{e} x-x$
<br/>$g\left(o^{+}\right)     &lt; 0, g(1)&gt;0, g(e)&gt;0, g\left(e^{2}\right) &lt; 0$
<br/>and value of $g(x)$ for all $x \geq e^{2}$ is negative.
<br/>$\therefore \mathrm{g}(\mathrm{x})=0$ has two roots in $(0,1)$ and $\left(\mathrm{e}, \mathrm{e}^{2}\right)$</div>


tags: ['Physics', 'Thermodynamics', 'WBJEE', 'WBJEE 2019']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$T$</span> </div>
source_db: db\MarksBatch1_P2.db
title:
consider-the-given-diagram-an-ideal-gas-is-contained-in-a-chamber-left-of-volume-v-and-is-at-an-absolute-temperature-t-it-is-allowed-to-rush-freely-in

slug:
consider-the-given-diagram-an-ideal-gas-is-contained-in-a-chamber-left-of-volume-v-and-is-at-an-absolute-temperature-t-it-is-allowed-to-rush-freely-in-12866

question:
<div class="question">Consider the given diagram. An ideal gas is contained in a chamber (left) of volume $V$ and is at an absolute temperature $T$. It is allowed to rush freely into the right chamber of volume $V$ which is initially vacuum. The whole system is thermally isolated. What will be the final temperature of the equilibrium has been attained? <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2019_phy_q17.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$T$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{T}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2 T$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{T}{4}$</span> </li> </ul>

answer:
<div class="solution">Since, the whole system is isolated, this means, there is no transfer of heat between the system and the surrounding. Also, the right side container is initially vacuum, so the gas could easily rush there without any resistive force. As the right side container has no temperature. Thus, the temperature of the ideal gas would remain same even if it enters right side chamber. Therefore, final temperature attained at the equilibrium will be $T$</div>


tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2023']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: db\MarksBatch1_P2.db
title:
consider-the-logic-circuit-with-inputs-a-b-c-and-output-y-how-many-combinations-of-a-b-and-c-gives-the-output-y0

slug:
consider-the-logic-circuit-with-inputs-a-b-c-and-output-y-how-many-combinations-of-a-b-and-c-gives-the-output-y0-93917

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/P98_pvLXBGW5YTtJb3FHhWCrz8arBGxd31I-aRfz4bk.original.fullsize.png"/><br/><br/>Consider the logic circuit with inputs A, B, C and output \(Y\). How many combinations of \(A, B\) and \(C\) gives the output \(Y=0\) ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">8</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">5</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">7</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1</span> </li> </ul>

answer:
<div class="solution">Hint : <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/j0kr2K4m6y6bcMJT9Bcizq8EqTsVhLhTP8KVplDTnNM.original.fullsize.png"/><br/><br/>\(\begin{aligned}<br/>&amp; \overline{(A+\overline{B})+\overline{C}}=\overline{A+\overline{B}} \cdot C=(\overline{A} \cdot B \cdot C) \\<br/>&amp; \therefore y=1 \\<br/>&amp; \text { if } A=0, B=1, C=1<br/>\end{aligned}\)<br/>For rest of all cases \(Y=O\)<br/>Total cases \(=8\)<br/>\(\therefore\) Ans \((8-1)=7\)</div>


tags: ['Mathematics', 'Differentiation', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch1_P2.db
title:
consider-the-nonconstant-differentiable-function-f-of-one-variable-which-obeys-the-relation-f-y-f-x-f-x-y-if-f-0-p-and-f-5-q-then-f-5-is

slug:
consider-the-nonconstant-differentiable-function-f-of-one-variable-which-obeys-the-relation-f-y-f-x-f-x-y-if-f-0-p-and-f-5-q-then-f-5-is-26263

question:
<div class="question">Consider the non-constant differentiable function $f$ of one variable which obeys the relation $\frac{f(x)}{f(y)}=f(x-y) .$ If $f^{\prime}(0)=p$ and $f^{\prime}(5)=q,$ then $f^{\prime}(-5)$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{p^{2}}{q}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{q}{p}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{p}{q}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$q$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{p^{2}}{q}$</span> </div>

answer:
<div class="solution">We have, $\frac{f(x)}{f(y)}=f(x-y)$
<br/>$\Rightarrow \quad f(x)=a^{k x}$
<br/>$\therefore \quad f^{\prime}(x)=k a^{b x} \log a$
<br/>$\begin{array}{lr}\text { Again, } &amp; f^{\prime}(0)=P \\ \Rightarrow &amp; k a^{\circ} \log a=P \\ \Rightarrow &amp; k \log a=P\end{array}$
<br/>Also, $\quad f^{\prime}(5)=q$
<br/>$\Rightarrow \quad k a^{5 k} \log a=q$
<br/>$a^{5 k} p=q$
<br/>$a^{5 k}=\frac{q}{P}$
<br/>Now,  $\begin{aligned} f^{\prime}(-5) &amp;=k a^{-4} \log a \\ &amp;=\frac{k \log a}{a^{\Delta}} \end{aligned}$ $=\frac{P}{\left(\frac{q}{p}\right)}=\frac{p^{2}}{q}$</div>


tags: ['Mathematics', 'Parabola', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch1_P2.db
title:
consider-the-parabola-y-2-4-x-let-p-and-q-be-points-on-the-parabola-where-p-4-4-and-q-9-6-let-r-be-a-point-on-the-arc-of-the-parabola-between-p-and-q-

slug:
consider-the-parabola-y-2-4-x-let-p-and-q-be-points-on-the-parabola-where-p-4-4-and-q-9-6-let-r-be-a-point-on-the-arc-of-the-parabola-between-p-and-q-89262

question:
<div class="question">Consider the parabola $y^{2}=4 x$. Let $P$ and $Q$ be points on the parabola where $P(4,-4)$ and $Q (9,6)$. Let $R$ be a point on the arc of the parabola between $P$ and $Q$. Then, the area of $\Delta P Q R$ is largest when</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\angle P Q A=90^{\circ}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$R(4,4)$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$R\left(\frac{1}{4}, 1\right)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$R\left(1, \frac{1}{4}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$R\left(\frac{1}{4}, 1\right)$</span> </div>

answer:
<div class="solution">Let $\quad f(x)=x \log x+x-3$
<br/>$\Rightarrow \quad f^{\prime}(x)=x \cdot \frac{1}{x}+\log x+1$
<br/>$\Rightarrow \quad f^{\prime}(x)=\log x+2&gt;0$
<br/>$\Rightarrow f(1)=-2$ and $f(3)=3 \log 3, f(1) \cdot f(3    &lt; 0)$
<br/>Hence, exactly one root in $x \in(1,3)$ as $f(x)&gt;0$
<br/> <br/>Equation of $P Q$ is $2 x-y=12$
<br/>Perpendicular distance $A R=\left|\frac{2 t^{2}-2 t-12}{\sqrt{5}}\right|=\frac{2}{\sqrt{5}}(t-3 \cdot(t+4)$
<br/>$A R$ is Maximum, at $t=\frac{1}{2}$ 
<br/>$\therefore R$ is $\left(\frac{1}{4}, 1\right)$<img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_mat_a65.png"/></div>


tags: ['Physics', 'Thermodynamics', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch1_P2.db
title:
consider-the-pv-diagram-for-1-mole-of-an-ideal-monatomic-gas-shown-in-the-figure-which-of-the-following-statements-isare-true

slug:
consider-the-pv-diagram-for-1-mole-of-an-ideal-monatomic-gas-shown-in-the-figure-which-of-the-following-statements-isare-true-69828

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/StrmVT7euG6mSTtCqw-v-KxkxhczOKUuDqK_2RSp4FI.original.fullsize.png"/><br/> <br/>Consider the P-V diagram for 1 mole of an ideal monatomic gas shown in the figure. Which of the following statements is/are true?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">The change in internal energy for the whole process is zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Heat is rejected during the process</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Change in internal energy for process $A \rightarrow B$ is $-\frac{3}{2} P_{0} V_{0}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Work done by the gas during the entire process is $2 \mathrm{P}_{0} \mathrm{~V}_{0}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">The change in internal energy for the whole process is zero, Heat is rejected during the process, Change in internal energy for process $A \rightarrow B$ is $-\frac{3}{2} P_{0} V_{0}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/dxq-iwmwjc4JCSD0b1DV5BZ9rwsD3qsaeQuIR3H4vfo.original.fullsize.png"/><br/> <br/>$$
<br/>\begin{array}{l}
<br/>\Delta \mathrm{U}=\mathrm{n} \mathrm{Cv} \Delta \mathrm{T} \\
<br/>\Delta \mathrm{T}=\frac{\mathrm{P}_{\mathrm{c}} \mathrm{V}_{\mathrm{c}}}{\mathrm{nR}}-\frac{\mathrm{P}_{\mathrm{A}} \mathrm{V}_{\mathrm{A}}}{\mathrm{nR}}=0
<br/>\end{array}
<br/>$$
<br/>Hence $\Delta \mathrm{U}=0$ (option $\mathrm{A}$ is correct)
<br/>$$
<br/>\begin{array}{l}
<br/>\Delta \mathrm{Q}=\Delta \mathrm{U}+\text { work } \\
<br/>\Delta \mathrm{U}=0, \text { work }=(-)
<br/>\end{array}
<br/>$$
<br/>$\Rightarrow \Delta Q=(-)$; Hence heat is rejected during the process (option B is correct) for process $A B$
<br/>$\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{v}}\left(\frac{\mathrm{P}_{\mathrm{C}} \mathrm{V}_{\mathrm{B}}}{\mathrm{nR}}-\frac{\mathrm{P}_{\mathrm{A}} \mathrm{V}_{\mathrm{A}}}{\mathrm{nR}}\right)=\frac{3 \mathrm{R}}{2}\left(\frac{\mathrm{P}_{0} \mathrm{~V}_{0}}{\mathrm{R}}-\frac{\mathrm{P}_{0} 2 \mathrm{~V}_{0}}{\mathrm{R}}\right)=-\frac{3}{2} \mathrm{P}_{0} \mathrm{~V}_{0}$ (option $\mathrm{C}$ is correct)
<br/>during entire process work done by gas is $-P_{0} V_{0} \quad$ (option $D$ is correct)</div>


title: consider-the-radioactive-disintegration-82-a-210-b-c-82-d-206-the-sequence-of-emission-can-be
slug: consider-the-radioactive-disintegration-82-a-210-b-c-82-d-206-the-sequence-of-emission-can-be-89113
tags: ['Chemistry', 'Chemical Kinetics', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch1_P2.db
question:
<div class="question">Consider, the radioactive disintegration ${ }_{82} A^{210} \rightarrow B \rightarrow C \rightarrow{ }_{82} D^{206}$, The sequence of emission can be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\beta, \beta, \beta$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\alpha, \alpha, \beta$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\beta, \beta, \gamma$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\beta, \beta, \alpha$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\beta, \beta, \alpha$</span> </div>

answer:
<div class="solution">Given, $82^{A^{210}} \longrightarrow B \longrightarrow C \longrightarrow{ }_{82} D^{206}$
<br/>i.e. difference in mass no. between $A$ and $D$ is of 4 units i.e., mass no. is decreased by 4 units while atomic no. remains the same, i.e. 82 for $A$ and $D$.
<br/>Also,
<br/>(i) On emission of each $\beta$ -particle, mass no. remains the same but atomic no. is increased by one unit.
<br/>(ii) On emission of each $\alpha$ -particle, mass no. is decreased by 4 units, while atomic no. is decreased by 2 units.
<br/>Thus, on emission of $2-\beta$ and $1-\alpha$ particle, we get $_{82} D^{206}$
<br/>i.e. ${ }_{82} A^{210} \stackrel{-\beta}{\longrightarrow}{ }_{83} A^{210} \stackrel{-\beta}{\longrightarrow}{ }_{84} A^{210} \stackrel{-a}{\longrightarrow}{ }_{82} A^{206}$
<br/>Thus, option (d) is the correct answer.</div>


tags: ['Mathematics', 'Sequences and Series', 'WBJEE', 'WBJEE 2021']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$5.15$</span> </div>
source_db: db\MarksBatch1_P2.db
title:
consider-the-real-valued-function-h-0-1-2-100-r-such-that-h-0-5-h-100-20-and-satisfying-h-p-2-1-h-p-1-h-p-1-for-every-p-1-2-99-then-the-value-of-h-1-i

slug:
consider-the-real-valued-function-h-0-1-2-100-r-such-that-h-0-5-h-100-20-and-satisfying-h-p-2-1-h-p-1-h-p-1-for-every-p-1-2-99-then-the-value-of-h-1-i-28298

question:
<div class="question">Consider the real valued function $\mathrm{h}:\{0,1,2 \ldots \ldots 100\} \rightarrow \mathrm{R}$ such that $\mathrm{h}(0)=5, \mathrm{~h}(100)=20$ and satisfying $h(p)=\frac{1}{2}\{h(p+1)+h(p-1)\}$ for every $p=1,2 \ldots .99 .$ Then the value of $h(1)$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$5.15$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$5.5$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">6</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$6.15$</span> </li> </ul>

answer:
<div class="solution">$h(p)=\frac{1}{2}(h(p+1)+h(p-1)) \Rightarrow h(p-1), h(p), h(p+1)$ are in A.P.
<br/>$h(100)=h(0)+99 d$
<br/>$\Rightarrow \frac{20-5}{99}=d \Rightarrow d=\frac{15}{99} \Rightarrow h(1)=h(0)+d=5+\frac{15}{99}=5.15$</div>


tags: ['Mathematics', 'Linear Programming', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P2.db
title:
consider-the-system-of-equations-beginarraycc-xyz-0-alpha-xbeta-ygamma-z-0-alpha2-xbeta2-ygamma2-z-0-endarray-then-the-system-of-equations-has

slug:
consider-the-system-of-equations-beginarraycc-xyz-0-alpha-xbeta-ygamma-z-0-alpha2-xbeta2-ygamma2-z-0-endarray-then-the-system-of-equations-has-25126

question:
<div class="question">Consider the system of equations
<br/>\(\begin{array}{cc}
<br/>x+y+z &amp; =0 \\
<br/>\alpha x+\beta y+\gamma z &amp; =0 \\
<br/>\alpha^{2} x+\beta^{2} y+\gamma^{2} z &amp; =0
<br/>\end{array}\)
<br/>Then the system of equations has</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">a unique solution for all values of $\alpha, \beta$ and $\gamma$.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">infinite number of solutions, if any two of $\alpha, \bar{\beta},$ yare equal.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">a unique solution, if $\alpha, \beta$ and $\gamma$ are distinct.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">more than one, but finite number of solutions depending on values of $\alpha, \beta$ and $\gamma$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">infinite number of solutions, if any two of $\alpha, \bar{\beta},$ yare equal., a unique solution, if $\alpha, \beta$ and $\gamma$ are distinct.</span> </div>

answer:
<div class="solution">Given system of equations is $x+y+z=0$<br/>$\begin{array}{l}<br/>\alpha x+\beta y+\gamma z=0 \\<br/>\alpha^{2} x+\beta^{2} y+\gamma^{2} z=0<br/>\end{array}$<br/>The coefficient matrix, $A=\left[\begin{array}{ccc}1 &amp; 1 &amp; 1 \\ \alpha &amp; \beta &amp; \gamma \\ \alpha^{2} &amp; \beta^{2} &amp; \gamma^{2}\end{array}\right]$<br/>Now, $|A|=\left|\begin{array}{ccc}1 &amp; 1 &amp; 1 \\ \alpha &amp; \beta &amp; \gamma \\ \alpha^{2} &amp; \beta^{2} &amp; \gamma^{2}\end{array}\right|=(\alpha-\beta)(\beta-\gamma)(\gamma-\alpha)$<br/>(i) The system of equations has a unique solution, if $\alpha, \beta$ and $\gamma$ are distinct<br/>i.e. $|A| \neq 0$<br/>(ii) The system of equations has infinite number of solutions, if any two of $\alpha, \beta$ and $\gamma$ ar equal.<br/>i.e. $|A|=0$</div>


title: consider-the-vectors-a-i-j-k-b-2-i-j-k-c-5-1-i-2-j-2-k-what-is-the-value-of-c-a-b
slug: consider-the-vectors-a-i-j-k-b-2-i-j-k-c-5-1-i-2-j-2-k-what-is-the-value-of-c-a-b-79803
tags: ['Physics', 'Mathematics in Physics', 'WBJEE', 'WBJEE 2020']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: db\MarksBatch1_P2.db
question:
<div class="question">Consider the vectors
<br/>$\overrightarrow{\mathrm{A}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}, \overrightarrow{\mathrm{B}}=2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overrightarrow{\mathrm{C}}=\frac{1}{\sqrt{5}}(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})$. What is the value of $\overrightarrow{\mathrm{C}} .(\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}) ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">0</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3 \sqrt{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$18 \sqrt{5}$</span> </li> </ul>

answer:
<div class="solution">Hint: 
<br/>$\overrightarrow{\mathrm{C}}(\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}})=\left|\begin{array}{ccc}1 &amp; 1 &amp; -1 \\ 2 &amp; -1 &amp; 1 \\ 1 &amp; -2 &amp; 2\end{array}\right|=1(-2+2)-1(4-1)-1(-4+1)=-3+3=0$</div>


tags: ['Physics', 'Mathematics in Physics', 'WBJEE', 'WBJEE 2014']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$1: 1$</span> </div>
source_db: db\MarksBatch1_P2.db
title:
consider-three-vectors-a-i-j-2-k-b-i-j-k-and-c-2-i-3-j-4-k-a-vector-x-of-the-form-a-b-and-are-numbers-is-perpendicular-to-c-the-ratio-of-and-is

slug:
consider-three-vectors-a-i-j-2-k-b-i-j-k-and-c-2-i-3-j-4-k-a-vector-x-of-the-form-a-b-and-are-numbers-is-perpendicular-to-c-the-ratio-of-and-is-86830

question:
<div class="question">Consider three vectors $A=i+j-2 k,\mathbf{B}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}} \text { and } \mathbf{C}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}} . \text { A vector } \mathbf{X} \text { of }$ the form $\alpha A+\beta B(\alpha$ and $\beta$ are numbers) is perpendicular to C. The ratio of $\alpha$ and $\beta$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$1: 1$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2: 1$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$-1: 1$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3: 1$</span> </li> </ul>

answer:
<div class="solution">Vector $\mathrm{X}$ of the form $\alpha \mathrm{A}+\beta \mathrm{B}$<br/>$\begin{aligned}<br/>\mathrm{X} &amp;=\alpha \mathrm{A}+\beta \mathrm{B} \\<br/>&amp;=\alpha(\hat{i}+\hat{j}-2 \hat{k})+\beta(\hat{i}-\hat{j}+\hat{k}) \\<br/>X &amp;=\hat{i}(\alpha+\beta)+\hat{j}(\alpha-\beta)+\hat{k}(-2 \alpha+\beta)<br/>\end{aligned}$<br/>A vector $\mathrm{X}$ is perpendicular to $\mathrm{C},$ i.e., $\mathrm{X} \cdot \mathrm{C}=0$<br/>$\text {or } -9 \alpha+9 \beta=0 \text { or } \alpha=\beta$<br/>or $\frac{\alpha}{\beta}=\frac{1}{1} \text { or } \alpha: \beta=1: 1$</div>


tags: ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch1_P2.db
title:
consider-two-concentric-conducting-sphere-of-radii-r-and-2-r-respectively-the-inner-sphere-is-given-a-charge-q-the-other-sphere-is-grounded-the-potent

slug:
consider-two-concentric-conducting-sphere-of-radii-r-and-2-r-respectively-the-inner-sphere-is-given-a-charge-q-the-other-sphere-is-grounded-the-potent-84612

question:
<div class="question">Consider two concentric conducting sphere of radii $\mathrm{R}$ and $2 \mathrm{R}$ respectively. The inner sphere is given a charge $+\mathrm{Q}$. The other sphere is grounded. The potential at $r=\frac{3 R}{2}$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{1}{4 \pi \varepsilon_0} \frac{Q}{6 R}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{4 \pi \varepsilon_0} \frac{2 Q}{3 R}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{4 \pi \varepsilon_0} \frac{Q}{R}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{4 \pi \varepsilon_0} \frac{Q}{6 R}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/vyuoWtBnYCIJzHAmRj29IWgv6iMA-StAXsXMLsXC6aU.original.fullsize.png"/><br/><br/>$q \rightarrow$ Charge appearing on shell of radius $2 R$ after earthing<br/>Calculating $\mathrm{q} \quad \mathrm{V}_{\text {outer shell }}=\frac{\mathrm{KQ}}{2 \mathrm{R}}+\frac{\mathrm{Kq}}{2 \mathrm{R}}=0 \quad \mathrm{q}=-\mathrm{Q}$<br/>Calculating potential at $r=\frac{3 R}{2}$<br/>$$<br/>V_{\text {inner shell }}+V_{\text {outer shell }}=\frac{K Q}{r}+\frac{K q}{2 R}=\frac{K Q}{\frac{3 R}{2}}+\frac{K(-Q)}{2 R}=\frac{K Q}{6 R}=\frac{1}{4 \pi \varepsilon_0} \frac{Q}{6 R}<br/>$$</div>


tags: ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P2.db
title:
consider-two-concentric-spherical-metal-shells-of-radii-r-1-and-r-2-r-2-r-1-if-the-outer-shell-has-a-charge-q-and-the-inner-one-is-grounded-the-charge

slug:
consider-two-concentric-spherical-metal-shells-of-radii-r-1-and-r-2-r-2-r-1-if-the-outer-shell-has-a-charge-q-and-the-inner-one-is-grounded-the-charge-75938

question:
<div class="question">Consider two concentric spherical metal shells of radii $r_{1}$ and $r_{2}\left(r_{2}&gt;r_{1}\right)$. If the outer shell has a charge $q$ and the inner one is grounded, the charge on the inner shell is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{-r_{2}}{5}, q$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">zero</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{-r_{1}}{r_{2}} q$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-q$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{-r_{1}}{r_{2}} q$</span> </div>

answer:
<div class="solution">Let, the charge on the inner shell be $q^{\prime}$
<br/>The total charge will be zero
<br/>So, $\frac{k q^{\prime}}{r_{1}}+\frac{k q}{r_{2}}=0$
<br/>$\left(\because r_{2}&gt;r_{1}\right)$
<br/>$\Rightarrow \quad q^{\prime}=-\frac{K q / r_{2}}{K / r_{1}}$
<br/>$$
<br/>q^{\prime}=-\left(\frac{r_{1}}{r_{2}}\right) q
<br/>$$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Main']
source_db: db\MarksBatch1_P2.db
title:
consider-two-infinitely-long-wires-parallel-to-zaxis-carrying-same-current-i-in-the-positive-z-direction-one-wire-passes-through-the-point-l-at-coordi-1

slug:
consider-two-infinitely-long-wires-parallel-to-zaxis-carrying-same-current-i-in-the-positive-z-direction-one-wire-passes-through-the-point-l-at-coordi-1-94909

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/WAl-_stvMmyiHqnqZd-dCxkmki24xIe6CmlpvuM-2tg.original.fullsize.png"/><br/> <br/>Consider two infinitely long wires parallel to Z-axis carrying same current I in the positive Z direction. One wire passes through the point $L$ at coordinates $(-1,+1)$ and the other wire passes through the point $M$ at coordinates $(-1,-1)$. The resultant magnetic field at the origin $\mathrm{O}$ will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\mu_{0} I}{2 \sqrt{2 \pi}} \hat{\mathrm{j}}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{\mu_{0} I}{2 \pi} \hat{j}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mu_{0} \mathrm{I}}{2 \sqrt{2 \pi}} \hat{\mathrm{i}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\mu_{0} I}{4 \pi} \hat{j}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mu_{0} I}{2 \pi} \hat{j}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/00E2DlNgy2exKHR3CUGmQwPZTnoG3droyl7LPV2Tph4.original.fullsize.png"/><br/> <br/>$\mathrm{B}_{\text {net }}=\sqrt{2} \mathrm{~B}$ where $\mathrm{B}=\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{r}}$
<br/>$\mathrm{B}_{\text {net }}=\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{r}} \sqrt{2} \hat{\mathrm{j}}$
<br/>$=\frac{\mu_{0} \mathrm{I}}{2 \pi \sqrt{2}} \times \sqrt{2} \hat{\mathrm{j}}$ and $\mathrm{r}=\sqrt{2}$
<br/>$\mathrm{B}_{\text {net }}=\frac{\mu_{0} \mathrm{I}}{2 \pi} \hat{\mathrm{j}}$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch1_P2.db
title:
consider-two-infinitely-long-wires-parallel-to-zaxis-carrying-same-current-i-in-the-positive-z-direction-one-wire-passes-through-the-point-l-at-coordi

slug:
consider-two-infinitely-long-wires-parallel-to-zaxis-carrying-same-current-i-in-the-positive-z-direction-one-wire-passes-through-the-point-l-at-coordi-67701

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/WAl-_stvMmyiHqnqZd-dCxkmki24xIe6CmlpvuM-2tg.original.fullsize.png"/><br/> <br/>Consider two infinitely long wires parallel to Z-axis carrying same current I in the positive Z direction. One wire passes through the point $L$ at coordinates $(-1,+1)$ and the other wire passes through the point $M$ at coordinates $(-1,-1)$. The resultant magnetic field at the origin $\mathrm{O}$ will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\mu_{0} I}{2 \sqrt{2 \pi}} \hat{\mathrm{j}}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{\mu_{0} I}{2 \pi} \hat{j}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mu_{0} \mathrm{I}}{2 \sqrt{2 \pi}} \hat{\mathrm{i}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\mu_{0} I}{4 \pi} \hat{j}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mu_{0} I}{2 \pi} \hat{j}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/00E2DlNgy2exKHR3CUGmQwPZTnoG3droyl7LPV2Tph4.original.fullsize.png"/><br/> <br/>$\mathrm{B}_{\text {net }}=\sqrt{2} \mathrm{~B}$ where $\mathrm{B}=\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{r}}$
<br/>$\mathrm{B}_{\text {net }}=\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{r}} \sqrt{2} \hat{\mathrm{j}}$
<br/>$=\frac{\mu_{0} \mathrm{I}}{2 \pi \sqrt{2}} \times \sqrt{2} \hat{\mathrm{j}}$ and $\mathrm{r}=\sqrt{2}$
<br/>$\mathrm{B}_{\text {net }}=\frac{\mu_{0} \mathrm{I}}{2 \pi} \hat{\mathrm{j}}$</div>


tags: ['Physics', 'Dual Nature of Matter', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch1_P2.db
title:
consider-two-particles-of-different-masses-in-which-of-the-following-situations-the-heavier-of-the-two-particles-will-have-smaller-debroglie-wavelengt

slug:
consider-two-particles-of-different-masses-in-which-of-the-following-situations-the-heavier-of-the-two-particles-will-have-smaller-debroglie-wavelengt-41515

question:
<div class="question">Consider two particles of different masses, In which of the following situations the heavier of the two particles will have smaller de-Broglie wavelength?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Both have a free fall through the same height</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Both move with the same kinetic energy</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Both move with the same linear momentum</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Both move with the same speed</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">Both have a free fall through the same height, Both move with the same kinetic energy, Both move with the same speed</span> </div>

answer:
<div class="solution">The de-Broglie equation is
<br/>$$
<br/>\begin{aligned}
<br/>\lambda &amp;=\frac{h}{m v}=\frac{h}{\sqrt{2 m k}} \Rightarrow m=\frac{h}{\lambda v} \\
<br/>\Rightarrow \quad m \propto \frac{1}{\lambda}, \text { if } \frac{h}{v} &amp;=\mathrm{constant}
<br/>\end{aligned}
<br/>$$
<br/>Again, $\frac{h}{v}$ will be constant only when $v$ is constant
<br/>Thus, in present case the de-Broglie wavelength of heavier particle will be smaller. When the velocities of two particles will be same or both move with same kinetic energy(K).</div>


tags: ['Chemistry', 'General Organic Chemistry', 'JEE Main']
source_db: db\MarksBatch1_P2.db
title:
correct-pair-of-compounds-which-gives-blue-colourationprecipitate-and-white-precipitate-respectively-when-their-lassaignes-test-is-separately-done-is-1

slug:
correct-pair-of-compounds-which-gives-blue-colourationprecipitate-and-white-precipitate-respectively-when-their-lassaignes-test-is-separately-done-is-1-86278

question:
<div class="question">Correct pair of compounds which gives blue colouration/precipitate and white precipitate, respectively, when their Lassaigne's test is separately done is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">NH- $\mathrm{NH}_{2}$, HCl and CICH, COOH</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{NH}_{2} \mathrm{CSNH}_{2}$ and $\mathrm{PhCH}_{2} \mathrm{Cl}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{NH}_{2} \mathrm{NH}_{2}, \mathrm{COOH}$ and $\mathrm{NH}_{2} \mathrm{CONH}_{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q13_optd.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q13_optd.png"/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_a13.png"/> <br/> <br/>$\begin{array}{ll}\text {Hydrozine, } &amp; \mathrm{NH}_{2} \cdot \mathrm{NH}_{2} \text { does not respond }\end{array}$
<br/>Lassaigne's test because it does not contain any carbon and hence, NaCN is not formed. Compound, $\mathrm{NH}_{2}-\mathrm{CS}-\mathrm{NH}_{2}$ contains both $\mathrm{N}$ and $\mathrm{S}$, hence, it will give red colour in Lassaigne test.</div>


tags: ['Chemistry', 'General Organic Chemistry', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P2.db
title:
correct-pair-of-compounds-which-gives-blue-colourationprecipitate-and-white-precipitate-respectively-when-their-lassaignes-test-is-separately-done-is

slug:
correct-pair-of-compounds-which-gives-blue-colourationprecipitate-and-white-precipitate-respectively-when-their-lassaignes-test-is-separately-done-is-72132

question:
<div class="question">Correct pair of compounds which gives blue colouration/precipitate and white precipitate, respectively, when their Lassaigne's test is separately done is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">NH- $\mathrm{NH}_{2}$, HCl and CICH, COOH</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{NH}_{2} \mathrm{CSNH}_{2}$ and $\mathrm{PhCH}_{2} \mathrm{Cl}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{NH}_{2} \mathrm{NH}_{2}, \mathrm{COOH}$ and $\mathrm{NH}_{2} \mathrm{CONH}_{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q13_optd.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q13_optd.png"/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_a13.png"/> <br/> <br/>$\begin{array}{ll}\text {Hydrozine, } &amp; \mathrm{NH}_{2} \cdot \mathrm{NH}_{2} \text { does not respond }\end{array}$
<br/>Lassaigne's test because it does not contain any carbon and hence, NaCN is not formed. Compound, $\mathrm{NH}_{2}-\mathrm{CS}-\mathrm{NH}_{2}$ contains both $\mathrm{N}$ and $\mathrm{S}$, hence, it will give red colour in Lassaigne test.</div>


title: correct-statements-in-cases-of-n-butanol-and-t-butanol-is-are
slug: correct-statements-in-cases-of-n-butanol-and-t-butanol-is-are-17400
question: <div class="question">Correct statement(s) in cases of $n$ -butanol and $t$ -butanol is (are)</div>
tags: ['Chemistry', 'Hydrocarbons', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">both are having equal solubility in water</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$t$ -butanol is more soluble in water than $n$ -butanol</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">boiling point of $t$ -butanol is lower than $n$ -butanol</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">boiling point of $n$ -butanol is lower than $t$ -butanol</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">$t$ -butanol is more soluble in water than $n$ -butanol, boiling point of $t$ -butanol is lower than $n$ -butanol</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_a57.png"/> <br/> <br/>More branching results high solubility and low boiling point.</div>


title: cos-2-x-7-a-2-sin-x-can-have-a-real-solution-for
slug: cos-2-x-7-a-2-sin-x-can-have-a-real-solution-for-55183
question: <div class="question">$\cos (2 x+7)=a(2-\sin x)$ can have a real solution for</div>
tags: ['Mathematics', 'Limits', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">all real values of a</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$a \in[2,6]$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{a} \in[-\infty, 2] \backslash\{0\}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{a} \in(0, \infty)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$a \in[2,6]$</span> </div>

answer:
<div class="solution">Step 1. find the solution of given equation:<br/>\(\begin{aligned}<br/>&amp;\cos 2 x+a \sin x=2 a-7 \\<br/>&amp;\Rightarrow 1-2 \sin ^2 x+a \sin x=2 a-7 ;\left[\because \cos 2 x=1-2 \sin ^2 x\right] \\<br/>&amp;\Rightarrow 2 \sin ^2 x-a \sin x+2 a-8=0<br/>\end{aligned}\)<br/>Step 2. Find the roots of above equation:<br/>\(\begin{aligned}<br/>&amp;\Rightarrow \sin x=\frac{a \pm \sqrt{a^2-16(a-4)}}{4} ;\left[\because \boldsymbol{x}=\frac{-\mathbf{b} \pm \sqrt{\mathbf{b}^2-4 \mathbf{a c}}}{2 \mathbf{a}}\right] \\<br/>&amp;=\frac{a \pm(a-8)}{4} \\<br/>&amp;\Rightarrow \sin x=\frac{a-4}{2} \text { or } \sin x=2(\text { not possible }) \\<br/>&amp;\Rightarrow \sin x=\frac{a-4}{2} \\<br/>&amp;\because-1 \leq \sin x \leq 1 \\<br/>&amp;\therefore-1 \leq \frac{a-4}{2} \leq 1 \\<br/>&amp;\Rightarrow 2 \leq a \leq 6 \\<br/>&amp;\Longrightarrow a \in[2,6]<br/>\end{aligned}\)</div>


