# questions

tags: ['Physics', 'Waves and Sound', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch2_P3.db
title:
two-monochromatic-coherent-light-beams-a-and-b-have-intensities-l-and-4-l-respectively-if-these-beams-are-superposed-the-maximum-and-minimum-intensiti

slug:
two-monochromatic-coherent-light-beams-a-and-b-have-intensities-l-and-4-l-respectively-if-these-beams-are-superposed-the-maximum-and-minimum-intensiti-71673

question:
<div class="question">Two monochromatic coherent light beams $A$ and $B$ have intensities $L$ and $\frac{L}{4},$ respectively. If these beams are superposed, the maximum and minimum intensities will be</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{9 L}{4}, \frac{L}{4}$</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">$\frac{5 L}{4}, 0$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{5 L}{2}, 0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 L, \frac{L}{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{9 L}{4}, \frac{L}{4}$</span> </div>

answer:
<div class="solution">For maximum intensity,
<br/>$$
<br/>I_{\max }=I_{1}+I_{2}+2 \sqrt{I_{1} I_{2}} \cos \delta
<br/>$$
<br/>$$
<br/>\begin{aligned}
<br/>\delta &amp;=0 \\
<br/>I_{\max } &amp;=L+\frac{L}{4}+2 \sqrt{L \times \frac{L}{4}} \cdot \cos 0 \\
<br/>&amp;=\frac{5 L}{4}+\frac{2 L}{2} \\
<br/>&amp;=\frac{5 L+4 L}{4} \\
<br/>&amp;=\frac{9 L}{4} \\
<br/>I_{\min } &amp;=I_{1}+I_{2}-2 \sqrt{I_{1} I_{2}} \cos \theta \\
<br/>\theta &amp;=0^{\circ} \\
<br/>&amp;=L+\frac{L}{4}-2 \sqrt{L \times \frac{L}{4}} \times 1 \\
<br/>&amp;=\frac{5 L}{4}-L=\frac{L}{4}
<br/>\end{aligned}
<br/>$$
<br/>Thus, maximum and minimum intensities will be $\left(\frac{9 L}{4}, \frac{L}{4}\right)$</div>


tags: ['Physics', 'Rotational Motion', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch2_P3.db
title:
two-particles-a-and-b-are-moving-as-shown-in-the-figure-their-total-angular-momentum-about-the-point-o-is-1

slug:
two-particles-a-and-b-are-moving-as-shown-in-the-figure-their-total-angular-momentum-about-the-point-o-is-1-26811

question:
<div class="question">"Two particles $A$ and $B$ are moving as shown. in the figure.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_q17.png"/> <br/>Their total angular momentum about the point $O$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$9.8 \mathrm{kg} \mathrm{m}^{2} / \mathrm{s}$</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">zero</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$52.7 \mathrm{kg} \mathrm{m}^{2} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$37.9 \mathrm{kg} \mathrm{m}^{2} / \mathrm{s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$9.8 \mathrm{kg} \mathrm{m}^{2} / \mathrm{s}$</span> </div>

answer:
<div class="solution">Total angular momentum about $O$ is given as,
<br/>$$
<br/>\begin{aligned}
<br/>\mathbf{L} &amp;=\mathbf{L}_{1}+\mathbf{L}_{2}=m_{1} V_{1} I_{1}+m_{2} V_{2} I_{2} \\
<br/>&amp;=-6.5 \times 2.2 \times 1.5+3.1 \times 3.6 \times 2.8 \\
<br/>&amp;=-21.45+31.248=9.8 \mathrm{kgm}^{2} / \mathrm{s}
<br/>\end{aligned}
<br/>$$</div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'WBJEE', 'WBJEE 2017']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">zero</span> </div>
source_db: db\MarksBatch2_P3.db
title:
two-particles-a-and-b-both-initially-at-rest-start-moving-towards-each-other-under-a-mutual-force-of-attraction-at-the-instant-when-the-speed-of-a-is-

slug:
two-particles-a-and-b-both-initially-at-rest-start-moving-towards-each-other-under-a-mutual-force-of-attraction-at-the-instant-when-the-speed-of-a-is-79463

question:
<div class="question">Two particles $A$ and $B$ (both initially at rest) start moving towards each other under a mutual force of attraction. At the instant, when the speed of $A$ is $v$ and the speed of $B$ is $2 v$, the speed of the centre of mass is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</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">B</span> <span class="option-data">$v$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{3 v}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-\frac{3 v}{2}$</span> </li> </ul>

answer:
<div class="solution">In the absence of external force the speed
<br/>$$
<br/>u_{\mathrm{co}}=0
<br/>$$
<br/>$F_{ext}=0$ then
<br/>$$
<br/>v_{\mathrm{cm} .}=0 \text { always }
<br/>$$</div>


tags: ['Physics', 'Motion In One Dimension', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch2_P3.db
title:
two-particles-a-and-b-having-different-masses-are-projected-from-a-tower-with-same-speed-a-is-projected-vertically-upward-and-b-vertically-downward-on

slug:
two-particles-a-and-b-having-different-masses-are-projected-from-a-tower-with-same-speed-a-is-projected-vertically-upward-and-b-vertically-downward-on-35571

question:
<div class="question">Two particles $A$ and $B$ having different masses are projected from a tower with same speed. $A$ is projected vertically upward and $B$ vertically downward. On reaching the ground</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">velocity of $A$ is greator than that of $B$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">velocity of $B$ is greater than that of $A$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">both $A$ and $B$ attain the same velocity</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 particle with the larger mass attains higher velocily</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">both $A$ and $B$ attain the same velocity</span> </div>

answer:
<div class="solution">The situation is diagrammatically as below
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_a26.png"/> <br/> <br/>When $A$ is projected with a vertical speed after sometime it comes on the same level with same
<br/>speed as it was projected. Now, the downward speeds of $A$ and $B$ at the level- $X$ is same. So, on reaching the ground, velocity of $A$ and $B$ are same.</div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch2_P3.db
title:
two-particles-a-and-b-having-equal-charges-after-being-accelerated-through-the-same-potential-difference-enter-into-a-region-of-uniform-magnetic-field

slug:
two-particles-a-and-b-having-equal-charges-after-being-accelerated-through-the-same-potential-difference-enter-into-a-region-of-uniform-magnetic-field-23382

question:
<div class="question">Two particles, $A$ and $B$, having equal charges, after being accelerated through the same potential difference enter into a region of uniform magnetic field and the particles describe circular paths of radii $R_{1}$ and $R_{2}$ resporctively. The ratio of the masses of $A$ and $B$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\sqrt{R_{1}} / R_{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$R_{1} / R_{2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\left(R_{1} / R_{2}\right)^{2}$</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">$\left(R_{2} / R_{1}\right)^{2}$</span> </li> </ul>

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

answer:
<div class="solution">Radius of circular path followed by charged particle is given by
<br/>$$
<br/>R=\frac{m v}{q B}=\frac{\sqrt{2 m K}}{q B} \quad[\because p=m v=\sqrt{2 m K}]
<br/>$$
<br/>where, $K$ is kinetic energy of particle. Charged particle $q$ is accelerated through some potential difference $V$, such that kinetic energy of particle is
<br/>$\therefore$
<br/>$$
<br/>\begin{aligned}
<br/>K &amp;=q V \\
<br/>R &amp;=\frac{\sqrt{2 m q V}}{q B}
<br/>\end{aligned}
<br/>$$
<br/>As the two charged particles of same magnitude and being accelerated through same potential, enters into a uniform magnetic field region, then $R \propto \sqrt{m}$
<br/>So,
<br/>$$
<br/>\frac{R_{1}}{R_{2}}=\sqrt{\frac{m_{A}}{m_{B}}} \Rightarrow \frac{m_{A}}{m_{B}}=\left(\frac{R_{1}}{R_{2}}\right)^{2}
<br/>$$</div>


tags: ['Mathematics', 'Application of Derivatives', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch2_P3.db
title:
two-particles-a-and-b-move-from-rest-along-a-straight-line-with-constant-accelerations-f-and-f-respectively-if-a-takes-m-sec-more-than-that-of-b-and-d

slug:
two-particles-a-and-b-move-from-rest-along-a-straight-line-with-constant-accelerations-f-and-f-respectively-if-a-takes-m-sec-more-than-that-of-b-and-d-64494

question:
<div class="question">Two particles $A$ and $B$ move from rest along a straight line with constant accelerations $f$ and $f$ ' respectively. If $A$ takes $\mathrm{m}$ sec. more than that of $\mathrm{B}$ and describes $\mathrm{n}$ units more than that of $\mathrm{B}$ in acquiring the same velocity, then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left(f+f^{\prime}\right) m^{2}=$ ff'n</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left(f-f f^{\prime}\right) m^{2}=f f^{\prime} n$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\left(f^{\prime}-f\right) n=\frac{1}{2} f f^{\prime} m^{2}$</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><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{2}\left(\mathrm{f}+\mathrm{f}^{\prime}\right) \mathrm{m}=\mathrm{ff}^{\prime} \mathrm{n}^{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(f^{\prime}-f\right) n=\frac{1}{2} f f^{\prime} m^{2}$</span> </div>

answer:
<div class="solution">$\begin{array}{llll}A:\quad u=0 &amp; a_{1}=f &amp; t_{1}=t+m &amp; s_{1}=n+s \\ B: \quad u=0 &amp; a_{2}=f^{\prime} &amp; t_{2}=t &amp; s_{2}=s\end{array}$
<br/>$\mathrm{s}+\mathrm{n}=\frac{1}{2} \mathrm{f} .(\mathrm{t}+\mathrm{m})^{2} \ldots \ldots(\mathrm{i}) \quad$ and $\mathrm{s}=\frac{1}{2} \mathrm{f}^{\prime}(\mathrm{t})^{2} \ldots(\mathrm{ii}) \quad \therefore \mathrm{f}^{\prime}(\mathrm{t})^{2}+\mathrm{n}=\frac{1}{2} \mathrm{f}(\mathrm{t}+\mathrm{m})^{2} \ldots (iii)$
<br/>$\begin{array}{l}
<br/>v_{1}=u_{1}+a_{1} t_{1}=0+f .(t+m) \\
<br/>v_{2}=u_{2}+a_{2} t_{2}=0+f^{\prime} . t \\
<br/>\therefore f(t+m)=f^{\prime} t \\
<br/>t=\frac{f m}{f^{\prime}-f}
<br/>\end{array}$
<br/>from (iii)
<br/>$\frac{1}{2} f^{\prime} \cdot\left(\frac{f m}{f^{\prime}-f}\right)^{2}+n=\frac{1}{2} f\left(\frac{f m}{f^{\prime}-f}+m\right)^{2}$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/CDyhZd61FNn0CEu7Wm3zW5Q56fG_FwHiL0sTOSg56wA.original.fullsize.png"/></div>


tags: ['Mathematics', 'Functions', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch2_P3.db
title:
two-particles-a-and-b-move-from-rest-along-a-straight-line-with-constant-accelerations-f-and-h-respectively-if-a-takes-m-seconds-more-than-b-and-descr

slug:
two-particles-a-and-b-move-from-rest-along-a-straight-line-with-constant-accelerations-f-and-h-respectively-if-a-takes-m-seconds-more-than-b-and-descr-15007

question:
<div class="question">Two particles $A$ and $B$ move from rest along a straight line with constant accelerations $f$ and $h,$ respectively. If $A$ takes $m$ seconds more than $B$ and describes $n$ units more than that of $B$ acquiring the same speed, then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(f+h) m^{2}=h n$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(f-f h) m^{2}=f h n$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$(h-f) n=\frac{1}{2}$ $fhm^{2}$</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">$\frac{1}{2}(f+h) n=$ $fhm^{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">$(h-f) n=\frac{1}{2}$ $fhm^{2}$</span> </div>

answer:
<div class="solution">Let $B$ travels $x$ units, $v=u+a t$
<br/>According to problem, $h t=f(t+m)$ $\begin{aligned} h t=&amp; f t+f m \\ h t-f t &amp;=f m \\ t(h-f) &amp;=f m \\ \frac{h-f}{f} &amp;=\frac{m}{t} \end{aligned}$
<br/>$t=m\left(\frac{f}{h-f}\right)$
<br/>$\Rightarrow \quad t^{2}=m^{2}\left(\frac{f}{h-f}\right)^{2}$
<br/>Again, $n+x=\frac{1}{2} f(t+m)^{2}$
<br/>$\Rightarrow \quad h+\frac{1}{2} h t^{2}=\frac{1}{2} f(t+m)^{2}$
<br/>From Eqs. (i) and (ii) $\frac{m}{n}=\frac{2(h-f)}{m f h}$
<br/>$\Rightarrow \quad(h-f) n=\frac{m^{2} f h}{2}$</div>


tags: ['Physics', 'Motion In One Dimension', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch2_P3.db
title:
two-particles-are-simultaneously-projected-in-the-horizontal-direction-from-a-point-p-at-a-certain-height-the-initial-velocities-of-the-particles-are-

slug:
two-particles-are-simultaneously-projected-in-the-horizontal-direction-from-a-point-p-at-a-certain-height-the-initial-velocities-of-the-particles-are-32704

question:
<div class="question">Two particles are simultaneously projected in the horizontal direction from a point $P$ at a certain height. The initial velocities of the particles are oppositely directed to each other and have magnitude $v$ each. The separation between the particles at a time when their position vectors (drawn from the point $P$ ) are mutually perpendicular, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{v^{2}}{2 g}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{v^{2}}{g}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{4 v^{2}}{g}$</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">$\frac{2 v^{2}}{g}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{4 v^{2}}{g}$</span> </div>

answer:
<div class="solution">According to the question,
<br/>Representation of position vectors of two particles (drawn from the point $P$ 
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2019_phy_a11.png"/> <br/>In two dimension, the position vectors $\mathbf{r}_{1}$ and $\mathbf{r}_{2}$ represented as
<br/>$$
<br/>\begin{array}{l}
<br/>\mathbf{r}_{1}=v t \hat{\mathbf{i}}-\frac{1}{2} g t^{2} \mathbf{j} ...(i) \\
<br/>\mathbf{r}_{2}=v t(-\hat{\mathbf{i}})-\frac{1}{2} g t^{2}(\mathbf{j})...(ii)
<br/>\end{array}
<br/>$$
<br/>$\because$ We know that, when the two vectors are mutually perpendicular, i.e.
<br/>$$
<br/>\theta=90^{\circ}
<br/>$$
<br/>So,
<br/>$$
<br/>\begin{array}{l}
<br/>\mathbf{r}_{1} \cdot \mathbf{r}_{2}=r_{1} r_{2} \cos 90^{\circ} \\
<br/>\mathbf{r}_{1} \cdot \mathbf{r}_{2}=0
<br/>\end{array}
<br/>$$
<br/>Substituting the values $\mathbf{r}_{1}$ and $\mathbf{r}_{2}$ in the above relation, we get
<br/>$$
<br/>\left((v t) \hat{\mathbf{i}}-\frac{1}{2} g t^{2} \mathbf{j}\right) \cdot\left(v t(-\hat{\mathbf{i}})-\frac{1}{2} g t^{2}(\mathbf{j})\right)=0
<br/>$$
<br/>$-v^{2} t^{2}+\frac{1}{4} 4 g^{2} t^{4}=0($ where, $\hat{\mathbf{i}} \cdot \hat{\mathbf{i}}=\hat{\mathbf{j}} \cdot \hat{\mathbf{j}}=\mathbf{k} \cdot \mathbf{k}=1)$
<br/>$$
<br/>\begin{aligned}
<br/>v^{2} t^{2} &amp;=\frac{1}{4} g^{2} t^{4} \\
<br/>\Rightarrow \quad v^{2} &amp;=\frac{1}{4} g^{2} t^{2}
<br/>\end{aligned}
<br/>$$
<br/>$\therefore$ Magnitude of velocity of the particles, $v=\frac{1}{2} g t$
<br/>We know that, separation distance between particles at a time $t$
<br/>$$
<br/>\begin{array}{c}
<br/>\Delta x=2 v t \\
<br/>\Delta x=2 \times v \times \frac{2 v}{g} \Rightarrow \dot{\Delta} x=\frac{4 v^{2}}{g}
<br/>\end{array}
<br/>$$</div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'WBJEE', 'WBJEE 2009']
source_db: db\MarksBatch2_P3.db
title:
two-particles-have-masses-m-4-m-and-their-kinetic-energies-are-in-the-ratio-2-1-what-is-the-ratio-of-their-linear-momenta

slug:
two-particles-have-masses-m-4-m-and-their-kinetic-energies-are-in-the-ratio-2-1-what-is-the-ratio-of-their-linear-momenta-90477

question:
<div class="question">Two particles have masses $\mathrm{m} \&amp; 4 \mathrm{~m}$ and their kinetic energies are in the ratio $2: 1$. What is the ratio of their linear momenta?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</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">B</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{4}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{16}$</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">$\frac{K E_1}{K E_2}=\frac{\frac{p_1^2}{2 m}}{\frac{p_2^2}{2 \times 4 m}}=\frac{2}{1} \Rightarrow \frac{p_1}{p_2}=\frac{1}{\sqrt{2}}$</div>


tags: ['Mathematics', 'Application of Derivatives', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch2_P3.db
title:
two-particles-move-in-the-same-straight-line-starting-at-the-same-moment-from-the-same-point-in-the-same-direction-the-first-moves-with-constant-veloc

slug:
two-particles-move-in-the-same-straight-line-starting-at-the-same-moment-from-the-same-point-in-the-same-direction-the-first-moves-with-constant-veloc-29722

question:
<div class="question">Two particles move in the same straight line starting at the same moment from the same point in the same direction. The first moves with constant velocity $u$ and the second starts from rest with constant acceleration $f$. Then,</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">they will be at the greatest distance at the end of time $\frac{u}{2 f}$ from the start</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">they will be at the greatest distance at the end of time $\frac{u}{f}$ from the start</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">their greatest distance is $\frac{u^{2}}{2 f}$</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">their greatest distance is $\frac{u^{2}}{f}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">they will be at the greatest distance at the end of time $\frac{u}{f}$ from the start, their greatest distance is $\frac{u^{2}}{2 f}$</span> </div>

answer:
<div class="solution">We know, $S=u t+\frac{1}{2} a t^{2}$
<br/>Condition for first, As, velocity is constant $u=u, v=u$ (constant)
<br/>$\therefore \quad a=0, s=u t \ldots(i)$
<br/>[from Eq. (i) Condition for second $u=0, a=f$ (constant)
<br/>$\therefore$
<br/>$$
<br/>s=\frac{1}{2}a t^{2}
<br/>$$
<br/>$s=\frac{1}{2} f t^{2}$
<br/>(ui) [from Eq. (i))
<br/>On differentiating Eqs. (ii) and (iui), we get $\frac{d S}{d t}=u$
<br/>and $\frac{d S}{d t}=\frac{1}{2} f(2t)$
<br/>$\frac{d S}{d t}=f t$
<br/>$u=f t$
<br/>[from Eq.
<br/>$t=\frac{u}{f}$
<br/>Thus, they will be at the greatest distance at the end of the $\frac{u}{f}$ from the start. For greatest distance
<br/>$$
<br/>S=\frac{1}{2} f t^{2}
<br/>$$
<br/>Put $\quad t=\frac{u}{f}$
<br/>$$
<br/>\begin{array}{l}
<br/>S=\frac{1}{2} f\left(\frac{u^{2}}{f^{2}}\right) \\
<br/>S=\frac{u^{2}}{2 f}
<br/>\end{array}
<br/>$$
<br/>Hence, option (b) and (c) are correct.</div>


tags: ['Physics', 'Gravitation', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch2_P3.db
title:
two-particles-of-mass-m-1-and-m-2-approach-each-other-due-to-their-mutual-gravitational-attraction-only-then

slug:
two-particles-of-mass-m-1-and-m-2-approach-each-other-due-to-their-mutual-gravitational-attraction-only-then-52080

question:
<div class="question">Two particles of mass $m_{1}$ and $m_{2}$; approach each other due to their mutual gravitational attraction only. Then,</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">accelerations of both the particles are equal</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">acceleration of the particle of mass $m_{1}$ is proportional to $\overline{m_{1}}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">acceleration of the particle of mass $m_{1}$ is proportional to $m_{2}$</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><li class=""> <span class="option-label">D</span> <span class="option-data">acceleration of the particle of mass $m_{1}$ is inversely proportional to $m_{1}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">acceleration of the particle of mass $m_{1}$ is proportional to $m_{2}$</span> </div>

answer:
<div class="solution">The gravitational force acting between the two masses $m_{1}$ and $m_{2}$ is given by
<br/>$$
<br/>F_{O}=\frac{G m_{1} m_{2}}{r^{2}}
<br/>$$
<br/>Force on mass $m_{1}$.
<br/>$$
<br/>F_{1}=\frac{G m_{1} m_{2}}{r^{2}}=m_{1} a_{1}
<br/>$$
<br/>where, $a_{1}=$ acceleration
<br/>$$
<br/>\Rightarrow \quad a_{1}=\frac{G m_{2}}{I^{2}} \Rightarrow a_{1} \propto m_{2}
<br/>$$
<br/>and similarly, $a_{2} \propto m_{1}$</div>


tags: ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch2_P3.db
title:
two-pith-balls-each-carrying-charge-q-are-hung-from-a-hook-by-two-strings-it-is-found-that-when-each-charge-is-tripled-angle-between-the-strings-doubl

slug:
two-pith-balls-each-carrying-charge-q-are-hung-from-a-hook-by-two-strings-it-is-found-that-when-each-charge-is-tripled-angle-between-the-strings-doubl-25972

question:
<div class="question">Two pith balls, each carrying charge $+q$ are hung from a hook by two strings. It is found that when each charge is tripled, angle between the strings double. What was the initial angle between the strings?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$30^{\circ}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$60^{\circ}$</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">$45^{\circ}$</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">$60^{\circ}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/l560Wm-h7Kt0Prm-zYokeSVJA651QftOYIjBJYHaxnc.original.fullsize.png"/><br/> <br/>Hint:
<br/>$\mathrm{T} \sin \theta=\mathrm{Fe}, \mathrm{T} \cos \theta=\mathrm{mg}$
<br/>$\tan \theta=\frac{\mathrm{Fe}}{\mathrm{mg}}=\frac{\mathrm{k} \cdot \mathrm{q}^{2}}{(2 \mathrm{~L} \sin \theta)^{2} \mathrm{mg}}$
<br/>In 2 nd case
<br/>$\begin{array}{l}
<br/>\tan 2 \theta=\frac{\mathrm{kq} \mathrm{q}^{2}}{(2 \mathrm{~L} \sin 2 \theta)^{2} \cdot \mathrm{mg}} \\
<br/>\frac{\tan 2 \theta}{\tan \theta}=\frac{9 \sin ^{2} \theta}{\sin ^{2} 2 \theta} \\
<br/>\frac{2}{1-\tan ^{2} \theta}=\frac{9}{4 \cos ^{2} \theta}=\frac{9}{4} \sec ^{2} \theta \\
<br/>\frac{2}{1-\tan ^{2} \theta}=\frac{9}{4}\left(1-\tan ^{2} \theta\right)
<br/>\end{array}$
<br/>$\tan ^{2} \theta=x, \frac{2}{1-x}=\frac{9}{4}(1+x)$
<br/>$\Rightarrow 8=9-9 x^{2} \Rightarrow x=\frac{1}{3} \Rightarrow \tan ^{2} \theta=\frac{1}{3} \Rightarrow \theta=30^{\circ}$
<br/>Angle between the strings $=2 \theta=60^{\circ}$</div>


tags: ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch2_P3.db
title:
two-point-charges-q-1-and-q-2-are-placed-a-finite-distance-d-apart-it-is-desired-to-put-a-third-charge-q-3-in-between-these-two-charges-so-that-q-3-is

slug:
two-point-charges-q-1-and-q-2-are-placed-a-finite-distance-d-apart-it-is-desired-to-put-a-third-charge-q-3-in-between-these-two-charges-so-that-q-3-is-83193

question:
<div class="question">Two point charges $+\mathrm{q}_{1}$ and $+\mathrm{q}_{2}$ are placed a finite distance ' $\mathrm{d}$ ' apart. It is desired to put a third charge $\mathrm{q}_{3}$ in between these two charges so that $\mathrm{q}_{3}$ is in equilibrium. This is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">possible only if $q_{3}$ is negative.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">possible only if $\mathrm{q}_{3}$ is positive.</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">possible irrespective of the sign of $q_{3}$.</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">not possible at all.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">possible irrespective of the sign of $q_{3}$.</span> </div>

answer:
<div class="solution">At null point $\vec{E}=0$
<br/>$\therefore$ any charge placed at that point will remain in equilibrium.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2oTpscfeg0AneUAMcb35wvwaAuuZSW0yTmh1G50wME8.original.fullsize.png"/></div>


tags: ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch2_P3.db
title:
two-positive-charges-q-and-4-q-are-placed-at-points-a-and-b-respectively-where-b-is-at-a-distance-d-units-to-the-right-of-a-the-total-electric-potenti

slug:
two-positive-charges-q-and-4-q-are-placed-at-points-a-and-b-respectively-where-b-is-at-a-distance-d-units-to-the-right-of-a-the-total-electric-potenti-62878

question:
<div class="question">Two positive charges $Q$ and $4 Q$ are placed at points $A$ and $B$ respectively, where $B$ is at a distance $d$ units to the right of $A$. The total electric potential due to these charges is minimum at $P$ on the line through $A$ and $B$. What is (are) the distance (s) of $P$ from $A ?$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{d}{3}$ units to the right of $A$</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">$\frac{d}{3}$ units to the left of $A$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{d}{5}$ units to the right of $A$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$d$ units to the left of $A$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">$\frac{d}{3}$ units to the right of $A$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_a40.png"/> <br/> <br/>$\because V_{P}$ is minimum. $\therefore$
<br/>$E_{p}=0 \Rightarrow E_{A}=E_{B}$
<br/>$\Rightarrow \quad \frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q}{r^{2}}=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{4 Q}{(d-r)^{2}}$
<br/>$\Rightarrow \quad \frac{1}{r}=\frac{2}{d-r} \Rightarrow d-r=2 r$
<br/>$\therefore$ Distance of $P$ from the $A r=\frac{d}{3}$ units to the right of $A .$</div>


tags: ['Physics', 'Nuclear Physics', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch2_P3.db
title:
two-radionctive-substances-a-and-b-have-decay-constants-5-and-respectively-at-t-0-they-have-the-same-number-of-nuclei-the-ratio-of-number-of-nuclei-of

slug:
two-radionctive-substances-a-and-b-have-decay-constants-5-and-respectively-at-t-0-they-have-the-same-number-of-nuclei-the-ratio-of-number-of-nuclei-of-91230

question:
<div class="question">Two radionctive substances $A$ and $B$ have decay constants $5 \lambda$ and $\lambda$ respectively. At $t=0,$ they have the same number of nuclei. The ratio of number of nuclei of $A$ to that of $B$ will be $(1 / e)^{2}$
<br/>after a time interval of</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{\lambda}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{1}{2 \lambda}$</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">$\frac{1}{3 \lambda}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{4 \lambda}$</span> </li> </ul>

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

answer:
<div class="solution">We know that<br/>$N=N_{0} e^{-\lambda t}$<br/>For $A$,<br/>$N_{A}=N_{0} e^{-5 \lambda_{L}}$<br/>For $B$,<br/>$N_{B}=N_{0} e^{-\lambda t}$<br/>Given,<br/>$\begin{aligned}<br/>\frac{N_{A}}{N_{B}} &amp;=\frac{1}{e^{2}} \\<br/>\frac{N}{N_{B}} &amp;=\frac{1}{e^{4 \lambda t}} \\<br/>t &amp;=\frac{1}{2 \lambda}<br/>\end{aligned}$</div>


tags: ['Physics', 'Thermal Properties of Matter', 'WBJEE', 'WBJEE 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$3.43$</span> </div>
source_db: db\MarksBatch2_P3.db
title:
two-rods-of-equal-length-and-diameter-have-thermal-conductivities-3-and-4-units-respectively-if-they-are-joined-in-series-the-thermal-conductivity-of-

slug:
two-rods-of-equal-length-and-diameter-have-thermal-conductivities-3-and-4-units-respectively-if-they-are-joined-in-series-the-thermal-conductivity-of-35041

question:
<div class="question">Two rods of equal length and diameter have thermal conductivities 3 and 4 units respectively. If they are joined in series, the thermal conductivity of the combination would be</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$3.43$</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">$3.5$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3.4$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3.34$</span> </li> </ul>

answer:
<div class="solution">In series $R=R_1+R_2$<br/>$\begin{aligned} &amp; \frac{2 \ell}{K_{e f f} A}=\frac{\ell}{K_1 A}+\frac{\ell}{K_2 A} \\ &amp; K_{e f f}=\frac{24}{7}=3.43\end{aligned}$</div>


tags: ['Physics', 'Oscillations', 'JEE Main']
source_db: db\MarksBatch2_P3.db
title:
two-simple-harmonic-motions-are-given-by-x-1-a-sin-t-a-cos-t-and-x-2-a-sin-t-3-a-cos-t-the-ratio-of-the-amplitudes-of-first-and-second-motion-and-the--1

slug:
two-simple-harmonic-motions-are-given-by-x-1-a-sin-t-a-cos-t-and-x-2-a-sin-t-3-a-cos-t-the-ratio-of-the-amplitudes-of-first-and-second-motion-and-the-1-36209

question:
<div class="question">Two simple harmonic motions are given by $x_{1}=a \sin \omega t+a \cos \omega t$ and $x_{2}=a \sin \omega t+\frac{a}{\sqrt{3}} \cos \omega t$ The ratio of the amplitudes of first and second motion and the phase difference between them are respectively</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\sqrt{\frac{3}{2}}$ and $\frac{\pi}{12}$</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">$\frac{\sqrt{3}}{2}$ and $\frac{\pi}{12}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{2}{\sqrt{3}}$ and $\frac{\pi}{12}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\sqrt{\frac{3}{2}}$ and $\frac{\pi}{6}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\sqrt{\frac{3}{2}}$ and $\frac{\pi}{12}$</span> </div>

answer:
<div class="solution">The given situation can be shown as <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_phy_a51.png"/> <br/> <br/>Fon second SHM
<br/>Ratio of amplitude $=\frac{a_{1}}{a_{2}}=\frac{\sqrt{3}}{\sqrt{2}}$
<br/>and phase difference, $\frac{\pi}{4}-\frac{\pi}{6}=\frac{\pi}{12}$</div>


tags: ['Physics', 'Oscillations', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch2_P3.db
title:
two-simple-harmonic-motions-are-given-by-x-1-a-sin-t-a-cos-t-and-x-2-a-sin-t-3-a-cos-t-the-ratio-of-the-amplitudes-of-first-and-second-motion-and-the-

slug:
two-simple-harmonic-motions-are-given-by-x-1-a-sin-t-a-cos-t-and-x-2-a-sin-t-3-a-cos-t-the-ratio-of-the-amplitudes-of-first-and-second-motion-and-the-32357

question:
<div class="question">Two simple harmonic motions are given by $x_{1}=a \sin \omega t+a \cos \omega t$ and $x_{2}=a \sin \omega t+\frac{a}{\sqrt{3}} \cos \omega t$ The ratio of the amplitudes of first and second motion and the phase difference between them are respectively</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\sqrt{\frac{3}{2}}$ and $\frac{\pi}{12}$</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">$\frac{\sqrt{3}}{2}$ and $\frac{\pi}{12}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{2}{\sqrt{3}}$ and $\frac{\pi}{12}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\sqrt{\frac{3}{2}}$ and $\frac{\pi}{6}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\sqrt{\frac{3}{2}}$ and $\frac{\pi}{12}$</span> </div>

answer:
<div class="solution">The given situation can be shown as <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_phy_a51.png"/> <br/> <br/>Fon second SHM
<br/>Ratio of amplitude $=\frac{a_{1}}{a_{2}}=\frac{\sqrt{3}}{\sqrt{2}}$
<br/>and phase difference, $\frac{\pi}{4}-\frac{\pi}{6}=\frac{\pi}{12}$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch2_P3.db
title:
two-soap-bubbles-of-radii-mathrmx-and-mathrmy-coalesee-to-constitute-a-bubble-of-radius-mathrmz-then-mathrmz-is-requal-to

slug:
two-soap-bubbles-of-radii-mathrmx-and-mathrmy-coalesee-to-constitute-a-bubble-of-radius-mathrmz-then-mathrmz-is-requal-to-99143

question:
<div class="question">Two soap bubbles of radii \(\mathrm{x}\) and \(\mathrm{y}\) coalesee to constitute a bubble of radius \(\mathrm{z}\). Then \(\mathrm{z}\) is requal to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\(\sqrt{x^2+y^2}\)</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">\(\sqrt{x+y}\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(x+y\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(\frac{x+y}{2}\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\sqrt{x^2+y^2}\)</span> </div>

answer:
<div class="solution">Hints: \(\mathrm{n}=\mathrm{n}_1+\mathrm{n}_2\)<br/>\(\mathrm{pv}=\mathrm{p}_1 \mathrm{v}_1+\mathrm{p}_2 \mathrm{v}_2\)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/XMbF46P1_4rauZD99MrGtCywrlzAbXwRbTsy7Nfaq8g.original.fullsize.png"/><br/><br/>\(\mathrm{p}_1=\mathrm{p}_0+\frac{4 \mathrm{~T}}{\mathrm{x}}, \mathrm{p}_2=\mathrm{p}_0+\frac{4 \mathrm{~T}}{\mathrm{y}}, \mathrm{p}=\mathrm{p}_0+\frac{4 \mathrm{~T}}{\mathrm{z}}\)<br/>If the process takes place is vaccume then \(\mathrm{p}_0=0\)<br/>\(\mathrm{p}_1=\frac{4 \mathrm{~T}}{\mathrm{x}}, \mathrm{p}_2=\frac{4 \mathrm{~T}}{\mathrm{y}}, \mathrm{p}=\frac{4 \mathrm{~T}}{\mathrm{z}}\)<br/>If process is isothermal<br/>\(\begin{aligned}<br/>&amp; \therefore \mathrm{p}_1 \mathrm{v}_1+\mathrm{p}_2 \mathrm{v}_2=\mathrm{pv} \\<br/>&amp; \therefore \mathrm{z}=\sqrt{\mathrm{x}^2+\mathrm{y}^2}<br/>\end{aligned}\)</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch2_P3.db
title:
two-soap-bubbles-of-radii-r-and-2-r-are-arrangement-shown-in-the-diagram-the-valve-is-now-opened-then-which-one-of-the-following-will-result

slug:
two-soap-bubbles-of-radii-r-and-2-r-are-arrangement-shown-in-the-diagram-the-valve-is-now-opened-then-which-one-of-the-following-will-result-98920

question:
<div class="question">Two soap bubbles of radii $r$ and $2 r$ are arrangement shown in the diagram. The valve is now opened. Then which one of the following will result.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_phy_q5_.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The radii of the bubbles will remain unchanged</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The bubbles will have equal radii</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The radius of the smaller bubble will decrease and that of the bigger bubble will decrease</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">The radius of the smaller bubble will decrease and that of the bigger bubble will increase</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">The radius of the smaller bubble will decrease and that of the bigger bubble will increase</span> </div>

answer:
<div class="solution">Pressure difference $=\frac{4 T}{r}$ 
<br/>For smaller soap. $\mathrm{p_{atm}}-\mathrm{p}_{i1}=\frac{4 \mathrm{T}}{\mathrm{r}}$
<br/>For bigger soap, $\mathrm{p_{atm}}-\mathrm{p}_{i2}=\frac{4 \mathrm{T}}{2 \mathrm{r}}$
<br/>As the pressure inside smaller bubble is greater than pressure inside bigger bubble, so ar fown from smaller to bigger and thu's radius of the smaller bubble will decrease and that of the bigger bubble will increase.</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2010']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: db\MarksBatch2_P3.db
title:
two-solid-spheres-of-same-metal-but-of-mass-m-and-8-m-fall-simultaneously-on-a-viscous-liquid-and-their-terminal-velocities-are-v-and-n-v-then-value-o

slug:
two-solid-spheres-of-same-metal-but-of-mass-m-and-8-m-fall-simultaneously-on-a-viscous-liquid-and-their-terminal-velocities-are-v-and-n-v-then-value-o-78040

question:
<div class="question">Two solid spheres of same metal but of mass $\mathrm{M}$ and $8 \mathrm{M}$ fall simultaneously on a viscous liquid and their terminal velocities are $v$ and $n v$ then value of $n$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">16</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">8</span> </li><li class="correct"> <span class="option-label">C</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">D</span> <span class="option-data">2</span> </li> </ul>

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>&amp; \text { Hints: } m=\frac{4}{3} \pi r^3 \times \rho \\<br/>&amp; m \propto r^3 \\<br/>&amp; \left(\frac{r_1}{r_2}\right)^3=\frac{1}{8} \\<br/>&amp; \frac{r_1}{r_2}=\frac{1}{2} \\<br/>&amp; 6 \pi n r \mathrm{~V}=\frac{4}{3} \pi r^3(d=\rho) \\<br/>&amp; \mathrm{V} \propto r^2, \frac{\mathrm{V}_1}{\mathrm{~V}_2}=\frac{1}{4} \\<br/>&amp; n=4<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2021']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: db\MarksBatch2_P3.db
title:
two-solid-spheres-s-1-and-s-2-of-same-uniform-density-fall-from-rest-under-gravity-in-a-viscous-medium-and-after-some-time-reach-terminal-velocities-v

slug:
two-solid-spheres-s-1-and-s-2-of-same-uniform-density-fall-from-rest-under-gravity-in-a-viscous-medium-and-after-some-time-reach-terminal-velocities-v-96819

question:
<div class="question">Two solid spheres $S_{1}$ and $S_{2}$ of same uniform density fall from rest under gravity in a viscous medium and after some time, reach terminal velocities $v_{1}$ and $v_{2}$ respectively. If ratio of masses $\frac{m_{1}}{m_{2}}=8$, then $\frac{v_{1}}{v_{2}}$ will be equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2</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">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{4}$</span> </li> </ul>

answer:
<div class="solution">$\mathrm{v}=\frac{2 \mathrm{r}^{2}}{9 \mathrm{n}}(\mathrm{d}-\rho) \mathrm{y}$
<br/>$\mathrm{m}=\frac{4}{3} \pi \mathrm{r}^{3} \cdot \mathrm{d}$
<br/>$\mathrm{r} \propto \mathrm{m}^{1 / 3}$
<br/>$\Rightarrow \mathrm{v}_{\mathrm{T}} \propto \mathrm{r}^{2} \propto \mathrm{m}^{2 / 3}$
<br/>$\therefore \frac{\mathrm{v}_{1}}{\mathrm{v}_{2}}=\left[\frac{\mathrm{m}_{1}}{\mathrm{~m}_{2}}\right]^{2 / 3}=(8)^{2 / 3}=4$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2009']
source_db: db\MarksBatch2_P3.db
title:
two-spheres-of-equal-masses-but-radii-r-1-and-r-2-are-allowed-to-fall-in-a-liquid-of-infinite-column-the-ratio-of-their-terminal-velocities-is

slug:
two-spheres-of-equal-masses-but-radii-r-1-and-r-2-are-allowed-to-fall-in-a-liquid-of-infinite-column-the-ratio-of-their-terminal-velocities-is-85075

question:
<div class="question">Two spheres of equal masses but radii $r_1$ and $r_2$ are allowed to fall in a liquid of infinite column. The ratio of their terminal velocities 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">$r_1: r_2$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{r}_2: \mathrm{r}_1$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">None of the above</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>

answer:
<div class="solution">We have $\mathrm{v}_{\mathrm{T}}=\frac{2 r^2(\sigma-\rho) g}{9 \eta}$<br/>$\frac{\mathrm{v}_1}{\mathrm{v}_2}=\left(\frac{\mathrm{r}_1}{\mathrm{r}_2}\right)^2 \frac{\left(\sigma_1-\rho\right)}{\left(\sigma_2-\rho\right)} ;$ given $\mathrm{m}_1=\mathrm{m}_2 \Rightarrow\left(\frac{\mathrm{r}_1}{\mathrm{r}_2}\right)^3=\frac{\sigma_2}{\sigma_1}$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$1: 9$</span> </div>
source_db: db\MarksBatch2_P3.db
title:
two-spheres-of-the-same-material-but-of-radii-r-and-3-r-are-allowed-to-fall-vertically-downwards-through-a-liquid-of-density-the-ratio-of-their-termin

slug:
two-spheres-of-the-same-material-but-of-radii-r-and-3-r-are-allowed-to-fall-vertically-downwards-through-a-liquid-of-density-the-ratio-of-their-termin-23075

question:
<div class="question">Two spheres of the same material, but of radii $R$ and $3 R$ are allowed to fall vertically downwards through a liquid of density $\rho$. The ratio of their terminal velocities is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1: 3$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1: 6$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$1: 9$</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">$1: 1$</span> </li> </ul>

answer:
<div class="solution">The terminal velocity, $v=\frac{2 r^{2}(p-\sigma) g}{9 \eta}$
<br/>As, all other parameters are constant, therefore $v\propto r^{2}$
<br/>$\Rightarrow \quad \frac{v_{R}}{v_{3 R}}=\frac{(R)^{2}}{(3 R)^{2}}=\frac{1}{9}$</div>


tags: ['Physics', 'Thermodynamics', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch2_P3.db
title:
two-substance-a-and-b-of-same-mass-are-heated-at-constant-rate-the-variation-of-temperature-theta-of-the-substance-with-time-mathrmt-is-shown-in-the-f

slug:
two-substance-a-and-b-of-same-mass-are-heated-at-constant-rate-the-variation-of-temperature-theta-of-the-substance-with-time-mathrmt-is-shown-in-the-f-96662

question:
<div class="question">Two substance \(A\) and \(B\) of same mass are heated at constant rate. The variation of temperature \(\theta\) of the substance with time \(\mathrm{t}\) is shown in the figure. Choose the correct statement<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/ccSauqwXcVu54I_HPIJe0EFmTcK443auWof6hyxKVuY.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Specific heat of \(A\) is greater than that of \(B\)</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">Specific heat of \(B\) is greater than that of \(A\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Both have same specific heat</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Specific heat of \(A\) is greater than that of \(B\)</span> </div>

answer:
<div class="solution">Hint : <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/4Hast7wAh7ENs-5mGJRApF0kx-JDYx7YVfcfRFmtIuU.original.fullsize.png"/><br/><br/>\(\begin{aligned} &amp; \Delta \mathrm{H}=\mathrm{mC} \Delta \theta \\ &amp; \frac{\mathrm{dH}}{\mathrm{dt}}=\mathrm{mC} \frac{\mathrm{d} \theta}{\mathrm{dt}} \quad \frac{\mathrm{dH}}{\mathrm{dt}}=\mathrm{a} \text { constant } \\ &amp; \therefore \frac{d \theta}{d t} \propto \frac{1}{C} \\ &amp; \text { i.e. slope } \propto \frac{1}{C} \quad \therefore C_B &lt; C_A \\ &amp; \end{aligned}\)</div>


tags: ['Mathematics', 'Straight Lines', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch2_P3.db
title:
two-tangents-to-the-circle-x-2-y-2-4-at-the-points-a-and-b-meet-at-m-4-0-the-area-of-the-quadrilateral-maob-where-o-is-the-origin-is

slug:
two-tangents-to-the-circle-x-2-y-2-4-at-the-points-a-and-b-meet-at-m-4-0-the-area-of-the-quadrilateral-maob-where-o-is-the-origin-is-22806

question:
<div class="question">Two tangents to the circle $x^{2}+y^{2}=4$ at the points $A$ and $B$ meet at $M(-4,0)$. The area of the quadrilateral MAOB, where $O$ is the origin is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$4 \sqrt{3}$ 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">B</span> <span class="option-data">$2 \sqrt{3}$ sq. units</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\sqrt{3}$ sq. units</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3 \sqrt{3}$ sq. units</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4 \sqrt{3}$ sq. units</span> </div>

answer:
<div class="solution">$\begin{aligned} &amp; O M=4, O A=2 \\ \therefore &amp; M A=\sqrt{16-4}=\sqrt{12}=2 \sqrt{3} \\ \therefore &amp; \text { Area }(M A O B) \\=&amp; 2 \times \text { area } \Delta M A O \\=&amp; 2 \times \frac{1}{2} \times M A \times O A \\=&amp; 2 \sqrt{3} \times 2=4 \sqrt{3} \text { sq. units } \end{aligned}$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/mHbngJDPQA34-M3ZfLeYOZk_FSwYLa44yNd4f-ZX-do.original.fullsize.png"/></div>


tags: ['Physics', 'Thermal Properties of Matter', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch2_P3.db
title:
two-temperature-scales-mathrma-and-mathrmb-are-related-by-fracmathrma42110fracmathrmb72220-at-which-temperature-two-scales-have-the-same-reading

slug:
two-temperature-scales-mathrma-and-mathrmb-are-related-by-fracmathrma42110fracmathrmb72220-at-which-temperature-two-scales-have-the-same-reading-50035

question:
<div class="question">Two temperature scales \(\mathrm{A}\) and \(\mathrm{B}\) are related by \(\frac{\mathrm{A}-42}{110}=\frac{\mathrm{B}-72}{220}\). At which temperature two scales have the same reading ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(-42^0\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(-72^0\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(+12^0\)</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">\(-40^{\circ}\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(+12^0\)</span> </div>

answer:
<div class="solution">Hints: \(\frac{\mathrm{A}-42}{110}=\frac{\mathrm{B}-72}{220}, \mathrm{~A}=\mathrm{B}\)<br/>\(\frac{A-42}{110}=\frac{A-72}{220}\)<br/>\(\begin{aligned}<br/>&amp; 2 \mathrm{A}-84=\mathrm{A}-72 \\<br/>&amp; \mathrm{~A}=12<br/>\end{aligned}\)</div>


tags: ['Physics', 'Ray Optics', 'WBJEE', 'WBJEE 2011']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">9D</span> </div>
source_db: db\MarksBatch2_P3.db
title:
two-thin-lenses-of-focal-lengths-20-mathrmcm-and-25-mathrmcm-are-placed-in-cotact-the-effective-power-of-the-combination-is

slug:
two-thin-lenses-of-focal-lengths-20-mathrmcm-and-25-mathrmcm-are-placed-in-cotact-the-effective-power-of-the-combination-is-81337

question:
<div class="question">Two thin lenses of focal lengths \(20 \mathrm{~cm}\) and \(25 \mathrm{~cm}\) are placed in cotact. The effective power of the combination is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">9D</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">\(2 \mathrm{D}\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">3D</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(\mathrm{TD}\)</span> </li> </ul>

answer:
<div class="solution">Hints: \(P=P_1+P_2\)<br/>\(=\frac{1}{f_1}+\frac{1}{f_2}=\frac{100}{20}+\frac{100}{25}=5+4=9 D\)</div>


tags: ['Physics', 'Laws of Motion', 'JEE Main']
source_db: db\MarksBatch2_P3.db
title:
two-weights-of-the-mass-m-1-and-m-2-m-1-are-joined-by-an-inextensible-string-of-negligible-mass-passing-over-a-fixed-frictionless-pulley-the-magnitude-1

slug:
two-weights-of-the-mass-m-1-and-m-2-m-1-are-joined-by-an-inextensible-string-of-negligible-mass-passing-over-a-fixed-frictionless-pulley-the-magnitude-1-12093

question:
<div class="question">Two weights of the mass $m_{1}$ and $m_{2}\left(&gt;m_{1}\right)$ are joined by an inextensible string of negligible mass passing over a fixed frictionless pulley. The magnitude of the acceleration of the loads is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$g$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{m_{2}-m_{1}}{m_{2}} g$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{m_{1}}{m_{2}+m_{1}} g$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{m_{2}-m_{1}}{m_{2}+m_{1}} g$</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">$\frac{m_{2}-m_{1}}{m_{2}+m_{1}} g$</span> </div>

answer:
<div class="solution">According to the question, we can draw the following diagram
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2019_phy_a9.png"/> <br/>Here, $T$ is the tension in the string. 
<br/>In equilibrium condition. 
<br/>For mass $m_{1}, \quad T-m_{1} g=m_{1} a$....(i)
<br/>For mass $m_{2}, \quad m_{2} g-T=m_{2} a$....(ii)
<br/>After adding Eqs. (i) and (ii), we get
<br/>$$
<br/>\begin{aligned}
<br/>m_{2} g-m_{1} g &amp;=m_{1} a+m_{2} a \\
<br/>\left(m_{2}-m_{1}\right) g &amp;=\left(m_{1}+m_{2}\right) a \\
<br/>a &amp;=\frac{\left(m_{2}-m_{1}\right)}{\left(m_{1}+m_{2}\right)} g
<br/>\end{aligned}
<br/>$$</div>


tags: ['Physics', 'Laws of Motion', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch2_P3.db
title:
two-weights-of-the-mass-m-1-and-m-2-m-1-are-joined-by-an-inextensible-string-of-negligible-mass-passing-over-a-fixed-frictionless-pulley-the-magnitude

slug:
two-weights-of-the-mass-m-1-and-m-2-m-1-are-joined-by-an-inextensible-string-of-negligible-mass-passing-over-a-fixed-frictionless-pulley-the-magnitude-97245

question:
<div class="question">Two weights of the mass $m_{1}$ and $m_{2}\left(&gt;m_{1}\right)$ are joined by an inextensible string of negligible mass passing over a fixed frictionless pulley. The magnitude of the acceleration of the loads is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$g$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{m_{2}-m_{1}}{m_{2}} g$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{m_{1}}{m_{2}+m_{1}} g$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{m_{2}-m_{1}}{m_{2}+m_{1}} g$</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">$\frac{m_{2}-m_{1}}{m_{2}+m_{1}} g$</span> </div>

answer:
<div class="solution">According to the question, we can draw the following diagram
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2019_phy_a9.png"/> <br/>Here, $T$ is the tension in the string. 
<br/>In equilibrium condition. 
<br/>For mass $m_{1}, \quad T-m_{1} g=m_{1} a$....(i)
<br/>For mass $m_{2}, \quad m_{2} g-T=m_{2} a$....(ii)
<br/>After adding Eqs. (i) and (ii), we get
<br/>$$
<br/>\begin{aligned}
<br/>m_{2} g-m_{1} g &amp;=m_{1} a+m_{2} a \\
<br/>\left(m_{2}-m_{1}\right) g &amp;=\left(m_{1}+m_{2}\right) a \\
<br/>a &amp;=\frac{\left(m_{2}-m_{1}\right)}{\left(m_{1}+m_{2}\right)} g
<br/>\end{aligned}
<br/>$$</div>


tags: ['Physics', 'Mechanical Properties of Solids', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch2_P3.db
title:
two-wires-a-and-b-of-same-length-are-made-of-same-material-load-f-vs-elongation-x-graph-for-these-two-wires-is-shown-in-the-figure-then-which-of-the-f

slug:
two-wires-a-and-b-of-same-length-are-made-of-same-material-load-f-vs-elongation-x-graph-for-these-two-wires-is-shown-in-the-figure-then-which-of-the-f-39337

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/_IRs8XSqlH0Lgp6LzCpj8jLSxBkar6MeIIHge0eSpY8.original.fullsize.png"/><br/><br/>Two wires $A$ and $B$ of same length are made of same material. Load $(F)$ vs. elongation $(x)$ graph for these two wires is shown in the figure. Then which of the following statement(s) is / are true?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">The cross-section area of $A$ is greater than that of $B$.</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">Young's modulus of $A$ is greater than Young's modulus of $B$.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The cross-sectional area of $B$ is greater than that of $A$.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Young's modulus of both A and B are 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 answers are:
<span class="option-value">The cross-section area of $A$ is greater than that of $B$., Young's modulus of both A and B are same.</span> </div>

answer:
<div class="solution">same material have identical Young's Modulus.<br/>For a given strain and Young's Modulus.<br/>stress in same<br/>$$<br/>\begin{aligned}<br/>&amp;\frac{F_A}{A_A}=\frac{F_B}{A_B} \Rightarrow \frac{F_A}{F_B}=\frac{A_A}{A_B} \\<br/>&amp;\text { as } F_A&gt;F_B, A_A&gt;A_B<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch2_P3.db
title:
two-wires-of-same-radius-having-lengths-l-1-and-i-2-and-resistivities-1-and-2-are-connected-in-series-the-equivalent-resistivity-will-be

slug:
two-wires-of-same-radius-having-lengths-l-1-and-i-2-and-resistivities-1-and-2-are-connected-in-series-the-equivalent-resistivity-will-be-53177

question:
<div class="question">Two wires of same radius having lengths $l_{1}$
<br/>and $I_{2}$ and resistivities $\rho_{1}$ and $\rho_{2}$ are connected in series. The equivalent resistivity will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\rho_{1} l_{2}+\rho_{2} I_{1}}{\rho_{1}+\rho_{2}}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{\rho_{1} l_{1}+\rho_{2} /_{2}}{l_{1}+l_{2}}$</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">$\frac{\rho_{1} l_{1}-\rho_{2} /_{2}}{l_{1}-l_{2}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\rho_{1} l_{2}+\rho_{2} l_{1}}{l_{1}+l_{2}}$</span> </li> </ul>

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

answer:
<div class="solution">$R=\frac{\rho l}{A}$
<br/>where, $\rho=$ resistivity $l=$ length of the resistance wire $A=$ area of cross-section
<br/>When the wires are connected in senes, then
<br/>$$
<br/>\begin{aligned}
<br/>R &amp;=R_{1}+R_{2} \\
<br/>R &amp;=\frac{\rho_{1} l_{1}}{A_{1}}+\frac{\rho_{2}l_{2}}{A_{2}} \\
<br/>R &amp;=\frac{\rho_{1} l_{1}}{A}+\frac{\rho_{2}l_{2}}{A} \\
<br/>\end{aligned}
<br/>$$
<br/>$\mathrm{\rho}_{\mathrm{eq}}=$ resistivity of combination
<br/>$$
<br/>\begin{array}{l}
<br/>I=I_{1}+I_{2} \\
<br/>A=A
<br/>\end{array}
<br/>$$
<br/>Thus, $\rho_{\mathrm{eq}} \frac{I_{1}+I_{2}}{A}=\frac{\rho _{1}l_{1}+\rho_{2} l_{2}}{A}$
<br/>$$
<br/>\rho_{e q}=\frac{\rho_{1}l_{1}+\rho_{2} l_{2}}{I_{1}+I_{2}}
<br/>$$</div>


title: under-identical-conditions-the-s-n-1-reaction-will-occur-most-efficiently-with-1
slug: under-identical-conditions-the-s-n-1-reaction-will-occur-most-efficiently-with-1-92997
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Main']
source_db: db\MarksBatch2_P3.db
question:
<div class="question">Under identical conditions, the $\mathrm{S}_{\mathrm{N}} 1$ reaction will occur most efficiently with</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">tert-butyl chloride</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 -chlorobutane</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2 -methyl- 1 -chloropropane</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">2 -chlorobutane</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">tert-butyl chloride</span> </div>

answer:
<div class="solution">$\mathrm{S}_{\mathrm{N}^{1}}$ reaction is most effective in $3^{\circ}$ carbon. 
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_a29.png"/></div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch2_P3.db
title:
under-isothermal-conditions-two-soap-bubbles-of-radii-a-and-b-coalesce-to-form-a-single-bubble-of-radius-c-if-the-external-pressure-is-p-then-surface-

slug:
under-isothermal-conditions-two-soap-bubbles-of-radii-a-and-b-coalesce-to-form-a-single-bubble-of-radius-c-if-the-external-pressure-is-p-then-surface-84760

question:
<div class="question">Under isothermal conditions, two soap bubbles of radii a and b coalesce to form a single bubble of radius c. If the external pressure is $\mathrm{P}$, then surface tension of the bubbles is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\mathrm{P}\left(\mathrm{c}^{3}-\mathrm{a}^{3}+\mathrm{b}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{\mathrm{P}\left(\mathrm{c}^{3}-\mathrm{a}^{3}-\mathrm{b}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$</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">C</span> <span class="option-data">$\frac{\mathrm{P}\left(\mathrm{c}^{2}+\mathrm{a}^{2}-\mathrm{b}^{2}\right)}{4\left(\mathrm{a}^{3}+\mathrm{b}^{3}-\mathrm{c}^{3}\right)}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\mathrm{P}\left(\mathrm{c}^{3}+\mathrm{b}^{3}-\mathrm{c}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{P}\left(\mathrm{c}^{3}-\mathrm{a}^{3}-\mathrm{b}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$</span> </div>

answer:
<div class="solution">Total number of moles $=$ constant
<br/>$$
<br/>\begin{array}{l}
<br/>\frac{P_{1} V_{1}}{R T}+\frac{P_{2} V_{2}}{R T}=\frac{P V}{R T} \Rightarrow P_{1} V_{1}+P_{2} V_{2}=P V \Rightarrow\left(P+\frac{4 T}{a}\right) \frac{4}{3} \pi a^{3}+\left(P+\frac{4 T}{b}\right) \frac{4}{3} \pi b^{3}=\left(P+\frac{4 T}{c}\right) \frac{4}{3} \pi c^{3} \\
<br/>\Rightarrow P\left(a^{3}+b^{3}-c^{3}\right)=4 T\left(c^{2}-a^{2}-b^{2}\right) \Rightarrow T=\frac{P\left(a^{3}+b^{3}-c^{3}\right)}{4\left(c^{2}-a^{2}-b^{2}\right)} \Rightarrow T=\frac{P}{4} \frac{\left(c^{3}-a^{3}-b^{3}\right)}{\left(a^{2}+b^{2}-c^{2}\right)}
<br/>\end{array}
<br/>$$</div>


tags: ['Chemistry', 'Chemical Kinetics', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch2_P3.db
title:
under-the-same-reaction-conditions-initial-concentration-of-1386-mol-dm-3-of-a-substance-becomes-half-in-40-s-and-20-s-through-firstorder-and-zeroorde

slug:
under-the-same-reaction-conditions-initial-concentration-of-1386-mol-dm-3-of-a-substance-becomes-half-in-40-s-and-20-s-through-firstorder-and-zeroorde-92055

question:
<div class="question">Under the same reaction conditions, initial concentration of $1.386 \mathrm{~mol} \mathrm{dm}^{-3}$ of a substance becomes half in $40 \mathrm{~s}$ and 20 s through first-order and zero-order kinetics respectively. Ratio $\left(\frac{k_{1}}{k_{0}}\right)$ of the rate constants for first-order $\left(k_{1}\right)$ and zero-order $\left(\mathrm{k}_{0}\right)$ of the reactions is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$0.5 \mathrm{~mol}^{-1} \mathrm{dm}^{3}$</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">$0.5 \mathrm{~mol} \mathrm{dm}^{-3}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1.0 \mathrm{~mol} \mathrm{dm}^{-3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2.0 \mathrm{~mol}^{-1} \mathrm{dm}^{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.5 \mathrm{~mol}^{-1} \mathrm{dm}^{3}$</span> </div>

answer:
<div class="solution">For First order reaction
<br/>$\mathrm{t}_{1 / 2}=\frac{0.693}{\mathrm{k}_{1}} \Rightarrow \mathrm{k}_{1}=\frac{0.693}{40} \mathrm{~s}^{-1}\quad_{-} \text {(i) }$
<br/>For Zero order reaction
<br/>$\mathrm{t}_{1 / 2}=\frac{[\mathrm{R}]_{0}}{2 \mathrm{k}_{0}} \Rightarrow \mathrm{k}_{0}=\frac{1.386}{2 \times 20} \mathrm{~mol} / \mathrm{dm}^{3} / \mathrm{s} \quad_{-} \text {(ii) }$
<br/>$\underline{\text { Using (i) and (ii) }}$
<br/>$\frac{\mathrm{k}_{1}}{\mathrm{k}_{0}}=\frac{0.693 / 40}{1.386 / 2 \times 20}=\frac{0.693}{1.386}=0.5 \mathrm{~mol}^{-1}-\mathrm{dm}^{3}$</div>


title: under-which-of-the-following-condition-is-the-relation-h-e-p-v-valid-for-a-closed-system
slug: under-which-of-the-following-condition-is-the-relation-h-e-p-v-valid-for-a-closed-system-13115
tags: ['Chemistry', 'Thermodynamics (C)', 'WBJEE', 'WBJEE 2009']
answer: <div class="solution">This is applicable when pressure remains constant.</div>
source_db: db\MarksBatch2_P3.db
question:
<div class="question">Under which of the following condition is the relation $\Delta \mathrm{H}=\Delta \mathrm{E}+\mathrm{P} \Delta \mathrm{V}$ valid for a closed system?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Constant Pressure</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">Constant temperature</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Constant temperature and pressure</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Constant temperature, pressure and composition</span> </li> </ul>

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


tags: ['Mathematics', 'Determinants', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch2_P3.db
title:
under-which-of-the-following-conditions-doesdo-the-system-of-equations-1-2-1-2-1-2-4-2-a-4-x-y-z-6-4-a-possesses-possess-unique-solution

slug:
under-which-of-the-following-conditions-doesdo-the-system-of-equations-1-2-1-2-1-2-4-2-a-4-x-y-z-6-4-a-possesses-possess-unique-solution-38474

question:
<div class="question">Under which of the following condition(s) does(do) the system of equations $\left(\begin{array}{ccc}1 &amp; 2 &amp; 4 \\ 2 &amp; 1 &amp; 2 \\ 1 &amp; 2 &amp; (a-4)\end{array}\right)\left(\begin{array}{l}x \\ y \\ z\end{array}\right)=\left(\begin{array}{l}6 \\ 4 \\ a\end{array}\right)$ possesses (possess) unique solution?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\forall \mathrm{a} \in \mathrm{R}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$a=8$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">for all integral values of a</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$a \neq 8$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$a \neq 8$</span> </div>

answer:
<div class="solution">$\Delta \neq 0$<br/>$\Rightarrow\left|\begin{array}{ccc}<br/>1 &amp; 2 &amp; 4 \\<br/>2 &amp; 1 &amp; 2 \\<br/>1 &amp; 2 &amp; \mathrm{a}-4<br/>\end{array}\right| \neq 0 \Rightarrow \mathrm{a} \neq 8$</div>


title: underlinemathrmg-in-the-above-sequence-of-reactions-is
slug: underlinemathrmg-in-the-above-sequence-of-reactions-is-64338
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch2_P3.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/75dUMfi5RC3_pkEIu2xAm9DrTjZ5ByoZvFDx1fqM3-o.original.fullsize.png"/><br/><br/>' \(\underline{\mathrm{G}}\) ' in the above sequence of reactions is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(\left(\mathrm{CH}_3\right)_2 \mathrm{CHCOOCH}_2 \mathrm{CH}_3\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{COOCH}_2 \mathrm{CH}_3\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{COOCH}_2 \mathrm{CH}_2 \mathrm{CH}_3\)</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">\(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{COOCH}\left(\mathrm{CH}_3\right)_2\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{COOCH}_2 \mathrm{CH}_2 \mathrm{CH}_3\)</span> </div>

answer:
<div class="solution">Hint : <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/kpyHpn74EfUglOq1_B6BSzjL2lbawRgUy7giSrr1Fv4.original.fullsize.png"/><br/></div>


title: upon-treatment-with-aloet-3-followed-by-usual-reactions-work-up-ch-3-cho-will-produce
slug: upon-treatment-with-aloet-3-followed-by-usual-reactions-work-up-ch-3-cho-will-produce-40243
tags: ['Chemistry', 'Aldehydes and Ketones', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch2_P3.db
question:
<div class="question">Upon treatment with Al(OEt) $_{3}$ followed by usual reactions (work up), CH $_{3} \mathrm{CHO}$ will produce</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">only $\mathrm{CH}_{3} \mathrm{COOCH}_{2} \mathrm{CH}_{3}$</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">a mixture of $\mathrm{CH}_{3} \mathrm{COOH}$ and ErOH</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">only $\mathrm{CH}_{3} \mathrm{COOH}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">only EtOH</span> </li> </ul>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_a25.png"/></div>


title: upon-treatment-with-i-2-and-aqueous-naoh-which-of-the-following-compounds-will-form-iodoform
slug: upon-treatment-with-i-2-and-aqueous-naoh-which-of-the-following-compounds-will-form-iodoform-25683
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch2_P3.db
question:
<div class="question">Upon treatment with $I_{2}$ and aqueous $\mathrm{NaOH}$, which of the following compounds will form iodoform?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CHO}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COCH}_{2} \mathrm{CH}_{3}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \cdot \mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{3}$</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">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \cdot \mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{3}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_a24.png"/></div>


title: using-binomial-theorem-the-value-of-0999-3-correct-to-3-decimal-places-is
slug: using-binomial-theorem-the-value-of-0999-3-correct-to-3-decimal-places-is-10675
tags: ['Mathematics', 'Binomial Theorem', 'WBJEE', 'WBJEE 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0.997</span> </div>
source_db: db\MarksBatch2_P3.db
question:
<div class="question">Using binomial theorem, the value of $(0.999)^3$ correct to 3 decimal places is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0.999</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">0.998</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">0.997</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">0.995</span> </li> </ul>

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>&amp; \text { Hints : }{ }^3 C_0-{ }^3 C_1(.001)+{ }^3 C_2(.001)^2-{ }^3 C_3(.001)^3 \\<br/>&amp; =1-.003+3(.000001)-(.000000001)=0.997<br/>\end{aligned}<br/>$$</div>


title: value-of-tan-1-c-o-s-2-s-i-n-2-1-is
slug: value-of-tan-1-c-o-s-2-s-i-n-2-1-is-94107
question: <div class="question">Value of $\tan ^{-1}\left(\frac{\sin 2-1}{\cos 2}\right)$ is</div>
tags: ['Mathematics', 'Inverse Trigonometric Functions', 'WBJEE', 'WBJEE 2010']
source_db: db\MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\pi}{2}-1$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$1-\frac{\pi}{4}$</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">$2-\frac{\pi}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\pi}{4}-1$</span> </li> </ul>

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

answer:
<div class="solution">Hints : $\tan ^{-1}\left(\frac{\sin 2-1}{\cos 2}\right)=\tan ^{-1}\left(\frac{-(\sin 1-\cos 1)^2}{(\cos 1-\sin 1)(\cos 1+\sin 1)}\right) \quad=-\tan ^{-1}\left(\frac{\cos 1-\sin 1}{\cos 1+\sin 1}\right)=1-\frac{\pi}{4}$</div>


title: vitamin-c-is
slug: vitamin-c-is-84975
question: <div class="question">Vitamin $\mathrm{C}$ is</div>
tags: ['Chemistry', 'Biomolecules', 'WBJEE', 'WBJEE 2010']
answer: <div class="solution">No Solution Available</div>
source_db: db\MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Citric acid</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Lactic acid</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Paracetamol</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Ascorbic 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> </ul>

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


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch2_P3.db
title:
water-is-flowing-in-streamline-motion-through-a-horizontal-tube-the-pressure-at-a-point-in-the-tube-is-p-where-the-velocity-of-flow-is-v-at-another-po

slug:
water-is-flowing-in-streamline-motion-through-a-horizontal-tube-the-pressure-at-a-point-in-the-tube-is-p-where-the-velocity-of-flow-is-v-at-another-po-22995

question:
<div class="question">Water is flowing in streamline motion through a horizontal tube. The pressure at a point in the tube is $p$ where the velocity of flow is $v$. At another point, where the pressure is $p / 2,$ the velocity of flow is [density of water $=\rho]$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\sqrt{v^{2}+\frac{p}{\rho}}$</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">$\sqrt{v^{2}-\frac{p}{\rho}}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\sqrt{v^{2}+\frac{2 p}{\rho}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\sqrt{v^{2}-\frac{2 p}{\rho}}$</span> </li> </ul>

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

answer:
<div class="solution">As the water is flowing through the horizontal tube, so in the streamline flow of water, the sun of static pressure and dynamic pressure is constant $i, e$
<br/>$$
<br/>P+\frac{1}{2} \rho v^{2}=\frac{P}{2}+\frac{1}{2} \rho v_{1}^{2}
<br/>$$
<br/>$\Rightarrow \quad v_{1}=\sqrt{\frac{P}{\rho}+v^{2}}$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch2_P3.db
title:
water-is-flowing-through-a-very-narrow-tube-the-velocity-of-water-below-which-the-flow-remains-a-streamline-flow-is-known-as

slug:
water-is-flowing-through-a-very-narrow-tube-the-velocity-of-water-below-which-the-flow-remains-a-streamline-flow-is-known-as-15831

question:
<div class="question">Water is flowing through a very narrow tube. The velocity of water below which the flow remains a streamline flow is known as</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">relative velocity</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">terminal velocity</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">critical velocity</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">particle velocity</span> </li> </ul>

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

answer:
<div class="solution">The velocity of water below which the flow remains streamline flow is known as critical velocity.</div>


tags: ['Mathematics', 'Sets and Relations', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch2_P3.db
title:
we-define-a-binary-relation-on-the-set-of-all-3-3-real-matrices-as-a-b-if-and-only-if-there-exist-invertible-matrices-p-and-q-such-that-b-p-a-q-1-the-

slug:
we-define-a-binary-relation-on-the-set-of-all-3-3-real-matrices-as-a-b-if-and-only-if-there-exist-invertible-matrices-p-and-q-such-that-b-p-a-q-1-the-31589

question:
<div class="question">We define a binary relation - on the set of all $3 \times 3$ real matrices as $A \sim B,$ if and only if there exist invertible matrices $P$ and $Q$ such that $B=P A Q^{-1} .$ The binary relation $\sim$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">neither reflexive nor symmetric</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">reflexive and symmetric but not transitive</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">symmetric and transitive but not reflexive</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">an equivalence relation</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>

answer:
<div class="solution">Let the relation defined as $R=\left\{(A, B): B=P A Q^{-1}\right\}$
<br/>For reflexive
<br/>$A=I A I^{-1}$
<br/>$\Rightarrow(A, A) \in R$
<br/>$\Rightarrow R$ is reflexive
<br/>For symmetric
<br/>$\operatorname{Let}(A, B) \in R$
<br/>$\therefore B=P A Q^{-1}$
<br/>$\Rightarrow \quad B Q=P A\left(Q^{-1} Q\right)$
<br/>$\Rightarrow \quad B Q=P A$
<br/>$\Rightarrow \quad P^{-1}(B Q)=P^{-1} P(A)$
<br/>$\Rightarrow \quad P^{-1} B Q=A$
<br/>$\Rightarrow(B, A) \in R$
<br/>$\Rightarrow R$ is symmetric.
<br/>For transitive Let $(A, B) \in R,(B, C) \in R$
<br/>Then, $\quad A=P B Q^{-1}$ and $B=R C S^{-1}$
<br/>$\Rightarrow \quad A=P R C S^{-1} Q^{-1}$
<br/>$\begin{array}{ll}\Rightarrow &amp; A=(P R) C(Q S)^{-1} \\ \Rightarrow &amp; (A, C) \in R\end{array}$
<br/>$\Rightarrow R$ is transitive. Hence, $R$ is an equivalence relation.</div>


tags: ['Chemistry', 'Electrochemistry', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch2_P3.db
title:
what-amount-of-clectricity-can-deposit-i-mole-of-al-metal-at-cathode-when-passed-through-molten-alcl-3

slug:
what-amount-of-clectricity-can-deposit-i-mole-of-al-metal-at-cathode-when-passed-through-molten-alcl-3-91280

question:
<div class="question">What amount of clectricity can deposit
<br/>I mole of Al metal at cathode when passed through molten $\mathrm{AlCl}_{3} ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.3 \mathrm{F}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1 \mathrm{F}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$3 \mathrm{F}$</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">$1 / 3 \mathrm{F}$</span> </li> </ul>

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

answer:
<div class="solution">The number of electrons involved in the reaction are three as shown below
<br/>$$
<br/>\mathrm{Al}^{3+}+3 e^{-} \longrightarrow \mathrm{Al}
<br/>$$
<br/>It means the conversion of every aluminium ion to aluminium atom requires three electrons. Therefore, the amount of electricity required for one mole of $\mathrm{Al}^{3+}$ ions $=3 \mathrm{F}$.</div>


title: what-current-will-flow-through-the-2-k-resistor-in-the-circuit-shown-in-the-figure-1
slug: what-current-will-flow-through-the-2-k-resistor-in-the-circuit-shown-in-the-figure-1-20393
tags: ['Physics', 'Current Electricity', 'JEE Main']
source_db: db\MarksBatch2_P3.db
question:
<div class="question">What current will flow through the $2 \mathrm{k} \Omega$ resistor in the circuit shown in the figure? <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_phy_q6.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$3 \mathrm{mA}$</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">$6 \mathrm{mA}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$12 \mathrm{mA}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$36 \mathrm{mA}$</span> </li> </ul>

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

answer:
<div class="solution">From KCL we have
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_phy_a6.png"/> <br/> <br/>$i=\frac{72}{8 \times 10^{3}}=9 \times 10^{-3} \mathrm{A}$
<br/>$$
<br/>\begin{aligned}
<br/>i \times 6 &amp;=(9-i) \times 3 \\
<br/>i &amp;=3 \mathrm{mA}
<br/>\end{aligned}
<br/>$$</div>


tags: ['Chemistry', 'Hydrocarbons', 'JEE Main']
source_db: db\MarksBatch2_P3.db
title:
what-is-obtained-when-nitrobenzene-is-treated-sequentially-with-i-nh-4-cl-zn-dust-and-ii-h-2-so-4-na-2-cr-2-o-7-1

slug:
what-is-obtained-when-nitrobenzene-is-treated-sequentially-with-i-nh-4-cl-zn-dust-and-ii-h-2-so-4-na-2-cr-2-o-7-1-75218

question:
<div class="question">What is obtained when nitrobenzene is treated sequentially with (i) $\mathrm{NH}_4 \mathrm{Cl} / \mathrm{Zn}$ dust and (ii) $\mathrm{H}_2 \mathrm{SO}_4 / \mathrm{Na}_2 \mathrm{Cr}_2 \mathrm{O}_7$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">meta-chloronitrobenzene</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">para-chloronitrobenzene</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">nitrosobenzene</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">benzene</span> </li> </ul>

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

answer:
<div class="solution">Hints: <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/HN2lOs7vJZgH1Nv4ZDY5IVQlJd5vhR9vrV9eZL79m5U.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Hydrocarbons', 'WBJEE', 'WBJEE 2010']
source_db: db\MarksBatch2_P3.db
title:
what-is-obtained-when-nitrobenzene-is-treated-sequentially-with-i-nh-4-cl-zn-dust-and-ii-h-2-so-4-na-2-cr-2-o-7

slug:
what-is-obtained-when-nitrobenzene-is-treated-sequentially-with-i-nh-4-cl-zn-dust-and-ii-h-2-so-4-na-2-cr-2-o-7-62866

question:
<div class="question">What is obtained when nitrobenzene is treated sequentially with (i) $\mathrm{NH}_4 \mathrm{Cl} / \mathrm{Zn}$ dust and (ii) $\mathrm{H}_2 \mathrm{SO}_4 / \mathrm{Na}_2 \mathrm{Cr}_2 \mathrm{O}_7$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">meta-chloronitrobenzene</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">para-chloronitrobenzene</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">nitrosobenzene</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">benzene</span> </li> </ul>

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

answer:
<div class="solution">Hints: <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/HN2lOs7vJZgH1Nv4ZDY5IVQlJd5vhR9vrV9eZL79m5U.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Carboxylic Acid Derivatives', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch2_P3.db
title:
what-is-the-correct-order-of-acidity-of-salicylic-acid-4hydroxybenzoic-acid-and-2-6-dihydroxybenzoic-acid

slug:
what-is-the-correct-order-of-acidity-of-salicylic-acid-4hydroxybenzoic-acid-and-2-6-dihydroxybenzoic-acid-50486

question:
<div class="question">What is the correct order of acidity of salicylic acid, 4-hydroxybenzoic acid, and $2,6-$ dihydroxybenzoic acid?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">2,6-dihydroxybenzoic acid &gt; salicylic acid &gt; 4-hydroxybenzoic 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">2,6-dihydroxybenzoic acid &gt; 4-hydroxybenzoic acid &gt; salicylic acid</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">salicylic acid &gt; 2, 6-dihydroxybenzoic acid &gt; 4-hydroxybenzoic acid</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">salicylic acid &gt; 4-hydroxybenzoic acid &gt; 2,6-dihydroxybenzoic acid</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">2,6-dihydroxybenzoic acid &gt; salicylic acid &gt; 4-hydroxybenzoic acid</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/FmbqN947Br3Km8UOHvjxBhmQkcvzaFHtM-lUI4J_7nQ.original.fullsize.png"/><br/><br/>The conjugate base of 2, 6-dihydroxybenzoic acid is highly stabilised by $\mathrm{H}$-bonding. The effect is lesser in salicyclic acid.</div>


title: what-is-the-current-i-shown-in-the-given-circuit
slug: what-is-the-current-i-shown-in-the-given-circuit-24983
tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch2_P3.db
question:
<div class="question">What is the current $I$ shown in the given circuit?
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2019_phy_q25.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{V}{2 R}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{V}{R}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{V}{16 R}$</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">D</span> <span class="option-data">$\frac{V}{8 R}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{V}{16 R}$</span> </div>

answer:
<div class="solution">According to the question,
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2019_phy_a25.png"/> <br/>Total resistance of the given circuit
<br/>$$
<br/>R_{\mathrm{eq}}=2 R
<br/>$$
<br/>$\therefore \quad I=\frac{V / 2 R}{8} \quad\left(\because I_{1}=V / 2 R\right)$
<br/>So, current $I$ in the circuit $I=\frac{V}{16 R} \quad\left(\because I=\frac{I_{1}}{8}\right)$</div>


tags: ['Chemistry', 'Solid State', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch2_P3.db
title:
what-is-the-edge-length-of-the-unit-cell-of-a-body-centred-cubic-crystal-of-an-element-whose-atomic-radius-is-75-mathrmpm

slug:
what-is-the-edge-length-of-the-unit-cell-of-a-body-centred-cubic-crystal-of-an-element-whose-atomic-radius-is-75-mathrmpm-70190

question:
<div class="question">What is the edge length of the unit cell of a body centred cubic crystal of an element whose atomic radius is \(75 \mathrm{pm}\) ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(170 \mathrm{pm}\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(175 \mathrm{pm}\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(178 \mathrm{pm}\)</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">\(173.2 \mathrm{pm}\)</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">\(173.2 \mathrm{pm}\)</span> </div>

answer:
<div class="solution">Hint : In BCC, \(4 r=\sqrt{3} a\)<br/>\(\therefore \mathrm{a}=\frac{4 \mathrm{r}}{\sqrt{3}}=\frac{4 \times 75}{\sqrt{3}}=\frac{300}{\sqrt{3}}=\sqrt{3} \times 100 \mathrm{pm}=173.2 \mathrm{pm}\)</div>


title: what-is-the-major-product-of-the-following-reaction-1
slug: what-is-the-major-product-of-the-following-reaction-1-39280
tags: ['Chemistry', 'Aldehydes and Ketones', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch2_P3.db
question:
<div class="question">What is the major product of the following reaction?
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/Bvifc3Ljvd4JKh4j-84vRpwE23bi0lRU93rs_vObRog.original.fullsize.png"/></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/bfX_CHCLuwedWXQInmg7WsJ8aPD517VPCqD5Seg3AGc.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/A0paJkFPU6zClHHw8FOgGSE44U4_x78igsCerP1Qig4.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/uQUWWCoox4Vl3cAJMnl8M5t96_X3cVAyt5viFsbAqhQ.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/IonlRzhf2DcBVeOiy1FpBeHcdOiAsELcx5eoT3_RmZY.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/bfX_CHCLuwedWXQInmg7WsJ8aPD517VPCqD5Seg3AGc.original.fullsize.png"/></span> </div>

answer:
<div class="solution">Hint: 
<br/>It's perkin reaction. The reaction starts with generation of nucleophile from propanoic anhydride as follows:
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/yrkmtfWOlrQyAGxlqZm8k56DvXk3VHBh7r7FnPbVZks.original.fullsize.png"/><br/> <br/>Then onwards, the nucleophile attacks the-CHO group as shown:<img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/O1okEVGCge4rAW0CzUohwsUFWhaL5-opxyATGcq30tk.original.fullsize.png"/><br/> <br/>Finally, it goes on to give:<img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/WrLCSxCpG264ztm4IGsqOsY4xYcT8mMWtOck5uKxzSc.original.fullsize.png"/></div>


tags: ['Mathematics', 'Permutation Combination', 'WBJEE', 'WBJEE 2021']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">10</span> </div>
source_db: db\MarksBatch2_P4.db
title:
what-is-the-number-of-ways-in-which-an-examiner-can-assign-10-marks-to-4-questions-giving-not-less-than-2-marks-to-any-questions

slug:
what-is-the-number-of-ways-in-which-an-examiner-can-assign-10-marks-to-4-questions-giving-not-less-than-2-marks-to-any-questions-83602

question:
<div class="question">What is the number of ways in which an examiner can assign 10 marks to 4 questions, giving not less than 2 marks to any questions?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">4</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">6</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">10</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">16</span> </li> </ul>

answer:
<div class="solution">$x_{1}+x_{2}+x_{3}+x_{4}=10 \quad x_{i} \geq 2$
<br/>$\Rightarrow\left(x_{1}-2\right)+\left(x_{2}-2\right)+\left(x_{3}-2\right)+\left(x_{4}-2\right)=2$
<br/>$\begin{array}{llll}\mathrm{y}_{1} &amp; \mathrm{y}_{2} &amp; \mathrm{y}_{3} &amp; \mathrm{y}_{4}\end{array}$
<br/>$\mathrm{y}_{1}+\mathrm{y}_{2}+\mathrm{y}_{3}+\mathrm{y}_{4}=2 ; \mathrm{y}_{i} \geq 0$
<br/>$\therefore$ N.O.W $={ }^{2+4-1} \mathrm{C}_{4-1}={ }^{5} \mathrm{C}_{3}=10$</div>


title: what-is-the-particle-x-in-the-following-nuclear-reaction-4-9-be-2-4-he-6-12-c-x
slug: what-is-the-particle-x-in-the-following-nuclear-reaction-4-9-be-2-4-he-6-12-c-x-93638
tags: ['Physics', 'Nuclear Physics', 'WBJEE', 'WBJEE 2009']
source_db: db\MarksBatch2_P4.db
question:
<div class="question">What is the particle $\mathrm{x}$ in the following nuclear reaction :<br/>${ }_4^9 \mathrm{Be}+{ }_2^4 \mathrm{He} \rightarrow{ }_6^{12} \mathrm{C}+\mathrm{x}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">electron</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">proton</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Photon</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Neutron</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">Neutron</span> </div>

answer:
<div class="solution">${ }_4^9 \mathrm{Be}+{ }_2^4 \mathrm{He} \rightarrow{ }_6^{12} \mathrm{C}+{ }_0^1 \mathrm{X}$<br/>Hence X represents neutron $\left({ }_0^1 n\right)$</div>


tags: ['Physics', 'Oscillations', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch2_P4.db
title:
what-is-the-phase-difference-between-two-simple-harmonic-motions-represented-by-x-1-a-sin-t-6-and-x-2-a-cos-t

slug:
what-is-the-phase-difference-between-two-simple-harmonic-motions-represented-by-x-1-a-sin-t-6-and-x-2-a-cos-t-80237

question:
<div class="question">What is the phase difference between two simple harmonic motions represented by $x_{1}=A \sin \left(\omega t+\frac{\pi}{6}\right)$ and $x_{2}=A \cos (\omega t) ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\pi}{6}$</span> </li><li class="correct"> <span class="option-label">B</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">C</span> <span class="option-data">$\frac{\pi}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{2 \pi}{3}$</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">Given,
<br/>$$
<br/>\begin{array}{l}
<br/>x_{1}=A \sin \left(\omega t+\frac{\pi}{6}\right) \\
<br/>x_{2}=A \cos (\omega t) \\
<br/>x_{2}=A \operatorname{sin}\left(\omega t+\frac{\pi}{2}\right)
<br/>\end{array}
<br/>$$
<br/>Phase difference
<br/>$$
<br/>\Delta \phi=\phi_{2}-\phi_{1}
<br/>$$
<br/>$$
<br/>\begin{array}{l}
<br/>\Delta \phi=\frac{\pi}{2}-\frac{\pi}{6} \\
<br/>\Delta \phi=\frac{3 \pi-\pi}{6}=\frac{\pi}{3}
<br/>\end{array}
<br/>$$</div>


title: what-is-the-value-of-current-through-the-diode-in-the-circuit-given
slug: what-is-the-value-of-current-through-the-diode-in-the-circuit-given-34520
tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2021']
answer: <div class="solution">Since diode is reverse biased</div>
source_db: db\MarksBatch2_P4.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/R7VX4yotvHWhSjKc7LtE5rkdIekkfKSbORDzM7UnmzM.original.fullsize.png"/><br/> <br/>What is the value of current through the diode in the circuit given?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$0 \mathrm{~mA}$</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">$1 \mathrm{~mA}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$19 \mathrm{~mA}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$9 \mathrm{~mA}$</span> </li> </ul>

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


title: what-type-of-orbital-hybridisation-is-considered-on-p-in-pcl-5
slug: what-type-of-orbital-hybridisation-is-considered-on-p-in-pcl-5-21009
tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'WBJEE', 'WBJEE 2010']
answer: <div class="solution">No Solution Available</div>
source_db: db\MarksBatch2_P4.db
question:
<div class="question">What type of orbital hybridisation is considered on $\mathrm{P}$ in $\mathrm{PCl}_5$ ?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{sp}^3 \mathrm{~d}$</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">$\mathrm{dsp}^3$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{sp}^3 \mathrm{~d}^2$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{d}^2 \mathrm{sp}^3$</span> </li> </ul>

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


tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch2_P4.db
title:
what-will-be-current-through-the-200-resistor-in-the-given-circuit-a-long-time-after-the-switch-k-is-made-on

slug:
what-will-be-current-through-the-200-resistor-in-the-given-circuit-a-long-time-after-the-switch-k-is-made-on-51372

question:
<div class="question">What will be current through the $200 \Omega$
<br/>resistor in the given circuit, a long time after the switch $K$ is made on?
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_q2.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Zero</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$100 \mathrm{mA}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$10 \mathrm{mA}$</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">$1 \mathrm{mA}$</span> </li> </ul>

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

answer:
<div class="solution">In steady state, arm having capacitors does not flow current. So, we can neglect them.
<br/>$\therefore$ The given circuit reduces to
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_a2.png"/> <br/> <br/>$$
<br/>R_{\text {net }}=200+400=600 \Omega
<br/>$$
<br/>$\therefore$ Current in circuit,
<br/>$$
<br/>\begin{aligned}
<br/>I=\frac{V}{R} &amp;=\frac{6}{600}=0.01 \mathrm{A} \\
<br/>&amp;=10 \mathrm{mA}
<br/>\end{aligned}
<br/>$$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch2_P4.db
title:
what-will-be-the-approximate-terminal-velocity-of-a-rain-drop-of-diameter-18-1-0-3-m-when-density-of-rain-water-1-0-3-kgm-3-and-the-coefficient-of-vis

slug:
what-will-be-the-approximate-terminal-velocity-of-a-rain-drop-of-diameter-18-1-0-3-m-when-density-of-rain-water-1-0-3-kgm-3-and-the-coefficient-of-vis-37038

question:
<div class="question">What will be the approximate terminal velocity of a rain drop of diameter $1.8 \times 10^{-3} \mathrm{m}$, when density of rain water $\approx 10^{3} \mathrm{kgm}^{-3}$ and the coefficient of viscosity of air $\approx 1.8 \times 10^{-5} \mathrm{N}-sm^{-2}$ ? (Neglect buoyancy of air)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$49 \mathrm{ms}^{-1}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$98 \mathrm{ms}^{-1}$</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">$392 \mathrm{ms}^{-1}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$980 \mathrm{ms}^{-1}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$98 \mathrm{ms}^{-1}$</span> </div>

answer:
<div class="solution">Terminal velocity, $v=\frac{2}{9} r^{2} \frac{(\rho-\sigma)}{\eta}$ g
<br/>Neglecting buoyancy effect of the fluid, $v=\frac{2}{9} \cdot \frac{\rho}{\eta} r^{2} g$
<br/>Putting the given values, we get $v=\frac{2}{9} \times \frac{10^{3} \times\left(0.9 \times 10^{-3}\right)^{2}}{1.8 \times 10^{-5}} \times 9.8=98 \mathrm{ms}^{-1}$</div>


tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch2_P4.db
title:
what-will-be-the-current-flowing-through-the-6-k-resistor-in-the-circuit-shown-where-the-breakdown-voltage-of-the-zener-is-6-v

slug:
what-will-be-the-current-flowing-through-the-6-k-resistor-in-the-circuit-shown-where-the-breakdown-voltage-of-the-zener-is-6-v-88838

question:
<div class="question">What will be the current flowing through the $6 \mathrm{k} \Omega$ resistor in the circuit shown, where the breakdown voltage of the Zener is $6 \mathrm{V} ?$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_q11.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{2}{3} m A$</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">$1 \mathrm{mA}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$10 \mathrm{mA}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{3}{2} m A$</span> </li> </ul>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_a11.png"/> <br/> <br/>In the given circuit, the zener diode is used as a voltage regulating device. The voltage across $6 \mathrm{k} \Omega$ resistance is $(10-6) \mathrm{V}=4 \mathrm{V}$
<br/>Current through $6 \mathrm{k} \Omega$ resistor, $I=\frac{4 \mathrm{V}}{6 \mathrm{k} \Omega}=\frac{4}{6 \times 10^{3}}=\frac{2}{3} \times 10^{-3}=\frac{2}{3} \mathrm{mA}$</div>


tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch2_P4.db
title:
what-will-be-the-equivalent-resistance-between-the-terminals-a-and-b-of-the-infinite-resistive-network-shown-in-the-figure

slug:
what-will-be-the-equivalent-resistance-between-the-terminals-a-and-b-of-the-infinite-resistive-network-shown-in-the-figure-75644

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/0pQ3RxKvgmldkYk9fDfScYZWeU4V7U3Tqtr2WUYgx64.original.fullsize.png"/><br/> <br/>What will be the equivalent resistance between the terminals A and B of the infinite resistive network shown in the figure?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{(\sqrt{3}+1) \mathrm{R}}{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{(\sqrt{3}-1) R}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3 \frac{R}{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$(\sqrt{3}+1) \mathrm{R}$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(\sqrt{3}+1) \mathrm{R}$</span> </div>

answer:
<div class="solution">Hint:
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/kOkTW84VK1gFCcyr4Tcx3FIl7YTFGbQgCJcC1KQxG1g.original.fullsize.png"/><br/> <br/>$x=2 R+\frac{R x}{R+x}$
<br/>$x^{2}-2 R x-2 R^{2}=0$
<br/>$x=(1+\sqrt{3}) R$</div>


title: what-will-be-the-mass-of-one-atom-of-12-c
slug: what-will-be-the-mass-of-one-atom-of-12-c-81833
question: <div class="question">What will be the mass of one atom of ${ }^{12} \mathrm{C}$ ?</div>
tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1 a.m.u.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$1.9923 \times 10^{-23} \mathrm{~g}$</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">$1.6603 \times 10^{-22} \mathrm{~g}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">6 a.m.u.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1.9923 \times 10^{-23} \mathrm{~g}$</span> </div>

answer:
<div class="solution">Hint: 
<br/>Mass of 1 atom of ${ }^{12} \mathrm{C}=12$ a.m.u. $=12 \times 1.66 \times 10^{-24} \mathrm{~g}=1.9923 \times 10^{-23} \mathrm{~g}$</div>


tags: ['Physics', 'Kinetic Theory of Gases', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch2_P4.db
title:
what-will-be-the-molar-specific-heat-at-constant-volume-of-an-ideal-gas-consisting-of-rigid-diatomic-molecules

slug:
what-will-be-the-molar-specific-heat-at-constant-volume-of-an-ideal-gas-consisting-of-rigid-diatomic-molecules-61341

question:
<div class="question">What will be the molar specific heat at constant volume of an ideal gas consisting of rigid diatomic molecules?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{3}{2} R$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{5}{2} R$</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">C</span> <span class="option-data">$R$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3 R$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{5}{2} R$</span> </div>

answer:
<div class="solution">For a gas at temperature $T$, the internal energy,
<br/>$$
<br/>U=\frac{f}{2} \mu R T
<br/>$$
<br/>where, $f=$ degree of freedom
<br/>$\Rightarrow$ Change in energy, $\Delta U=\frac{f}{2} \mu R \Delta T$
<br/>Also, as we know for any gas heat supplied at constant volume
<br/>$$
<br/>\left(\Delta Q_{V}\right)=\mu C_{V} \Delta T=\Delta U
<br/>$$
<br/>where, $C_{V}=$ molar specific heat at constant volume From Eqs. (i) and (ii), we get
<br/>$$
<br/>C_{V}=\frac{1}{2} f R
<br/>$$
<br/>For diatomic gas, degree of freedom, $f=5$
<br/>$$
<br/>C_{V}=\frac{5}{2} R
<br/>$$</div>


tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch2_P4.db
title:
what-will-be-the-normality-of-the-salt-solution-obtained-by-neutralising-x-ml-y-n-hcl-with-y-ml-x-n-naoh-and-finally-adding-x-y-ml-distilled-water

slug:
what-will-be-the-normality-of-the-salt-solution-obtained-by-neutralising-x-ml-y-n-hcl-with-y-ml-x-n-naoh-and-finally-adding-x-y-ml-distilled-water-98380

question:
<div class="question">What will be the normality of the salt solution obtained by neutralising $x$ mL. $y$ (N) HCl with $y \quad$ mL $x$ (N) $\mathrm{NaOH}$, and finally adding $(x+y) \mathrm{mL}$ distilled water</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{2(x+y)}{x y} N$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{x y}{2(x+y)} N$</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">$\left(\frac{2 x y}{x+y}\right) N$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left(\frac{x+y}{x y}\right) N$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{x y}{2(x+y)} N$</span> </div>

answer:
<div class="solution">The reaction for given reaction is $\mathrm{HCl}+\mathrm{NaOH} \longrightarrow \mathrm{NaCl}+\mathrm{H}_{2} \mathrm{O}$
<br/>Number of moles  	xy	xy	0	0
<br/>Added 		$\quad N V \quad N V$
<br/>Number of moles left 0 	0 	xy	xy
<br/>$\therefore N($ solution $)=\frac{\text { Number of milliequivalent }}{\text { vol. of solution in mililetre }}$</div>


tags: ['Chemistry', 'Solutions', 'WBJEE', 'WBJEE 2021']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$0.5$</span> </div>
source_db: db\MarksBatch2_P4.db
title:
when-20-g-of-naphthoic-acid-c-11-h-8-o-2-is-dissolved-in-50-g-of-benzene-a-freezing-point-depression-of-2-k-is-observed-the-vant-hoff-factor-i-is-k-f-

slug:
when-20-g-of-naphthoic-acid-c-11-h-8-o-2-is-dissolved-in-50-g-of-benzene-a-freezing-point-depression-of-2-k-is-observed-the-vant-hoff-factor-i-is-k-f-47867

question:
<div class="question">When $20 \mathrm{~g}$ of naphthoic acid $\left(\mathrm{C}_{11} \mathrm{H}_{8} \mathrm{O}_{2}\right)$ is dissolved in $50 \mathrm{~g}$ of benzene, a freezing point depression of $2 \mathrm{~K}$ is observed. The vant Hoff factor (i) is $\left[\mathrm{K}_{\mathrm{f}}=1.72^{\circ} \mathrm{K} \mathrm{kg} \mathrm{mol}^{-1}\right]$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$0.5$</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">$1.0$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2.0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3.0$</span> </li> </ul>

answer:
<div class="solution">$\begin{array}{l}
<br/>\Delta \mathrm{T}_{\mathrm{f}}=\mathrm{i} \mathrm{K}_{\mathrm{f}} \mathrm{m} \\
<br/>2=\mathrm{i} \times 1.72 \times \frac{20 \times 1000}{172 \times 50} \\
<br/>\therefore \mathrm{i}=\frac{2}{0.01 \times 2 \times 200}=\frac{1}{2}=0.5
<br/>\end{array}$</div>


tags: ['Physics', 'Thermal Properties of Matter', 'WBJEE', 'WBJEE 2020']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$0.1$</span> </div>
source_db: db\MarksBatch2_P4.db
title:
when-100-g-of-boiling-water-at-10-0-c-is-added-into-a-calorimeter-containing-300-g-of-cold-water-at-1-0-c-temperature-of-the-mixture-becomes-2-0-c-the

slug:
when-100-g-of-boiling-water-at-10-0-c-is-added-into-a-calorimeter-containing-300-g-of-cold-water-at-1-0-c-temperature-of-the-mixture-becomes-2-0-c-the-56878

question:
<div class="question">When $100 \mathrm{~g}$ of boiling water at $100^{\circ} \mathrm{C}$ is added into a calorimeter containing $300 \mathrm{~g}$ of cold water at $10^{\circ} \mathrm{C}$, temperature of the mixture becomes $20^{\circ} \mathrm{C}$. Then a metallic block of mass $1 \mathrm{~kg}$ at $10^{\circ} \mathrm{C}$ is dipped into the mixture in the calorimeter. After reaching thermal equilibrium, the final temperature becomes $19^{\circ} \mathrm{C}$. What is the specific heat of the metal in C.G.S. unit?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.01$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.3$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.09$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$0.1$</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>

answer:
<div class="solution">Hint: 
<br/>Let, heat capacity of calorimeter = ms
<br/>$\begin{aligned}
<br/>&amp; 100 \times 1 \times 80=300 \times 1 \times 10+\mathrm{ms} \times 10 \\
<br/>\therefore \mathrm{ms}=500 \mathrm{Cal} /{ }^{\circ} \mathrm{C}
<br/>\end{aligned}$
<br/>Again, $(100+300) \times 1 \times 1+500 \times 1=1000 \times S_{b} \times 9$
<br/>$\therefore \mathrm{S}_{\mathrm{b}}=0.1 \mathrm{Cal} / \mathrm{g}^{\circ} \mathrm{C}$</div>


tags: ['Physics', 'Alternating Current', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch2_P4.db
title:
when-a-60-mh-inductor-and-a-resistor-are-connected-in-series-with-an-ac-voltage-source-the-voltage-leads-the-current-by-6-0-if-the-inductor-is-replace

slug:
when-a-60-mh-inductor-and-a-resistor-are-connected-in-series-with-an-ac-voltage-source-the-voltage-leads-the-current-by-6-0-if-the-inductor-is-replace-35353

question:
<div class="question">When a $60 \mathrm{mH}$ inductor and a resistor are connected in series with an AC voltage source, the voltage leads the current by $60^{\circ}$. If the inductor is replaced by a $0.5 \mu \mathrm{F}$ capacitor, the voltage lags behind the current by $30^{\circ} .$ What is the frequency of the AC supply?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{1}{2 \pi} \times 10^{4} \mathrm{Hz}$</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">$\frac{1}{\pi} \times 10^{4} \mathrm{Hz}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{3}{2 \pi} \times 10^{4} \mathrm{Hz}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{2 \pi} \times 10^{8} \mathrm{Hz}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{2 \pi} \times 10^{4} \mathrm{Hz}$</span> </div>

answer:
<div class="solution">Given, inductance of inductor, $L=60 \mathrm{mH}$
<br/>$$
<br/>=60 \times 10^{-3} \mathrm{H}
<br/>$$
<br/>Phase difference between voltage and current in $L-R$ circuit, $\theta_{1}=60^{\circ}$
<br/>Capacitance of capacitor, $C=0.5 \mu \mathrm{F}=0.5 \times 10^{-6} \mathrm{F}$ Phase difference between voltage and current in $\vec{R}-C$ circuit, $\theta_{2}=30^{\circ}$
<br/>For $L-R$ circuit.
<br/>$$
<br/>\begin{array}{l}
<br/>\tan \theta_{1}=\frac{X_{L}}{R} \\
<br/>\tan \theta_{1}=\frac{\omega L}{R} \quad \ldots(\mathrm{i})\left[\because X_{L}=\omega L\right]
<br/>\end{array}
<br/>$$
<br/>Similarly, for $R$ - $C$ circuit,
<br/>$$
<br/>\tan \theta_{2}=\frac{X_{C}}{R}
<br/>$$
<br/>$$
<br/>\tan \theta_{2}=\frac{\frac{1}{{\omega C}}}{R} \quad \ldots(\mathrm{ii})\left[\because X_{C}=\frac{1}{\omega C}\right]
<br/>$$
<br/>From Eqs. (i) and (ii), we get
<br/>$$
<br/>\begin{array}{l}
<br/>\frac{\tan \theta_{1}}{\tan \theta_{2}}=\frac{\omega L}{R \times \frac{1}{\omega C R}}=\omega^{2} L C \\
<br/>\frac{\tan 60^{\circ}}{\tan 30^{\circ}}=\omega^{2} L C \\
<br/>\frac{\sqrt{3}}{1 / \sqrt{3}}=\omega^{2} L C \\
<br/>\omega^{2} L C=3 \\
<br/>\omega^{2}=\frac{3}{L C} \\
<br/>\omega^{2}=\frac{3}{60 \times 10^{-3} \times 0.5 \times 10^{-6}} \\
<br/>\omega^{2}=\frac{3}{30 \times 10^{-9}} \\
<br/>\omega=\sqrt{10^{8}} \\
<br/>\omega=10^{4}
<br/>\end{array}
<br/>$$
<br/>As we know that,
<br/>$$
<br/>\omega=2 \pi f
<br/>$$
<br/>$$
<br/>f=\frac{\omega}{2 \pi}=\frac{10^{4}}{2 \pi} \mathrm{Hz}=\frac{1}{2 \pi} \times 10^{4} \mathrm{Hz}
<br/>$$</div>


tags: ['Physics', 'Dual Nature of Matter', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch2_P4.db
title:
when-a-certain-metal-surface-is-illuminated-with-light-of-frequency-v-the-stopping-potential-for-photoelectric-current-is-v-0-when-the-same-surface-is

slug:
when-a-certain-metal-surface-is-illuminated-with-light-of-frequency-v-the-stopping-potential-for-photoelectric-current-is-v-0-when-the-same-surface-is-36598

question:
<div class="question">When a certain metal surface is illuminated with light of frequency $v$, the stopping potential for photoelectric current is $V_{0}$. When the same surface is illuminated by light of frequency $\frac{v}{2}$ the stopping potential is $\frac{V_{0}}{4} .$ The threshold
<br/>frequency for photoelectric, emission is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{v}{6}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{v}{3}$</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">$\frac{2 v}{3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{4 v}{3}$</span> </li> </ul>

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

answer:
<div class="solution">Ist case
<br/>$$
<br/>\begin{array}{l}
<br/>h v=h v_{0}+e V_{0} \\
<br/>\frac{h v}{2}=h v_{0}+\frac{e V_{0}}{4}
<br/>\end{array}
<br/>$$
<br/>Solving Eqs. (i) and (ii), we get
<br/>$$
<br/>v_{0}=\frac{v}{3}
<br/>$$</div>


tags: ['Physics', 'Electromagnetic Induction', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch2_P4.db
title:
when-a-dc-voltage-is-applied-at-the-two-ends-of-a-circuit-kept-in-closed-box-it-is-observed-that-the-current-gradually-increases-from-zero-to-a-certai

slug:
when-a-dc-voltage-is-applied-at-the-two-ends-of-a-circuit-kept-in-closed-box-it-is-observed-that-the-current-gradually-increases-from-zero-to-a-certai-46726

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/IT47_BpPG4TsYbLFXz8roz9CQCxzokYJP32oH7eMTXE.original.fullsize.png"/><br/> <br/>When a DC voltage is applied at the two ends of a circuit kept in closed box, it is observed that the current gradually increases from zero to a certain value and then remains constant. What do you think that the circuit contains?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">A resistor alone</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">A capacitor alone</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">A resistor and an inductor in series</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 resistor and a capacitor in series</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A resistor and an inductor in series</span> </div>

answer:
<div class="solution">Hint: 
<br/>LR circuit transient
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/Vx-pb4Ww6lb3QDCLzh8EYByxuW0hvoPWzQa6xkmoJuE.original.fullsize.png"/></div>


tags: ['Chemistry', 'd and f Block Elements', 'WBJEE', 'WBJEE 2010']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">+6</span> </div>
source_db: db\MarksBatch2_P4.db
title:
when-a-manganous-salt-is-fused-with-a-mixture-of-kno-3-and-solid-naoh-the-oxidation-number-of-mn-changes-from-2-to

slug:
when-a-manganous-salt-is-fused-with-a-mixture-of-kno-3-and-solid-naoh-the-oxidation-number-of-mn-changes-from-2-to-31499

question:
<div class="question">When a manganous salt is fused with a mixture of $\mathrm{KNO}_3$ and solid $\mathrm{NaOH}$ the oxidation number of Mn changes from +2 to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">+4</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">+3</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">+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">D</span> <span class="option-data">+7</span> </li> </ul>

answer:
<div class="solution">$$<br/>\text { Hints : } \mathrm{Mn}^{+2}+\mathrm{NO}_3^{-}+\mathrm{O} \overline{\mathrm{H}} \rightarrow \stackrel{(+6)}{\mathrm{M} \mathrm{nO}_4^{-2}}+\mathrm{H}_2 \mathrm{O}<br/>$$</div>


title: when-a-particle-executing-shm-oscillates-with-a-frequency-v-then-the-kinetic-energy-of-the-particle
tags: ['Physics', 'Oscillations', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch2_P4.db
slug:
when-a-particle-executing-shm-oscillates-with-a-frequency-v-then-the-kinetic-energy-of-the-particle-33729

question:
<div class="question">When a particle executing SHM oscillates with a frequency $v$, then the kinetic energy of the particle</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">changes periodically with a frequency of $v$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">changes periodically with a frequency of $2 \mathrm{v}$</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">changes periodically with a frequency of $\mathrm{v} / 2$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">remains constant</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">changes periodically with a frequency of $2 \mathrm{v}$</span> </div>

answer:
<div class="solution">We know that
<br/>Kinetic energy $K=\frac{1}{2} m u^{2}$
<br/>where $u=\frac{d y}{d t}=\omega a \cos \omega t$
<br/>So. $K=\frac{1}{2} m \omega^{2} a^{2} \cos ^{2} \omega t$
<br/>Hence, kinetic energy varies periodically with double the frequency of SHM. So, when a particle executing SHM oscillates with a frequency v, then the kinetic energy of particle changes periodically with a frequency of $2 v$.</div>


tags: ['Physics', 'Semiconductors', 'JEE Main']
source_db: db\MarksBatch2_P4.db
title:
when-a-semiconducting-device-is-connected-in-series-with-a-battery-and-a-resistance-a-current-is-found-to-flow-in-the-circuit-if-however-the-polarity--1

slug:
when-a-semiconducting-device-is-connected-in-series-with-a-battery-and-a-resistance-a-current-is-found-to-flow-in-the-circuit-if-however-the-polarity-1-53635

question:
<div class="question">When a semiconducting device is connected in series with a battery and a resistance, a current is found to flow in the circuit. If however, the polarity of the battery is reversed, practically no current flows in the circuit. The device may be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">a $p$ -type semiconductor</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">a $n$ -type semiconductor</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">an intrinsic semiconductor</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">a $p-n$ junction</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">a $p-n$ junction</span> </div>

answer:
<div class="solution">When the battery and resistance is connected with $p n$ diode,
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_phy_a26.png"/> <br/> <br/>In case of forward bias that $p$ is connected to + ve terminal of battery, current flows. If one reverse the polarity i.e., $p$ -end is made negative, no current flows in semiconductor diode.</div>


tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch2_P4.db
title:
when-a-semiconducting-device-is-connected-in-series-with-a-battery-and-a-resistance-a-current-is-found-to-flow-in-the-circuit-if-however-the-polarity-

slug:
when-a-semiconducting-device-is-connected-in-series-with-a-battery-and-a-resistance-a-current-is-found-to-flow-in-the-circuit-if-however-the-polarity-98097

question:
<div class="question">When a semiconducting device is connected in series with a battery and a resistance, a current is found to flow in the circuit. If however, the polarity of the battery is reversed, practically no current flows in the circuit. The device may be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">a $p$ -type semiconductor</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">a $n$ -type semiconductor</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">an intrinsic semiconductor</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">a $p-n$ junction</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">a $p-n$ junction</span> </div>

answer:
<div class="solution">When the battery and resistance is connected with $p n$ diode,
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_phy_a26.png"/> <br/> <br/>In case of forward bias that $p$ is connected to + ve terminal of battery, current flows. If one reverse the polarity i.e., $p$ -end is made negative, no current flows in semiconductor diode.</div>


tags: ['Physics', 'Work Power Energy', 'WBJEE', 'WBJEE 2012']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$4 E$</span> </div>
source_db: db\MarksBatch2_P4.db
title:
when-a-spring-is-stretched-by-10-cm-the-potential-energy-stored-is-e-when-the-spring-is-stretched-by-10-cm-more-the-potential-energy-stored-in-the-spr

slug:
when-a-spring-is-stretched-by-10-cm-the-potential-energy-stored-is-e-when-the-spring-is-stretched-by-10-cm-more-the-potential-energy-stored-in-the-spr-53052

question:
<div class="question">When a spring is stretched by $10 \mathrm{cm}$, the potential energy stored is $E$. When the spring is stretched by $10 \mathrm{cm}$ more, the potential energy stored in the spring becomes</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 E$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$4 E$</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">$6 E$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$10 E$</span> </li> </ul>

answer:
<div class="solution">For 1st situation,
<br/>$$
<br/>E=\frac{1}{2} k\left(10 \times 10^{-2}\right)^{2}
<br/>$$
<br/>For 2nd situation,
<br/>$$
<br/>E^{\prime}=\frac{1}{2} k\left(20 \times 10^{-2}\right)^{2}
<br/>$$
<br/>On comparing Eqs. (i) and (ii), we get
<br/>$$
<br/>E^{\prime}=4 E
<br/>$$</div>


title: when-agcl-is-treated-with-kcn
slug: when-agcl-is-treated-with-kcn-68468
question: <div class="question">When $\mathrm{AgCl}$ is treated with $\mathrm{KCN}$</div>
tags: ['Chemistry', 'Coordination Compounds', 'WBJEE', 'WBJEE 2010']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{Ag}$ is precipitated</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">a complex ion is formed</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">double decomposition takes place</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">no reaction takes place</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">a complex ion is formed</span> </div>

answer:
<div class="solution">Hints: $\mathrm{AgCl}+2 \mathrm{KCN} \rightarrow \mathrm{K}\left[\mathrm{Ag}(\mathrm{CN})_2\right]+\mathrm{KCl}$</div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: db\MarksBatch2_P4.db
title:
when-an-a-c-source-of-emf-e-with-frequency-100-hz-is-connected-across-a-circuit-the-phase-difference-between-e-and-current-i-in-the-circuit-is-observe-1

slug:
when-an-a-c-source-of-emf-e-with-frequency-100-hz-is-connected-across-a-circuit-the-phase-difference-between-e-and-current-i-in-the-circuit-is-observe-1-37656

question:
<div class="question">When an $A C$ source of emf $E$ with frequency $\omega=100 \mathrm{~Hz}$ is connected across a circuit, the phase difference between<br/>$E$ and current I in the circuit is observed to be $\frac{\pi}{4}$ as shown in the figure. If the circuit consist of only $\mathrm{RC}$ or $\mathrm{RL}$ in series, then<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/scgDMvLRCTaVROqZhcXm5lhCPNUh-IIFfpUDwYZCARI.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{R}=1 \mathrm{k} \Omega, \mathrm{C}=5 \mu \mathrm{F}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{R}=1 \mathrm{k} \Omega, \mathrm{L}=10 \mathrm{H}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{R}=1 \mathrm{k} \Omega, \mathrm{L}=1 \mathrm{H}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{R}=1 \mathrm{k} \Omega, \mathrm{C}=10 \mu \mathrm{F}$</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">$\mathrm{R}=1 \mathrm{k} \Omega, \mathrm{C}=10 \mu \mathrm{F}$</span> </div>

answer:
<div class="solution">.. Since supply voltage lags the current $\operatorname{By}(\phi=\pi / 4)$<br/>$$<br/>\begin{aligned}<br/>&amp;\tan \phi=\frac{\mathrm{X}_{\mathrm{C}}}{\mathrm{R}}=1, \mathrm{X}_{\mathrm{C}}=\mathrm{R} \ldots \ldots(1) \\<br/>&amp;\mathrm{X}_{\mathrm{C}}=\frac{1}{\omega \mathrm{C}}=\frac{1}{100 \times 10 \times 10^{-6}}=1 \mathrm{k} \Omega=\mathrm{R}<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Alternating Current', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch2_P4.db
title:
when-an-a-c-source-of-emf-e-with-frequency-100-hz-is-connected-across-a-circuit-the-phase-difference-between-e-and-current-i-in-the-circuit-is-observe

slug:
when-an-a-c-source-of-emf-e-with-frequency-100-hz-is-connected-across-a-circuit-the-phase-difference-between-e-and-current-i-in-the-circuit-is-observe-23926

question:
<div class="question">When an $A C$ source of emf $E$ with frequency $\omega=100 \mathrm{~Hz}$ is connected across a circuit, the phase difference between<br/>$E$ and current I in the circuit is observed to be $\frac{\pi}{4}$ as shown in the figure. If the circuit consist of only $\mathrm{RC}$ or $\mathrm{RL}$ in series, then<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/scgDMvLRCTaVROqZhcXm5lhCPNUh-IIFfpUDwYZCARI.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{R}=1 \mathrm{k} \Omega, \mathrm{C}=5 \mu \mathrm{F}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{R}=1 \mathrm{k} \Omega, \mathrm{L}=10 \mathrm{H}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{R}=1 \mathrm{k} \Omega, \mathrm{L}=1 \mathrm{H}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{R}=1 \mathrm{k} \Omega, \mathrm{C}=10 \mu \mathrm{F}$</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">$\mathrm{R}=1 \mathrm{k} \Omega, \mathrm{C}=10 \mu \mathrm{F}$</span> </div>

answer:
<div class="solution">.. Since supply voltage lags the current $\operatorname{By}(\phi=\pi / 4)$<br/>$$<br/>\begin{aligned}<br/>&amp;\tan \phi=\frac{\mathrm{X}_{\mathrm{C}}}{\mathrm{R}}=1, \mathrm{X}_{\mathrm{C}}=\mathrm{R} \ldots \ldots(1) \\<br/>&amp;\mathrm{X}_{\mathrm{C}}=\frac{1}{\omega \mathrm{C}}=\frac{1}{100 \times 10 \times 10^{-6}}=1 \mathrm{k} \Omega=\mathrm{R}<br/>\end{aligned}<br/>$$</div>


title: when-aniline-is-nitrated-with-nitrating-mixture-in-ice-cold-condition-the-major-product-obtained-is
tags: ['Chemistry', 'Amines', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch2_P4.db
slug:
when-aniline-is-nitrated-with-nitrating-mixture-in-ice-cold-condition-the-major-product-obtained-is-10843

question:
<div class="question">When aniline is nitrated with nitrating mixture in ice cold condition, the major product obtained is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$p$ -nitroaniline</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">2,4 dinitroaniline</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$o$ -nitroaniline</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$m$ nitroaniline</span> </li> </ul>

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

answer:
<div class="solution">Direct nitration of aniline with nitric acid gives a complex mixture of mono, di- and tri-nitro compounds and oxidation products. If $-\mathrm{NH}_{2}$ group is protected by acetylation and then nitrated with nitrating mixture, $p$ -isomer is the main product.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_a26.png"/></div>


tags: ['Chemistry', 'Practical Chemistry', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch2_P4.db
title:
when-bacl-2-is-added-to-an-aqueous-salt-solution-a-white-precipitate-is-obtained-the-anion-among-co-3-2-so-3-2-and-so-4-2-that-was-present-in-the-solu

slug:
when-bacl-2-is-added-to-an-aqueous-salt-solution-a-white-precipitate-is-obtained-the-anion-among-co-3-2-so-3-2-and-so-4-2-that-was-present-in-the-solu-86444

question:
<div class="question">When $\mathrm{BaCl}_{2}$ is added to an aqueous salt solution, a white precipitate is obtained. The anion among $\mathrm{CO}_{3}^{2-}, \mathrm{SO}_{3}^{2-}$ and $\mathrm{SO}_{4}^{2-}$ that was present in the solution can be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{CO}_{3}^{2-}$ but not any of the other two</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$S O_{3}^{2-}$ but not any of the other two</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{SO}_{4}^{2-}$ but not any of the other two</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Any of them</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">Any of them</span> </div>

answer:
<div class="solution">$\because$ If $\mathrm{CO}_{3}^{2-}, \mathrm{SO}_{3}^{2-}$ and $\mathrm{SO}_{4}^{2-}$ are present alongwith $\mathrm{BaCl}_{2}$, these can also show white precipitate (as precipitate of all these are also white ).</div>


tags: ['Chemistry', 'd and f Block Elements', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch2_P4.db
title:
when-h-2-o-2-is-shaken-with-an-acidified-solution-of-k-2-cr-2-o-7-in-the-presence-of-ether-the-cthereal-layer-turns-blue-due-to-the-formation-of

slug:
when-h-2-o-2-is-shaken-with-an-acidified-solution-of-k-2-cr-2-o-7-in-the-presence-of-ether-the-cthereal-layer-turns-blue-due-to-the-formation-of-79194

question:
<div class="question">When $\mathrm{H}_{2} \mathrm{O}_{2}$ is shaken with an acidified solution of $\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$ in the presence of ether, the cthereal layer turns blue due to the formation of</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{Cr}_{2} \mathrm{O}_{3}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{CrO}_{4}^{2-}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Cr}_{2}\left(\mathrm{SO}_{4}\right)_{3}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{CrO}_{5}$</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">$\mathrm{CrO}_{5}$</span> </div>

answer:
<div class="solution">$\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}+\mathrm{H}_{2} \mathrm{SO}_{4}+4 \mathrm{H}_{2} \mathrm{O}_{2} \rightarrow$ $\mathrm{K}_{2} \mathrm{SO}_{4}+5 \mathrm{H}_{2} \mathrm{O}+2 \mathrm{CrO}_{5}$</div>


title: when-light-is-refracted-from-a-surface-which-of-its-following-physical-parameters-does-not-change
tags: ['Physics', 'Ray Optics', 'WBJEE', 'WBJEE 2015']
answer: <div class="solution">When light is refracted its frequency will remain unchanged.</div>
source_db: db\MarksBatch2_P4.db
slug:
when-light-is-refracted-from-a-surface-which-of-its-following-physical-parameters-does-not-change-27115

question:
<div class="question">When light is refracted from a surface, which of its following physical parameters does not change?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Velocity</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Amplitude</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Frequency</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">Wavelength</span> </li> </ul>

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


tags: ['Physics', 'Dual Nature of Matter', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch2_P4.db
title:
when-light-of-frequency-v-1-is-incident-on-a-metal-with-work-function-w-where-h-v-1-w-then-photocurrent-falls-to-zero-at-a-stopping-potential-of-v-1-i

slug:
when-light-of-frequency-v-1-is-incident-on-a-metal-with-work-function-w-where-h-v-1-w-then-photocurrent-falls-to-zero-at-a-stopping-potential-of-v-1-i-12786

question:
<div class="question">When light of frequency $v_{1}$ is incident on a metal with work function $W$ (where $h v_{1}&gt;w$ ), then photocurrent falls to zero at a stopping potential of $V_{1}$. If the frequency of light is increased to $v_{2},$ the stopping potential changes to $V_{2}$. Therefore, the charge of an electron is given by</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{W\left(v_{2}+v_{1}\right)}{v_{1} V_{2}+v_{2} V_{1}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{W\left(v_{2}+v_{1}\right)}{v_{1} V_{1}+v_{2} V_{2}}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{W\left(v_{2}-v_{1}\right)}{v_{1} V_{2}-v_{2} V_{1}}$</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">$\frac{W\left(v_{2}-v_{1}\right)}{v_{2} V_{2}-v_{1} V_{1}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{W\left(v_{2}-v_{1}\right)}{v_{1} V_{2}-v_{2} V_{1}}$</span> </div>

answer:
<div class="solution">From Einstein's photoelectric equation,
<br/>$$
<br/>\begin{array}{l}
<br/>h v=W+e V \\
<br/>W=\text { Work function }
<br/>\end{array}
<br/>$$
<br/>$v=$ Frequency of incident photon 
<br/>$V=$ Stopping potential 
<br/>For a photon of frequency $v_{1},$
<br/>$$
<br/>h v_{1}=W+e V_{1}
<br/>$$
<br/>For photon of frequency $v_{2}$
<br/>$$
<br/>h v_{2}=W+e V_{2}
<br/>$$
<br/>Divided Eq. (i) by Eq. (ii),
<br/>$$
<br/>\begin{aligned}
<br/>\frac{h v_{1}}{h v_{2}} &amp;=\frac{W+e V_{1}}{W+e V_{2}} \\
<br/>\frac{v_{1}}{v_{2}} &amp;=\frac{W+e V_{1}}{W+e V_{2}}
<br/>\end{aligned}
<br/>$$
<br/>$\Rightarrow W v_{1}+e V_{2} v_{1}=W v_{2}+e V_{1} v_{2}$
<br/>Solving above equation, $\Rightarrow \quad e=\frac{W\left(v_{2}-v_{1}\right)}{V_{2} v_{1}-V_{1} v_{2}}$</div>


tags: ['Chemistry', 'General Organic Chemistry', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch2_P4.db
title:
when-phenol-is-treated-with-d-2-so-4-d-2-o-some-of-the-hydrogens-get-exchanged-the-final-product-in-this-exchange-reaction-is

slug:
when-phenol-is-treated-with-d-2-so-4-d-2-o-some-of-the-hydrogens-get-exchanged-the-final-product-in-this-exchange-reaction-is-39385

question:
<div class="question">When phenol is treated with $\mathrm{D}_{2} \mathrm{SO}_{4} / \mathrm{D}_{2} \mathrm{O},$ some of the hydrogens get exchanged. The final product in this exchange reaction is</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/2014_che_q47_opta.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/2014_che_q47_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/2014_che_q47_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/2014_che_q47_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/2014_che_q47_opta.png"/></span> </div>

answer:
<div class="solution">In acidic medium, phenol exists in following resonating structures.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_a47.png"/> <br/>Since, o/p positions are electron rich sites, so electrophile will attack on these site, i.e. hydrogen of these sites get exchanged by D (deuterium). Hence, the final product of the<img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_a47a.png"/></div>


tags: ['Physics', 'Alternating Current', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch2_P4.db
title:
when-the-frequency-of-the-a-c-voltage-applied-to-a-series-lcr-circuit-is-gradually-increased-from-a-low-value-the-impedance-of-the-circuit

slug:
when-the-frequency-of-the-a-c-voltage-applied-to-a-series-lcr-circuit-is-gradually-increased-from-a-low-value-the-impedance-of-the-circuit-93568

question:
<div class="question">When the frequency of the $A C$ voltage applied to a series LCR circuit is gradually increased from a low value, the impedance of the circuit</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">monotonically increases</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">first increases and then decreases</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">first decreases and then increases</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">monotonically decreases</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">first increases and then decreases</span> </div>

answer:
<div class="solution">The impedance of LCR circuit $Z=\sqrt{R^{2}+\left(\omega_{c}-\frac{1}{\omega_{c}}\right)^{2}}$
<br/>Where, $R=$ Resistance $L=$ Inductance
<br/>$C=$ Capacitance 
<br/>When frequency of AC voltage applied to a series LCR circuit, it will first increase and resonance state $\omega_{i}=\frac{1}{\omega_{c}},$ it will decrease. In that state $(Z=R),$ it will be minimum. So, it will first increases and then decreases.</div>


tags: ['Physics', 'Wave Optics', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch2_P4.db
title:
when-the-frequency-of-the-light-used-is-changed-from-4-1-0-14-s-1-to-5-1-0-14-s-1-the-angular-width-of-the-principal-central-maximum-in-a-single-slit-

slug:
when-the-frequency-of-the-light-used-is-changed-from-4-1-0-14-s-1-to-5-1-0-14-s-1-the-angular-width-of-the-principal-central-maximum-in-a-single-slit-27634

question:
<div class="question">When the frequency of the light used is changed from $4 \times 10^{14} \mathrm{s}^{-1}$ to $5 \times 10^{14} \mathrm{s}^{-1}$. the angular width of the principal (central) maximum in a single slit Fraunhoffer diffraction pattern changes by 0.6 radian. What is the width of the slit (assume that the experiment is performed in vacuum</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1.5 \times 10^{-7} \mathrm{m}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3 \times 10^{-7} \mathrm{m}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$5 \times 10^{-7} \mathrm{m}$</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><li class=""> <span class="option-label">D</span> <span class="option-data">$6 \times 10^{-7} \mathrm{m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$5 \times 10^{-7} \mathrm{m}$</span> </div>

answer:
<div class="solution">Given, initial frequency of light,
<br/>$$
<br/>f_{1}=4 \times 10^{14} \mathrm{s}^{-1}
<br/>$$
<br/>Final frequency of light, $f_{2}=5 \times 10^{14} \mathrm{s}^{-1}$
<br/>Change in wavelength $, \Delta \lambda=\lambda_{1}-\lambda_{2}$
<br/>or
<br/>$$
<br/>\Delta \lambda=\frac{c}{f_{1}}-\frac{c}{f_{2}}
<br/>$$
<br/>$$
<br/>\begin{array}{l}
<br/>=\frac{3 \times 10^{8}}{4 \times 10^{14}}-\frac{3 \times 10^{8}}{5 \times 10^{14}} \\
<br/>=\frac{3 \times 10^{8}}{10^{14}}\left(\frac{1}{4}-\frac{1}{5}\right) \\
<br/>=\frac{3 \times 10^{8}}{10^{14}} \times \frac{1}{20} \\
<br/>=1.5 \times 10^{-7} \mathrm{m}
<br/>\end{array}
<br/>$$
<br/>Now, we know that, Angular width of central maxima,
<br/>$$
<br/>\begin{array}{l}
<br/>\theta=\frac{2 \lambda}{d} \text { or } \Delta \theta=\frac{2 \Delta \lambda}{d} \\
<br/>d=\frac{2 \Delta \lambda}{\Delta \theta}
<br/>\end{array}
<br/>$$
<br/>Here, $\Delta \theta=0.6$ radian
<br/>$$
<br/>d=\frac{2 \times 1.5 \times 10^{-7}}{0.6}=5 \times 10^{-7} \mathrm{m}
<br/>$$</div>


tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch2_P4.db
title:
when-the-value-of-r-in-the-balanced-nheatstone-bridge-shown-in-the-figure-is-increased-from-5-to-7-the-value-of-shas-to-increased-by-3-in-order-to-mai

slug:
when-the-value-of-r-in-the-balanced-nheatstone-bridge-shown-in-the-figure-is-increased-from-5-to-7-the-value-of-shas-to-increased-by-3-in-order-to-mai-81566

question:
<div class="question">When the value of $R$ in the balanced Nheatstone bridge, shown in the figure, is increased from $5 \Omega$ to $7 \Omega$, the value of shas to increased by $3 \Omega$ in order to maintain the palance. What is the initial values of $S$ ?  <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2019_phy_q26.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2.5 \Omega$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3 \Omega$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$5 \Omega$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$7.5 \Omega$</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">$7.5 \Omega$</span> </div>

answer:
<div class="solution">According to the balanced condition of Wheatstone bridge.
<br/>In the first case,
<br/>$$
<br/>\begin{array}{l}
<br/>\frac{P}{Q}=\frac{R}{S} \\
<br/>\frac{P}{Q}=\frac{5}{S}....(i)
<br/>\end{array}
<br/>$$
<br/>In the second case
<br/>$$
<br/>\frac{P}{Q}=\frac{7}{S+3}....(ii)
<br/>$$
<br/>From Eqs. (i) and (ii), we get
<br/>$\begin{aligned} \frac{5}{S} &amp;=\frac{7}{S+3} \\ 5(S+3) &amp;=7 S \\ 5 S+15 &amp;=7 S \\ 2 S &amp;=15 \\ S &amp;=7.5 \Omega \end{aligned}$</div>


title: which-atomic-species-cannot-be-used-as-a-nuclear-fuel
slug: which-atomic-species-cannot-be-used-as-a-nuclear-fuel-86278
question: <div class="question">Which atomic species cannot be used as a nuclear fuel?</div>
tags: ['Chemistry', 'd and f Block Elements', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">${ }_{92}^{233} U$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">${ }_{92}^{235} U$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">${ }_{94}^{239} \mathrm{Pu}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">${ }_{92}^{238} U$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">${ }_{92}^{238} U$</span> </div>

answer:
<div class="solution">Among the given options, ${ }_{92} \mathrm{U}^{238}$ is an isotope of uranium but cannot be used as a nuclear-fuel. U- 238 is non-fissile, i.e., it does not undergo fission by thermal neutrons. The energy released when U-238 absorbs a neutron is insufficient to carry out nuclear fission. Hence, (d) is the correct option.</div>


title: which-information-below-regarding-this-reaction-is-applicable-1
slug: which-information-below-regarding-this-reaction-is-applicable-1-91982
tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'JEE Main']
source_db: db\MarksBatch2_P4.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/1X5Rib5rqxArK7UKVaSa9DbqK6vZM1mO1qfH75EiQ-c.original.fullsize.png"/><br/> <br/>Which information below regarding this reaction is applicable?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">It follows $\mathrm{S}_{\mathrm{N}} 2$ pathway, because it is a primary alkyl chloride.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">It follows $S_{N} 1$ pathway, because the intermediate carbocation is resonance stabilized.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{S}_{\mathrm{N}} 1$ pathway is not followed, because the intermediate carbocation is destabilised by $-1$ effect of oxygen</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">A mixed $\mathrm{S}_{\mathrm{N}} 1$ and $\mathrm{S}_{\mathrm{N}} 2$ pathway is followed.</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">A mixed $\mathrm{S}_{\mathrm{N}} 1$ and $\mathrm{S}_{\mathrm{N}} 2$ pathway is followed.</span> </div>

answer:
<div class="solution">Hint:
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/LSMlRvFXlsi5I9waaTJM8BTzXCVhV8Oe4FLCR0iuZTU.original.fullsize.png"/><br/> <br/>$\mathrm{S}_{\mathrm{N}} 2$ is also facilitated by OH due to resonance stablization of transition state.</div>


title: which-of-the-following-arrangements-is-correct-in-respect-of-solubility-in-water
slug: which-of-the-following-arrangements-is-correct-in-respect-of-solubility-in-water-62710
tags: ['Chemistry', 'Practical Chemistry', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch2_P4.db
question:
<div class="question">Which of the following arrangements is correct in respect of solubility in water?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{CaSO}_{4}&gt;\mathrm{BaSO}_{4}&gt;\mathrm{BeSO}_{4}&gt;\mathrm{MgSO}_{4}&gt;\mathrm{SrSO}_{4}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{BeSO}_{4}&gt;\mathrm{MgSO}_{4}&gt;\mathrm{CaSO}_{4}&gt;\mathrm{SrSO}_{4}&gt;\mathrm{BaSO}_{4}$</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">$\mathrm{BaSO}_{4}&gt;\mathrm{Sr} \mathrm{SO}_{4}&gt;\mathrm{CaSO}_{4}&gt;\mathrm{MgSO}_{4}&gt;\mathrm{BeSO}_{4}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{BeSO}_{4}&gt;\mathrm{CaSO}_{4}&gt;\mathrm{MgSO}_{4}&gt;\mathrm{SrSO}_{4}&gt;\mathrm{BaSO}_{4}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{BeSO}_{4}&gt;\mathrm{MgSO}_{4}&gt;\mathrm{CaSO}_{4}&gt;\mathrm{SrSO}_{4}&gt;\mathrm{BaSO}_{4}$</span> </div>

answer:
<div class="solution">The correct order of solubility of sulphates in water is
<br/>$\mathrm{BeSO}_{4}&gt;\mathrm{MgSO}_{4}&gt;\mathrm{CaSO}_{4}&gt;\mathrm{SrSO}_{4}&gt;\mathrm{BaSO}_{4}$
<br/>Solublity of 2nd group sulphates decreases as we down the group due to less release of hydration energy. $\mathrm{Be}^{2+}    &lt; \mathrm{Mg}^{2+} &lt; \mathrm{Ca}^{2+} &lt; \mathrm{Sr}^{2+} &lt; \mathrm{Ba}^{24}$ (lonic Size)
<br/>As hydration energy decreases more rapidly than latice energy, the solubility decreases down the group. Hydration Energy $=\frac{\text { Charge }}{\text { Size }}$
<br/>While lathice energy almost remains constant. Hence, solubility decreases.</div>


title: which-of-the-following-atoms-should-have-the-highest-1-electron-affinity
slug: which-of-the-following-atoms-should-have-the-highest-1-electron-affinity-65991
tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'WBJEE', 'WBJEE 2017']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">F</span> </div>
source_db: db\MarksBatch2_P4.db
question:
<div class="question">Which of the following atoms should have the highest $1^{\prime \prime}$ electron affinity?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">F</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">$\mathrm{N}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">C</span> </li> </ul>

answer:
<div class="solution">$\because$ F-atom has 2 nd highest electron affinity
<br/>(Cl has highest) in the periodic table
<br/>$\therefore$ Among the given options F-has highest electron gain affinity</div>


title: which-of-the-following-carbocations-will-be-most-stable
slug: which-of-the-following-carbocations-will-be-most-stable-27332
question: <div class="question">Which of the following carbocations will be most stable?</div>
tags: ['Chemistry', 'General Organic Chemistry', 'WBJEE', 'WBJEE 2009']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{Ph}_3 \mathrm{C}^{++}$</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">$\mathrm{CH}_3-\stackrel{+}{\mathrm{C}} \mathrm{H}_3$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left(\mathrm{CH}_3\right)_2 \stackrel{+}{\mathrm{C}} \mathrm{H}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{CH}_2=\mathrm{CH}-\stackrel{+}{\mathrm{C}} \mathrm{H}_2$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Ph}_3 \mathrm{C}^{++}$</span> </div>

answer:
<div class="solution">Hints: <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/khdJ9i8w1kbTz6FG-MFKtpEDjCsEoVVqIiIxbYNXjd8.original.fullsize.png"/><br/><br/>(Highly resonance stabilized)</div>


tags: ['Chemistry', 'Practical Chemistry', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch2_P4.db
title:
which-of-the-following-chemicals-may-be-used-to-identify-three-unlabelled-beakers-containing-concnaoh-conc-h-2-so-4-and-water

slug:
which-of-the-following-chemicals-may-be-used-to-identify-three-unlabelled-beakers-containing-concnaoh-conc-h-2-so-4-and-water-16640

question:
<div class="question">Which of the following chemicals may be used to identify three unlabelled beakers containing conc.NaOH, conc.$\mathrm{H}_{2}\mathrm{SO}_{4}$ and water?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{NH}_{4} \mathrm{NO}_{3}$</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">$\mathrm{NaCl}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}$</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">HCOONa</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">$\mathrm{NH}_{4} \mathrm{NO}_{3}$, $\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}$</span> </div>

answer:
<div class="solution">$\mathrm{NH}_{4} \mathrm{NO}_{3}$ will evolve $\mathrm{NH}_{3}$ pungent smelling gas with $\mathrm{NaOH}$.
<br/>- $\mathrm{NO}_{2}$ brown gas with $\operatorname{con} . \mathrm{H}_{2} \mathrm{SO}_{4}$
<br/>-  No reaction with water
<br/>Thus, $\mathrm{NH}_{4} \mathrm{NO}_{3}$ can be used to label all three beakers. 
<br/>(c) $\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}$ will evolve pungent smelling gas $\mathrm{NH}_{3}$ with $\mathrm{NaOH}$
<br/>- Effervescence of $\mathrm{CO}_{2}$ gas with con. $\mathrm{H}_{2} \mathrm{SO}_{4}$
<br/>- No reaction with water.
<br/>Thus, $\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}$ can be used to label all three beakers.
<br/>Thus, options $(a, c)$ are correct.</div>


title: which-of-the-following-compounds-does-not-exhibit-optical-isomerism-en-ethylenediamine
slug: which-of-the-following-compounds-does-not-exhibit-optical-isomerism-en-ethylenediamine-74326
tags: ['Chemistry', 'Coordination Compounds', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch2_P4.db
question:
<div class="question">Which of the following compounds does not exhibit optical isomerism?<br/>en = ethylenediamine).</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\operatorname{cis}-\left[\mathrm{CrCl}_{2}(\mathrm{Ox})_{2}\right]^{3-}$</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">B</span> <span class="option-data">$\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}$</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">$\operatorname{trans}-\left[\mathrm{CrCl}_{2}(\mathrm{ox})_{2}\right]^{3-}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\left[\mathrm{Co}(\mathrm{O} \mathrm{x})(\mathrm{en})_{2}\right]^{+}$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">$\operatorname{cis}-\left[\mathrm{CrCl}_{2}(\mathrm{Ox})_{2}\right]^{3-}$, $\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}$, $\left[\mathrm{Co}(\mathrm{O} \mathrm{x})(\mathrm{en})_{2}\right]^{+}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_che_a77.png"/> <br/> <br/>trans $\left[\mathrm{CrCl}_{2}(\mathrm{ox})_{2}\right]^{3-} \quad$ isomer-optically inactive (superimposable mirror images and plane of symmetry).
<br/>$\left.\mathrm{cis}-\mathrm{CrCl}_{2}(\mathrm{ox})_{2}\right]^{3-},\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}$ and $\left[\mathrm{Co}(\mathrm{ox})(\mathrm{en})_{2}\right]^{+}$
<br/>exhibited optical isomerism.</div>


title: which-of-the-following-compounds-has-maximum-volatility
slug: which-of-the-following-compounds-has-maximum-volatility-46314
question: <div class="question">Which of the following compounds has maximum volatility?</div>
tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'WBJEE', 'WBJEE 2011']
answer: <div class="solution">Hints: Due to intramolecular \(\mathrm{H}\) - bonding</div>
source_db: db\MarksBatch2_P4.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/BuFS9CryfWsskygNMQr_tYucxeBZM8EAedqXrdM_YS8.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/zJORQOPMAR_ABO_9CbQIHPcllZ4JYTr-xKNEf68MhUo.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/EZjQ-3e19y37ObXRH9ZDWuMxPbYnsitDLKFHLdfg7TM.original.fullsize.png"/><br/></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"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/zOMtTUlZ14YPiWAji2YyVfehpVjD6szQRGulpKBn3xs.original.fullsize.png"/><br/></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/EZjQ-3e19y37ObXRH9ZDWuMxPbYnsitDLKFHLdfg7TM.original.fullsize.png"/><br/></span> </div>


title: which-of-the-following-compounds-have-magnetic-moment-identical-with-cr-h-2-o-6-3-1
slug: which-of-the-following-compounds-have-magnetic-moment-identical-with-cr-h-2-o-6-3-1-81449
tags: ['Chemistry', 'Coordination Compounds', 'JEE Main']
source_db: db\MarksBatch2_P4.db
question:
<div class="question">Which of the following compounds have magnetic moment identical with $\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{4+}$</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">$\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{4+}$</span> </div>

answer:
<div class="solution">$\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$
<br/>$\mathrm{Cr} \Rightarrow(\mathrm{Ar}) 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{1}$
<br/>$\mathrm{Cr}^{+3} \Rightarrow(\mathrm{Ar}) 3 \mathrm{~d}^{3} 4 \mathrm{~s}^{0}$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/t6aZ3Ag18_5xKD3nj2HikZxX68apAfbwa5o-jXQ42rU.original.fullsize.png"/></div>


title: which-of-the-following-compounds-is-asymmetric
slug: which-of-the-following-compounds-is-asymmetric-47427
question: <div class="question">Which of the following compounds is asymmetric?</div>
tags: ['Chemistry', 'General Organic Chemistry', 'WBJEE', 'WBJEE 2020']
answer: <div class="solution">Hint: No plane of symmetry as well as centre of symmetry is present</div>
source_db: db\MarksBatch2_P4.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/pXPP4E_8zlt2gMFytD2IRPS0jaHzTkey2EwCXHByfEI.original.fullsize.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/AqCFrbISPWyznG1Vcv-89I9Lf9d69QT0CbzrxBVhvJg.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/zkFpiCjADvN8Oyec9P-fC11QCML53h9BeNRRlZoZ198.original.fullsize.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/n-rQVsW0mfrZ8SjLPhwT7wODKnDd1R6mhpt4IGuoM0Y.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> </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/n-rQVsW0mfrZ8SjLPhwT7wODKnDd1R6mhpt4IGuoM0Y.original.fullsize.png"/></span> </div>


title: which-of-the-following-compounds-is-not-formed-in-iodoform-reaction-of-acetone
slug: which-of-the-following-compounds-is-not-formed-in-iodoform-reaction-of-acetone-52334
tags: ['Chemistry', 'Aldehydes and Ketones', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch2_P4.db
question:
<div class="question">Which of the following compounds is not formed in iodoform reaction of acetone</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(\mathrm{CH}_3 \mathrm{COCH}_2 \mathrm{I}\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(\mathrm{ICH}_2 \mathrm{COCH}_2 \mathrm{I}\)</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">C</span> <span class="option-data">\(\mathrm{CH}_3 \mathrm{COCH}_2\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(\mathrm{CH}_3 \mathrm{COCI}_3\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\mathrm{ICH}_2 \mathrm{COCH}_2 \mathrm{I}\)</span> </div>

answer:
<div class="solution">Hints: <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/DEUZQFqhb_7dT9YdJAdduW78xPyNvHVm7nVfY17Xm18.original.fullsize.png"/><br/></div>


title: which-of-the-following-compounds-shows-evidence-of-the-strongest-hydrogen-bonding
slug: which-of-the-following-compounds-shows-evidence-of-the-strongest-hydrogen-bonding-49588
tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'WBJEE', 'WBJEE 2010']
source_db: db\MarksBatch2_P4.db
question:
<div class="question">Which of the following compounds shows evidence of the strongest hydrogen bonding?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Propan-1-ol</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Propan-2-ol</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Propan-1,2-diol</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Propan-1,2,3-triol</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">Propan-1,2,3-triol</span> </div>

answer:
<div class="solution">$$<br/>\text { Hints : Propan-1,2,3 triol have three polar }-\mathrm{OH} \text { group. }<br/>$$</div>


title: which-of-the-following-compounds-would-not-react-with-lucas-reagent-at-room-temperature
slug: which-of-the-following-compounds-would-not-react-with-lucas-reagent-at-room-temperature-79864
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch2_P4.db
question:
<div class="question">Which of the following compounds would not react with Lucas reagent at room temperature?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{H}_{2} \mathrm{C}=\mathrm{CHCH}_{2} \mathrm{OH}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{OH}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}$</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">$\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH}$</span> </li> </ul>

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

answer:
<div class="solution">Primary ( $1^{\circ}$ )-alcohols do not give Lucas reagent test at room temperature. $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}$ does not undergo $S_{N}1 or S_{N}2$ at room temperature.</div>


title: which-of-the-following-contributes-to-the-double-helical-structure-of-dna
slug: which-of-the-following-contributes-to-the-double-helical-structure-of-dna-34475
tags: ['Chemistry', 'Biomolecules', 'WBJEE', 'WBJEE 2009']
answer: <div class="solution">No Solution Available</div>
source_db: db\MarksBatch2_P4.db
question:
<div class="question">Which of the following contributes to the double helical structure of DNA</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">hydrogen bond</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">covalent bond</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">disulphide bond</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">van-der Waal's force</span> </li> </ul>

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


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch2_P4.db
title:
which-of-the-following-diagrams-correctly-shows-the-relation-between-the-terminal-velocity-v-t-of-a-spherical-body-falling-in-a-liquid-and-viscosity-o

slug:
which-of-the-following-diagrams-correctly-shows-the-relation-between-the-terminal-velocity-v-t-of-a-spherical-body-falling-in-a-liquid-and-viscosity-o-33936

question:
<div class="question">Which of the following diagrams correctly shows the relation between the terminal velocity $\mathrm{v}_{\mathrm{T}}$ of a spherical body falling in a liquid and viscosity $\eta$ of the liquid?</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/6Rzf58h4_NoTIvnDSvRMKCkxeqJjlTvvXZ8uq4sUOyw.original.fullsize.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/2HZN2afSylY13vjwzLWum656_78rSlvwHXlLSNA50gA.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/ZN0zYnjwCPUZdHY40DO5Q-79XpSY4ElhjdP4bOw-kgg.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">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/R9ZauFNACnpsBQqW_jVxmkGclplPz4pPLxkzwCsyWls.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/ZN0zYnjwCPUZdHY40DO5Q-79XpSY4ElhjdP4bOw-kgg.original.fullsize.png"/></span> </div>

answer:
<div class="solution">Hint : At terminal speed.
<br/>$\mathrm{V}_{\mathrm{T}}=\frac{2 \mathrm{r}^{2}}{9 \eta}\left(\rho_{\mathrm{s}}-\rho_{\mathrm{L}}\right) \mathrm{g} \quad$ (Assuming other factor constant)
<br/>So, $\mathrm{V}_{\mathrm{T}} \propto \frac{1}{\eta}$ (rectangular hyperbola)</div>


tags: ['Chemistry', 'Structure of Atom', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch2_P4.db
title:
which-of-the-following-does-not-represent-the-mathematical-expression-for-the-heisenberg-uncertainty-principle

slug:
which-of-the-following-does-not-represent-the-mathematical-expression-for-the-heisenberg-uncertainty-principle-96668

question:
<div class="question">Which of the following does not represent the mathematical expression for the Heisenberg uncertainty principle?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\Delta x \cdot \Delta P \geq h /(4 \pi)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\Delta x \cdot \Delta v \geq h /(4 \pi m)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\Delta E \cdot \Delta t \geq h /(4 \pi)$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\Delta E \cdot \Delta x \geq h /(4 \pi)$</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">$\Delta E \cdot \Delta x \geq h /(4 \pi)$</span> </div>

answer:
<div class="solution">From Heisenberg uncertainty principle, $\Delta x \cdot \Delta p \geq \frac{h}{4 \pi}$
<br/>or $\quad \Delta x \cdot m \Delta v \geq \frac{h}{4 \pi}$
<br/>or $\quad \Delta x \cdot \Delta v \geq \frac{h}{4 \pi m}$
<br/>This principle is also applicable for pairs like energy-time $(\Delta E \cdot \Delta t) \quad$ and $\quad$ angular $\begin{array}{llll}\text { moment-angle } &amp; (\Delta w \cdot \Delta \theta) &amp; \text { along } &amp; \text { with }\end{array}$
<br/>position-moment $(\Delta x \cdot \Delta p)$
<br/>Thus,
<br/>$$
<br/>\Delta E \cdot \Delta t \geq \frac{h}{4 \pi}
<br/>$$</div>


title: which-of-the-following-electronic-configuration-is-not-possible
slug: which-of-the-following-electronic-configuration-is-not-possible-39930
question: <div class="question">Which of the following electronic configuration is not possible?</div>
tags: ['Chemistry', 'Structure of Atom', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$n=3 l=0 m=0$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$n=3 l=1 m=-1$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$n=2.l=0 \mathrm{mm}-1$</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">$n=2, l=1 m=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$n=2.l=0 \mathrm{mm}-1$</span> </div>

answer:
<div class="solution">$n=2,1=0, m=-1$ is not a possible electronie configuration. With $n=2$ and $/-0$, the orbital is having only one $m_{1}$ value i.e. $0 .$ As the value of $m_{1}=-1 t 0+l$
<br/>Other options are correct.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_che_a52.png"/></div>


title: which-of-the-following-has-the-dimension-if-ml-2-t-2
slug: which-of-the-following-has-the-dimension-if-ml-2-t-2-79705
tags: ['Chemistry', 'Thermodynamics (C)', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch2_P4.db
question:
<div class="question">Which of the following has the dimension if $\left[\mathrm{ML}^{2} \mathrm{T}^{-2}\right] ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Coefficient of viscosity</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Surface tension</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">Vapour pressure</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Kinetic energy</span> </li> </ul>

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

answer:
<div class="solution">$\because$ Surface tension $(T)=$ Work done per unit area
<br/>$$
<br/>\begin{aligned}
<br/>\therefore \quad T &amp;=\frac{d W}{d A} \\
<br/>&amp;=\frac{F \cdot d x}{d A} \quad\left(\mathrm{FL}^{-1}=\mathrm{MT}^{-2}\right.
<br/>\end{aligned}
<br/>$$
<br/>$\therefore$ Dimension of surface tension $=\mathrm{ML}^{2} \mathrm{T}^{-2}$</div>


title: which-of-the-following-has-the-largest-number-of-atoms
slug: which-of-the-following-has-the-largest-number-of-atoms-91985
question: <div class="question">Which of the following has the largest number of atoms?</div>
tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 \mathrm{~g}$ of $\mathrm{Ag}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1 \mathrm{~g}$ of $\mathrm{Fe}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1 \mathrm{~g}$ of $\mathrm{Cl}_{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$1 \mathrm{~g}$ of $\mathrm{Mg}$</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">$1 \mathrm{~g}$ of $\mathrm{Mg}$</span> </div>

answer:
<div class="solution">Hint:
<br/>Number of atoms of $\mathrm{Ag}=\frac{1}{108} \times \mathrm{N}_{\mathrm{A}}=0.009 \mathrm{~N}_{\mathrm{A}}$
<br/>Number of atoms of $\mathrm{Fe}=\frac{1}{56} \times \mathrm{N}_{\mathrm{A}}=0.0178 \mathrm{~N}_{\mathrm{A}}$
<br/>Number of atoms of $\mathrm{Cl}_{2}=\frac{1}{71} \times 2 \times \mathrm{N}_{\mathrm{A}}=0.028 \mathrm{~N}_{\mathrm{A}}$
<br/>Number of atoms of $\mathrm{Mg}=\frac{1}{24} \mathrm{~N}_{\mathrm{A}}=0.041 \mathrm{~N}_{\mathrm{A}}$ [largest]</div>


title: which-of-the-following-has-the-strongest-hbond
slug: which-of-the-following-has-the-strongest-hbond-49059
question: <div class="question">Which of the following has the strongest H-bond?</div>
tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0-H-S$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{S}-\mathrm{H}-\mathrm{O}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$F-H$. F</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">$F-H-O$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$F-H$. F</span> </div>

answer:
<div class="solution">The strongest H-bond is $\mathrm{F}-\mathrm{H}-\mathrm{F}$ because in this case, a hydrogen is bonded to a most. electronegative atom i.e. fluorine. In all other options, hydrogen is bonded to oxygen and sulphur that are less electronegative atom than fluorine.
<br/>The correct electronegativity order of elements are as follows: $\mathrm{F}&gt;\mathrm{O}&gt;\mathrm{S}$</div>


title: which-of-the-following-is-correct-9
slug: which-of-the-following-is-correct-9-68411
question: <div class="question">Which of the following is correct?</div>
tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Radius of $\mathrm{Ca}^{2+}     &lt; \mathrm{Cl}^{-} &lt; \mathrm{S}^{2-}$</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">Radius of $\mathrm{Cl}^{-}     &lt; \mathrm{S}^{2-} &lt; \mathrm{Ca}^{2+}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Radius of $\mathrm{S}^{2-}=\mathrm{Cl}^{-}=\mathrm{Ca}^{2+}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Radius of $\mathrm{S}^{2-}     &lt; \mathrm{Cl}^{-} &lt; \mathrm{Ca}^{2+}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Radius of $\mathrm{Ca}^{2+}     &lt; \mathrm{Cl}^{-} &lt; \mathrm{S}^{2-}$</span> </div>

answer:
<div class="solution">\begin{array}{c|c|c}
<br/>\hline Species &amp; Atomic number &amp; Number of electrons \\
<br/>\hline \mathrm{Ca}^{2+} &amp; 20 &amp; 20-2=18 \\
<br/>\mathrm{Cl}^{-} &amp; 17 &amp; 17+1=18 \\
<br/>\mathrm{s}^{2-} &amp; 16 &amp; 16+2=18 \\
<br/>\hline
<br/>\end{array}
<br/>For isoelectronic species, an increase in atomic number, result in decreased size. Thus, order of radius will be
<br/>$$
<br/>\mathrm{Ca}^{2+}     &lt; \mathrm{Cl}^{-} &lt; \mathrm{S}^{2-}
<br/>$$</div>


title: which-of-the-following-is-correct-10
slug: which-of-the-following-is-correct-10-53000
question: <div class="question">Which of the following is correct?</div>
tags: ['Chemistry', 'Thermodynamics (C)', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Evaporation of water causes an increase in disorder of the system</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">Melting of ice causes a decrease in randomness of the system</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Condensation of steam causes an increase in disorder of the system</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">There is practically no change in the randomness of the system when water is evaporated</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Evaporation of water causes an increase in disorder of the system</span> </div>

answer:
<div class="solution">Water evaporates into steam. In this physical state its disorder or randomness increases.</div>


title: which-of-the-following-is-least-thermally-stable
slug: which-of-the-following-is-least-thermally-stable-10294
question: <div class="question">Which of the following is least thermally stable?</div>
tags: ['Chemistry', 'Practical Chemistry', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{MgCO}_{3}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{CaCO}_{3}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{SrCO}_{3}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{BeCO}_{3}$</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">$\mathrm{BeCO}_{3}$</span> </div>

answer:
<div class="solution">BeCO, is least thermally stable. The thermal stability of carbonates increases down the group
<br/>i.e from Be to Ba. $\mathrm{BeCO}_{3}    &lt; \mathrm{MgCO}_{3} &lt; \mathrm{CaCO}_{3} &lt; \mathrm{SrCO}_{3} &lt; \mathrm{BaCO}_{3}$
<br/>$(523 \mathrm{K}) \quad(813 \mathrm{K})$
<br/>$(1173 \mathrm{K}) \quad(1562 \mathrm{K}) \quad(1633 \mathrm{K})$
<br/>BeCO, is unstable to the extent that it is stable only in atmosphere of $\mathrm{CO}_{y}$. These carbonates show reversible decomposition in closed container.
<br/>$M \mathrm{CO}, \quad \rightarrow \mathrm{MO}+\mathrm{CO}_{2}$
<br/>More stable the oxide is formed, lesser will be stability of carbonates.</div>


title: which-of-the-following-is-not-always-true
slug: which-of-the-following-is-not-always-true-55951
question: <div class="question">Which of the following is not always true?</div>
tags: ['Mathematics', 'Vector Algebra', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mid a+b\mid^{2}=|a|^2+|b|^2. \text{if a and b are perpendicular to each other}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mid a+\lambda b| \geq|a|$ for all $\lambda \in R$ if a and b are perpendicular to each other</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mid a+b \mid^{2}+\mid a-b \mid^{2}=2(|a|^2+|b|^2)$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mid a+\lambda b| \geq|a|$ for all $\lambda \in R$ if a is parallel to b</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">$\mid a+\lambda b| \geq|a|$ for all $\lambda \in R$ if a is parallel to b</span> </div>

answer:
<div class="solution">(a) If a and b are perpendicular to each other, then<br/>$\mathbf{a} \cdot \mathbf{b}=0$<br/>Now consider,<br/>$\begin{aligned}<br/>|\mathbf{a}+\mathbf{b}|^{2} &amp;=(\mathbf{a}+\mathbf{b}) \cdot(\mathbf{a}+\mathbf{b}) \\<br/>&amp;=|\mathbf{a}|^{2}+|\mathbf{b}|^{2}<br/>\end{aligned}$<br/>So, option (a) is always true.<br/>(b) If $\mathbf{a}$ and $\mathbf{b}$ are perpendicular to each other, then<br/>$\mathbf{a} \cdot \mathbf{b}=0$<br/>Now consider, $\begin{aligned}|\mathbf{a}+\lambda \mathbf{b}|^{2} &amp;=(\mathbf{a}+\lambda \mathbf{b}) \cdot(\mathbf{a}+\lambda \mathbf{b}) \\ &amp;=|\mathbf{a}|^{2}+\lambda^{2}|\mathbf{b}|^{2} \\ \Rightarrow|\mathbf{a}+\lambda \mathbf{b}| &amp;=\sqrt{|\mathbf{a}|^{2}+\lambda^{2}|\mathbf{b}|^{2}} \end{aligned}$<br/>$\geq|\mathbf{a}|$ for all $\lambda \in R$<br/>So, option (b) is always true.<br/>(c) Consider,<br/>$\left|a+\left.b\right|^{2}+|a-b|^{2}=(a+b) \cdot(a+b) + (a-b) \cdot (a-b)\right.$<br/>$=|\mathbf{a}|^{2}+\mathbf{a} \cdot \mathbf{b}+\mathbf{b} \cdot \mathbf{a}+|\mathbf{b}|^{2}+|\mathbf{a}|^{2}-\mathbf{a} \cdot \mathbf{b} -b \cdot a + |b|^2$<br/>$=2\left(|\mathbf{a}|^{2}+|\mathbf{b}|^{2}\right)$<br/>So, option (c) is always true.<br/>(d) Consider.<br/>$\mathbf{a}=-\mathbf{b} \text { and } \mathbf{b} \neq 0$<br/>Then, $|\mathbf{a}+\lambda \mathbf{b}| \geq|\mathbf{a}|$<br/>$\Rightarrow|-\mathbf{b}+\lambda \mathbf{b}| \geq|-\mathbf{b}|$<br/>$\Rightarrow \quad|\mathbf{b}||\lambda-1| \geq|\mathbf{b}| \Rightarrow|\lambda-1| \geq 1$<br/>which is not true for all $\lambda,$ as we consider $\lambda=\frac{1}{2}$, then it is not true<br/>Hence, option (d) is not always true.</div>


title: which-of-the-following-is-present-in-maximum-amount-in-acid-rain-1
slug: which-of-the-following-is-present-in-maximum-amount-in-acid-rain-1-97473
question: <div class="question">Which of the following is present in maximum amount in 'acid rain'?</div>
tags: ['Chemistry', 'Environmental Chemistry', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{HNO}_{3}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{H}_{2} \mathrm{SO}_{4}$</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">C</span> <span class="option-data">HCI</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{H}_{2} \mathrm{CO}_{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{H}_{2} \mathrm{SO}_{4}$</span> </div>

answer:
<div class="solution">$\mathrm{H}_{2} \mathrm{SO}_{4}$ (sulphuric acid) is present in maximu $\mathrm{h}_{4}$ amount in 'acid rain'. Oxides of nitrogen and sulphur, released into the atmosphere from industries and automobiles thermal power plants, are the miain sources of acid rain. These oxides on oxidation followed by hydrolysis give sulphuric acid and nitric acid that alongwith $\mathrm{HCl}$ are responsible for the acidity of rain. The oxidation reaction is catalysed by particulate matter present in the polluted atmosphere. $2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)+2 \mathrm{H}, \mathrm{O}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{SO}_{4}(a q)$
<br/>$4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}\left(h \longrightarrow 4 \mathrm{HNO}_{3}(a q)\right.$</div>


title: which-of-the-following-is-radioactive
slug: which-of-the-following-is-radioactive-52333
question: <div class="question">Which of the following is radioactive?</div>
tags: ['Chemistry', 'Hydrogen', 'WBJEE', 'WBJEE 2022']
answer: <div class="solution">Fact</div>
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Hydrogen</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Deuterium</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Tritium</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">none</span> </li> </ul>

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


tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch2_P4.db
title:
which-of-the-following-is-used-to-prepare-mathrmcl2-gas-at-room-temperature-from-concentrated-mathrmhcl

slug:
which-of-the-following-is-used-to-prepare-mathrmcl2-gas-at-room-temperature-from-concentrated-mathrmhcl-27797

question:
<div class="question">Which of the following is used to prepare \(\mathrm{Cl}_2\) gas at room temperature from concentrated \(\mathrm{HCl}\) ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(\mathrm{MnO}_2\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(\mathrm{H}_2 \mathrm{~S}\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(\mathrm{KMnO}_4\)</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">D</span> <span class="option-data">\(\mathrm{Cr}_2 \mathrm{O}_3\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\mathrm{KMnO}_4\)</span> </div>

answer:
<div class="solution">Hints : \(2 \mathrm{MnO}_4^{-}+16 \mathrm{H}^{+}+10 \mathrm{Cl}^{-} \rightarrow 2 \mathrm{Mn}^{2+}+5 \mathrm{Cl}_2+8 \mathrm{H}_2 \mathrm{O}\)</div>


title: which-of-the-following-isare-always-false
slug: which-of-the-following-isare-always-false-84175
question: <div class="question">Which of the following is/are always false?</div>
tags: ['Mathematics', 'Quadratic Equation', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">A quadratic equation with rational coefficients hes zero or two irrational roots</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">A quadratic equation with real coefficients has zero or two non-real roots</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">A quadratic equation with irrational coeflicients has zero or two irrational roots</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 quadratic equation with integer coefficients has zero or two irrational roots</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">A quadratic equation with irrational coeflicients has zero or two irrational roots</span> </div>

answer:
<div class="solution">If a quadratic equation has irrational coefficients, then roots are also inational.
<br/>So, option (c) is always false.</div>


title: which-of-the-following-materials-is-the-best-conductor-of-electricity
slug: which-of-the-following-materials-is-the-best-conductor-of-electricity-71446
question: <div class="question">Which of the following materials is the best conductor of electricity?</div>
tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Copper</span> </div>
answer: <div class="solution">No Solution Available</div>
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Platinum</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Gold</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Silicon</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Copper</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>


title: which-of-the-following-metals-has-the-largest-abundance-in-the-earths-crust
slug: which-of-the-following-metals-has-the-largest-abundance-in-the-earths-crust-72106
tags: ['Chemistry', 'General Principles and Processes of Isolation of Metals', 'WBJEE', 'WBJEE 2010']
answer: <div class="solution">No Solution Available</div>
source_db: db\MarksBatch2_P4.db
question:
<div class="question">Which of the following metals has the largest abundance in the earth's crust ?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Aluminium</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">Calcium</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Magnesium</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Sodium</span> </li> </ul>

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


title: which-of-the-following-mixtures-acts-as-buffer-solution
slug: which-of-the-following-mixtures-acts-as-buffer-solution-62595
question: <div class="question">Which of the following mixtures act(s) as buffer solution?</div>
tags: ['Chemistry', 'Ionic Equilibrium', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(\mathrm{NaOH}+\mathrm{CH}_3 \mathrm{COOH}\) (1:1 mole ratio)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(\mathrm{NH}_4 \mathrm{OH}+\mathrm{HCl}(2: 1\) mole ratio)</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">\(\mathrm{CH}_3 \mathrm{COOH}+\mathrm{NaOH}(2: 1\) more ratio)</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">\(\mathrm{CH}_3 \mathrm{COOH}+\mathrm{NaOH}(1: 2\) mole ratio)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">\(\mathrm{NH}_4 \mathrm{OH}+\mathrm{HCl}(2: 1\) mole ratio), \(\mathrm{CH}_3 \mathrm{COOH}+\mathrm{NaOH}(2: 1\) more ratio)</span> </div>

answer:
<div class="solution">Hint : (B) \(\mathrm{NH}_4 \mathrm{OH}+\mathrm{HCl}~(2: 1 \text { mole ratio}) \rightarrow \underset{\large 1 \quad:\quad 1 \atop <br/>\large \text{Buffer} \quad \text{buffer}}{\mathrm{NH}_4 \mathrm{Cl}+\mathrm{NH}_4 \mathrm{OH}}\)<br/>(C) \(\mathrm{CH}_3 \mathrm{COOH}+\mathrm{NaOH}(2: 1\) mole ratio \() \rightarrow \underset{\large 1\quad : \quad 1 \atop \large \text{Acidic buffer}}{\mathrm{CH}_3 \mathrm{COONa}+\mathrm{CH}_3 \mathrm{COOH}}\)</div>


title: which-of-the-following-mixtures-will-have-the-lowest-ph-at-298-k
slug: which-of-the-following-mixtures-will-have-the-lowest-ph-at-298-k-71327
question: <div class="question">Which of the following mixtures will have the lowest pH at 298 K?</div>
tags: ['Chemistry', 'Ionic Equilibrium', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$10 \mathrm{mL}$ 0.05 $\mathrm{N}$ $\mathrm{CH}_{3} \mathrm{COOH}+5 \mathrm{mL}$ 0.1 $\mathrm{N}$ $\mathrm{NH}_{4} \mathrm{OH}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$5 \mathrm{mL}$ 0.2 $\mathrm{N}$ $\mathrm{NH}_{4} \mathrm{Cl}+5 \mathrm{mL}$. $0.2 \mathrm{N }$ $\mathrm{NH}_{4} \mathrm{OH}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$5 \mathrm{mL}$. $0.1 \mathrm{N}$ $\mathrm{CH}_{5} \mathrm{COOH}+10 \mathrm{mL}$ 0.05 $\mathrm{N}$ $\mathrm{CH}_{3} \mathrm{COONa}$</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=""> <span class="option-label">D</span> <span class="option-data">$5 \mathrm{mL}$ 0.1 $\mathrm{N}$ $\mathrm{CH}_{3} \mathrm{COOH}+5 \mathrm{mL}$ 0.1 $\mathrm{N}$ $\mathrm{NaOH}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$5 \mathrm{mL}$. $0.1 \mathrm{N}$ $\mathrm{CH}_{5} \mathrm{COOH}+10 \mathrm{mL}$ 0.05 $\mathrm{N}$ $\mathrm{CH}_{3} \mathrm{COONa}$</span> </div>

answer:
<div class="solution">Key Point For buffer solutions,
<br/>$$
<br/>\mathrm{pH}=\mathrm{pK}_{a}+\log \frac{[\text { Salt }]}{[\text { Acid }] /[\text { Base }]}
<br/>$$
<br/>Moles of $\mathrm{CH}_{3} \mathrm{COOH}=5 \mathrm{mL} \times 0.01 \mathrm{m} \mathrm{mol}=0.5 \mathrm{m} \mathrm{mol}$
<br/>Moles of $\mathrm{CH}_{3} \mathrm{COONa}=10 \mathrm{mL} \times 0.05 \mathrm{m} \mathrm{mol}$
<br/>$$
<br/>=0.5 \mathrm{m} \mathrm{mol}
<br/>$$
<br/>Total volume of solution $=5+10=15 \mathrm{mL}$
<br/>$$
<br/>\therefore \quad \mathrm{pH}=\mathrm{p} K_{a}+\log \frac{0.5 / 15}{0.5 / 15} \Rightarrow \mathrm{pH}=\mathrm{p} K_{a}
<br/>$$
<br/>The value of $\mathrm{p} K_{a}$ is the lowest for the mixture of $\begin{array}{llll}\mathrm{CH}_{3} \mathrm{COOH} &amp; \text { and } \mathrm{CH}_{3} \mathrm{COONa} &amp; \text { (acidic buffer). }\end{array}$
<br/>Therefore, it has lowest pH. Hence, pH value for option (c) is the lowest.</div>


title: which-of-the-following-orbitals-will-have-zero-probability-of-finding-the-electron-in-the-yz-plane
tags: ['Chemistry', 'Structure of Atom', 'WBJEE', 'WBJEE 2010']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$P_x$</span> </div>
answer: <div class="solution">Hints : $P_x$ orbital lies along $x$-axis only.</div>
source_db: db\MarksBatch2_P4.db
slug:
which-of-the-following-orbitals-will-have-zero-probability-of-finding-the-electron-in-the-yz-plane-27669

question:
<div class="question">Which of the following orbitals will have zero probability of finding the electron in the yz plane ?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$P_x$</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">$\mathrm{P}_{\mathrm{y}}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{P}_{\mathrm{z}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{d}_{\mathrm{yz}}$</span> </li> </ul>


title: which-of-the-following-orders-regarding-ionization-energy-is-correct
slug: which-of-the-following-orders-regarding-ionization-energy-is-correct-76504
question: <div class="question">Which of the following orders regarding ionization energy is correct?</div>
tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'WBJEE', 'WBJEE 2010']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{N}&gt;\mathrm{O}&gt;\mathrm{F}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{N} &lt; \mathrm{O} &lt; \mathrm{F}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{N}&gt;\mathrm{O} &lt; \mathrm{F}$</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">$\mathrm{N} &lt; \mathrm{O}&gt;\mathrm{F}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{N}&gt;\mathrm{O} &lt; \mathrm{F}$</span> </div>

answer:
<div class="solution">Hints : As IE $1 \mathrm{~N}&gt;\mathrm{O}$ (because of half filled orbitals of $\mathrm{N}$ ) and $\mathrm{O} &lt; \mathrm{F}$ (because of smaller size of $\mathrm{F}$ )</div>


title: which-of-the-following-plots-represent-an-exothermic-reaction-1
slug: which-of-the-following-plots-represent-an-exothermic-reaction-1-90711
question: <div class="question">Which of the following plots represent an exothermic reaction?</div>
tags: ['Chemistry', 'Chemical Equilibrium', 'JEE Main']
source_db: db\MarksBatch2_P4.db
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/2016_che_q23_opta.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/2016_che_q23_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/2016_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/2016_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/2016_che_q23_opta.png"/></span> </div>

answer:
<div class="solution">For exothermic reaction.
<br/>$\because$
<br/>$K_{p} \propto \frac{1}{T}$
<br/>Thus, as $\frac{1}{T}$ increases (i.e. $T$ decreases), $K_{p}$ increases.
<br/>$\because$ $\Delta$ H for exothermic reactions is negative.</div>


title: which-of-the-following-reactions-gives-a-mesocompound-as-the-main-product
slug: which-of-the-following-reactions-gives-a-mesocompound-as-the-main-product-56339
tags: ['Chemistry', 'Hydrocarbons', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch2_P4.db
question:
<div class="question">Which of the following reactions give(s) a meso-compound as the main product?</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/aS9YZpIWMhT51N8bY_dFEHSaLQrlrZV6vP_HsvTlZDw.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="correct"> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/ewsZ4h6rTHCJ7uH4WI68dcHFCzyQdRRcVsPXFaMRmlY.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">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/n_ojbOX5ilw031i86VMApxLCm0Mh3tNNX5ngpMwB6i8.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/mn1ZD_aEZSpFjKbncz9VWjWZjcpcxQO5lYf3imMkOJA.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/aS9YZpIWMhT51N8bY_dFEHSaLQrlrZV6vP_HsvTlZDw.original.fullsize.png"/>, <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/ewsZ4h6rTHCJ7uH4WI68dcHFCzyQdRRcVsPXFaMRmlY.original.fullsize.png"/></span> </div>

answer:
<div class="solution">Hint:
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/8UQtN2Md0f0ke6C3TYskl7_fGoSZl33eV2NDBgLt6zk.original.fullsize.png"/></div>


title: which-of-the-following-reactions-will-not-result-in-the-formation-of-carboncarbon-bonds-2
slug: which-of-the-following-reactions-will-not-result-in-the-formation-of-carboncarbon-bonds-2-40448
tags: ['Chemistry', 'Aldehydes and Ketones', 'JEE Main']
source_db: db\MarksBatch2_P4.db
question:
<div class="question">Which of the following reactions will not result in the formation of carbon-carbon bonds?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Cannizzaro reaction</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">Wurtz reaction</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Reimer-Tiemann reaction</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Friedel-Crafts acylation</span> </li> </ul>

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

answer:
<div class="solution">$\mathrm{C}-\mathrm{C}$ bond is not formed in Cannizaro reaction while other reactions result in the formation of $\mathrm{C}-\mathrm{C}$ bond.
<br/>Cannizaro reaction
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_che_a6.png"/> <br/> <br/>Wurtz reaction
<br/>$2 R-X+2 \mathrm{Na} \longrightarrow R-R+2 \mathrm{Na} \times$<img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_che_a6a.png"/></div>


title: which-of-the-following-real-valued-functions-isare-not-even-functions
slug: which-of-the-following-real-valued-functions-isare-not-even-functions-15639
question: <div class="question">Which of the following real valued functions is/are not even functions?</div>
tags: ['Mathematics', 'Functions', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$f(x)=x^{3} \sin x$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$f(x)=x^{2} \cos x$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$f(x)=e^{x} x^{3} \sin x$</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">$f(x)=x-[x]$, where $[x]$ denotes the greatest integer less than or equal to $x$</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">$f(x)=e^{x} x^{3} \sin x$, $f(x)=x-[x]$, where $[x]$ denotes the greatest integer less than or equal to $x$</span> </div>

answer:
<div class="solution">We know that, if $f(-x)=f(x)$, then function is even and $f(-x)=-f(x)$, then function is odd.
<br/>(a) $f(x)=x^{3} \sin x$
<br/>$$
<br/>\begin{aligned}
<br/>f(-x) &amp;=(-x)^{3} \sin (-x) \\
<br/>&amp;=-x^{3}(-\sin x) \\
<br/>&amp;=x^{3} \sin x=f(x)
<br/>\end{aligned}
<br/>$$
<br/>So, $f(x)$ is even.
<br/>(b) $f(x)=x^{2} \cos x$
<br/>$$
<br/>f(-x)=(-x)^{2} \cos (-x)=x^{2} \cos x=f(x)
<br/>$$
<br/>So, $f(x)$ is even.
<br/>(c) $f(x)=e^{x} x^{3} \sin x$
<br/>$$
<br/>\begin{array}{r}
<br/>f(-x)=e^{-x}(-x)^{3} \sin (-x) \\
<br/>=e^{-x} x^{3} \sin x \neq f(x)
<br/>\end{array}
<br/>$$
<br/>$\therefore \quad f(x)$ is not even.
<br/>(d) $f(x)=x-[x]$ $f(-x)=(-x)-[-x] \neq f(x)$
<br/>$\therefore f(x)$ is not even.</div>


