# questions

tags: ['Physics', 'Magnetic Effects of Current', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$-1$</span> </div>
source_db: db\MarksBatch1_P1.db
title:
a-straight-wire-is-placed-in-a-magnetic-field-that-varies-with-distance-x-from-origin-as-b-b-0-2-a-x-k-ends-of-wire-are-at-a-0-and-2-a-0-and-it-carrie-1

slug:
a-straight-wire-is-placed-in-a-magnetic-field-that-varies-with-distance-x-from-origin-as-b-b-0-2-a-x-k-ends-of-wire-are-at-a-0-and-2-a-0-and-it-carrie-1-84214

question:
<div class="question">A straight wire is placed in a magnetic field that varies with distance $x$ from origin as $\vec{B}=B_0\left(2-\frac{x}{a}\right) \hat{k}$. Ends of wire are at $(a, 0)$ and $(2 a, 0)$ and it carries a current $\mathrm{I}$. If force on wire is $\vec{F}=\mathrm{IB}_0\left(\frac{k a}{2}\right) \hat{\mathrm{j}}$, then value of $k$ 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">5</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$-1$</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">$\frac{1}{2}$</span> </li> </ul>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/piz3lbnlwCYlnS0RS5d1ZjG3jTXjAFBZ7r6tBksSbWs.original.fullsize.png"/><br/><br/>$\overrightarrow{\mathrm{dF}}=\mathrm{Idx} \times \overrightarrow{\mathrm{B}}=\operatorname{Idx} \hat{\mathrm{i}} \times \mathrm{B} \hat{\mathrm{k}}=\operatorname{IdxB}(-\hat{\mathrm{j}})$<br/>$\int \mathrm{dF}=\int_{\mathrm{a}}^{2 a} \mathrm{Id} x \mathrm{~B}_0\left(2-\frac{\mathrm{x}}{\mathrm{a}}\right)(-\hat{\mathrm{j}})$<br/>$$<br/>\begin{aligned}<br/>&amp;\mathrm{F}=\mathrm{IB}_0 \int_{\mathrm{a}}^{2 \mathrm{a}}\left(2-\frac{\mathrm{x}}{\mathrm{a}}\right) \mathrm{dx}(-\hat{\mathrm{j}}) \\<br/>&amp;=\operatorname{IB}_0\left(2 \mathrm{x}-\frac{\mathrm{x}^2}{2 \mathrm{a}}\right)_{\mathrm{a}}^{2 \mathrm{a}}(-\hat{\mathrm{j}}) \\<br/>&amp;=\mathrm{IB}_0\left[\left(2 \times 2 \mathrm{a}-\frac{(2 \mathrm{a})^2}{2 \mathrm{a}}\right)-\left(2 \mathrm{a}-\frac{\mathrm{a}^2}{2 \mathrm{a}}\right)\right](-\hat{\mathrm{j}}) \\<br/>&amp;=\mathrm{IB}_0\left[(4 \mathrm{a}-2 \mathrm{a})-\left(\frac{3 \mathrm{a}}{2}\right)\right](-\hat{\mathrm{j}}) \\<br/>&amp;=\mathrm{IB}_0\left[2 \mathrm{a}-\frac{3 \mathrm{a}}{2}\right](-\hat{\mathrm{j}}) \\<br/>&amp;=\operatorname{IB}_0\left[\frac{\mathrm{a}}{2}\right](-\hat{\mathrm{j}})<br/>\end{aligned}<br/>$$<br/>Comparing $\mathrm{F}$ with $\mathrm{IB}_0\left[\frac{\mathrm{ka}}{2}\right] \hat{\mathrm{j}}$, we get $\mathrm{k}=-1$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2022']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$-1$</span> </div>
source_db: db\MarksBatch1_P1.db
title:
a-straight-wire-is-placed-in-a-magnetic-field-that-varies-with-distance-x-from-origin-as-b-b-0-2-a-x-k-ends-of-wire-are-at-a-0-and-2-a-0-and-it-carrie

slug:
a-straight-wire-is-placed-in-a-magnetic-field-that-varies-with-distance-x-from-origin-as-b-b-0-2-a-x-k-ends-of-wire-are-at-a-0-and-2-a-0-and-it-carrie-13965

question:
<div class="question">A straight wire is placed in a magnetic field that varies with distance $x$ from origin as $\vec{B}=B_0\left(2-\frac{x}{a}\right) \hat{k}$. Ends of wire are at $(a, 0)$ and $(2 a, 0)$ and it carries a current $\mathrm{I}$. If force on wire is $\vec{F}=\mathrm{IB}_0\left(\frac{k a}{2}\right) \hat{\mathrm{j}}$, then value of $k$ 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">5</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$-1$</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">$\frac{1}{2}$</span> </li> </ul>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/piz3lbnlwCYlnS0RS5d1ZjG3jTXjAFBZ7r6tBksSbWs.original.fullsize.png"/><br/><br/>$\overrightarrow{\mathrm{dF}}=\mathrm{Idx} \times \overrightarrow{\mathrm{B}}=\operatorname{Idx} \hat{\mathrm{i}} \times \mathrm{B} \hat{\mathrm{k}}=\operatorname{IdxB}(-\hat{\mathrm{j}})$<br/>$\int \mathrm{dF}=\int_{\mathrm{a}}^{2 a} \mathrm{Id} x \mathrm{~B}_0\left(2-\frac{\mathrm{x}}{\mathrm{a}}\right)(-\hat{\mathrm{j}})$<br/>$$<br/>\begin{aligned}<br/>&amp;\mathrm{F}=\mathrm{IB}_0 \int_{\mathrm{a}}^{2 \mathrm{a}}\left(2-\frac{\mathrm{x}}{\mathrm{a}}\right) \mathrm{dx}(-\hat{\mathrm{j}}) \\<br/>&amp;=\operatorname{IB}_0\left(2 \mathrm{x}-\frac{\mathrm{x}^2}{2 \mathrm{a}}\right)_{\mathrm{a}}^{2 \mathrm{a}}(-\hat{\mathrm{j}}) \\<br/>&amp;=\mathrm{IB}_0\left[\left(2 \times 2 \mathrm{a}-\frac{(2 \mathrm{a})^2}{2 \mathrm{a}}\right)-\left(2 \mathrm{a}-\frac{\mathrm{a}^2}{2 \mathrm{a}}\right)\right](-\hat{\mathrm{j}}) \\<br/>&amp;=\mathrm{IB}_0\left[(4 \mathrm{a}-2 \mathrm{a})-\left(\frac{3 \mathrm{a}}{2}\right)\right](-\hat{\mathrm{j}}) \\<br/>&amp;=\mathrm{IB}_0\left[2 \mathrm{a}-\frac{3 \mathrm{a}}{2}\right](-\hat{\mathrm{j}}) \\<br/>&amp;=\operatorname{IB}_0\left[\frac{\mathrm{a}}{2}\right](-\hat{\mathrm{j}})<br/>\end{aligned}<br/>$$<br/>Comparing $\mathrm{F}$ with $\mathrm{IB}_0\left[\frac{\mathrm{ka}}{2}\right] \hat{\mathrm{j}}$, we get $\mathrm{k}=-1$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch1_P1.db
title:
a-straight-wire-of-length-2-m-carries-a-current-of-10-a-if-this-wire-is-placed-in-a-uniform-magnetic-field-of-015-t-making-an-angle-of-4-5-with-the-ma

slug:
a-straight-wire-of-length-2-m-carries-a-current-of-10-a-if-this-wire-is-placed-in-a-uniform-magnetic-field-of-015-t-making-an-angle-of-4-5-with-the-ma-42285

question:
<div class="question">A straight wire of length $2 \mathrm{m}$ carries a current of $10 \mathrm{A}$. If this wire is placed in a uniform magnetic field of 0.15 T making an angle of $45^{\circ}$ with the magnetic field, the applied force on the wire will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1.5 \mathrm{N}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3 \mathrm{N}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3 \sqrt{2} \mathrm{N}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{3}{\sqrt{2}} \mathrm{N}$</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> </ul>

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

answer:
<div class="solution">Given $i=10 \mathrm{A}, B=0.15 \mathrm{T}, \theta=45^{\circ}$ and $l=2 \mathrm{m}$
<br/>Here,
<br/>$$
<br/>\begin{aligned}
<br/>F &amp;=i L B \sin \theta \\
<br/>&amp;=10 \times 2 \times 0.15 ~ x ~ \sin 45^{\circ} \\
<br/>&amp;=\frac{3}{\sqrt{2}} \mathrm{N}
<br/>\end{aligned}
<br/>$$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
title:
a-stream-of-electrons-and-protons-are-directed-towards-a-narrow-slit-in-a-screen-see-figure-the-intervening-region-has-a-uniform-electric-field-vertic

slug:
a-stream-of-electrons-and-protons-are-directed-towards-a-narrow-slit-in-a-screen-see-figure-the-intervening-region-has-a-uniform-electric-field-vertic-84373

question:
<div class="question">A stream of electrons and protons are directed towards a narrow slit in a screen (see figure). The intervening region has a uniform electric field (vertically downwards) and a uniform magnetic field $\mathbf{B}$ (out of the plane of the figure) as shown. Then <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_phy_q60.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">electrons and protons with speed $\frac{|\mathrm{E}|}{|\mathbf{B}|}$ will pass through the slit</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">protons with speed $|\mathrm{E}| /|\mathrm{B}|$ will pass through the slit, electrons of the same speed will not</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">neither electrons nor protons will go through the sit irrespective of their speed</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">electrons will always be deflected upwards irrespective of their speed</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">neither electrons nor protons will go through the sit irrespective of their speed, electrons will always be deflected upwards irrespective of their speed</span> </div>

answer:
<div class="solution">of their speed.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_phy_a60.png"/> <br/> <br/>And electrons will always be deflected upwards irrespective of their speed.
<br/>So, (c) and (d) are correct options.</div>


tags: ['Mathematics', 'Probability', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
title:
a-student-answers-a-multiple-choice-question-with-5-alternatives-of-which-exactly-one-is-correct-the-probability-that-he-knows-the-correct-answer-is-p

slug:
a-student-answers-a-multiple-choice-question-with-5-alternatives-of-which-exactly-one-is-correct-the-probability-that-he-knows-the-correct-answer-is-p-23082

question:
<div class="question">A student answers a multiple choice question with 5 alternatives, of which exactly one is correct. The probability that he knows the correct answer is $p, 0    &lt; p &lt; 1 .$ If he does not know the correct answer, he randomly ticks one answer. Given that he has answered the question correctly, the probability that he did not tick the answer randomly, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{3 p}{4 p+3}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{5 p}{3 p+2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{5 p}{4 p+1}$</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">$\frac{4 p}{3 p+1}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{5 p}{4 p+1}$</span> </div>

answer:
<div class="solution">Let, $\quad E_{1}=$ Student does not know the answer
<br/>$E_{2}=$ Student knows the answer
<br/>and $\quad E=$ Student answer correctly.
<br/>$\therefore$
<br/>$P\left(E_{1}\right)=1-p$
<br/>$P\left(E_{2}\right)=p$
<br/>$P\left(\frac{E}{E_{2}}\right)=1$ and $P\left(\frac{E}{E_{1}}\right)=\frac{1}{5}$
<br/>$\therefore$ The probability that student did not tick the answer randomly
<br/>= The probability that student tick the answer correctly $=\frac{P\left(E_{2}\right) P\left(\frac{E}{E_{2}}\right)}{P\left(E_{1}\right) P\left(\frac{E}{E_{1}}\right)+P\left(E_{2}\right) P\left(\frac{E}{E_{2}}\right)}$
<br/>$=\frac{p(1)}{(1-p) \frac{1}{5}+p(1)}$
<br/>$=\frac{p}{\frac{1-p+5 p}{5}}=\frac{5 p}{1+4 p}$</div>


tags: ['Mathematics', 'Probability', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch1_P1.db
title:
a-student-appears-for-tests-1-11-and-iii-the-student-is-successful-if-he-passes-in-tests-iii-or-i-iii-the-probabilities-of-the-student-passing-in-test

slug:
a-student-appears-for-tests-1-11-and-iii-the-student-is-successful-if-he-passes-in-tests-iii-or-i-iii-the-probabilities-of-the-student-passing-in-test-87043

question:
<div class="question">$\mathrm{A}$ student appears for tests 1 , 11 and $\mathrm{III}$. The student is successful if he passes in tests I,II or I, III. The probabilities of the student passing in tests I. II and III are respectively,
<br/>p,q and $1 / 2 .$ If the probability of the student to be successful is $1 / 2 .$ Then</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$p(1+q)=1$</span> </div>

answer:
<div class="solution">Let $X$ be the event that student will be successful. $X_{1}$ be the event that student will be pass in test-I. $X_{2}$ be the event that student will be pass in test-II. $X_{3}$ be the event that student will be pass in test-III. $\therefore P(X)=P\left(X_{1} \cap X_{2} \cap X_{3}^{\prime}\right)+P\left(X_{1} \cap X_{2}^{\prime} \cap X_{3}\right)$
<br/>$P\left(X_{1}^{1} \cap X_{2} \cap X_{3}\right).$
<br/>$\Rightarrow P(X)=P\left(X_{1}\right) \cdot P\left(X_{2}\right) \cdot P\left(X_{3}^{1}\right)+P\left(X_{1}\right) \cdot P\left(X_{2}^{\prime}\right) \cdot P\left(X_{3}\right)$
<br/>$+P\left(X_{1}^{1}\right) \cdot P\left(X_{2}\right) \cdot P\left(X_{3}\right)$
<br/>$\Rightarrow \quad \frac{1}{2}=p \cdot q \cdot \frac{1}{2}+p(1-q) \frac{1}{2}+p q \frac{1}{2}$
<br/>$\Rightarrow \quad \frac{1}{2}=p \cdot q \cdot \frac{1}{2}+p \cdot \frac{1}{2}-p \cdot q \cdot \frac{1}{2}+p \cdot q \cdot \frac{1}{2}$
<br/>$\Rightarrow \quad \frac{1}{2}=p \cdot \frac{1}{2}+p \cdot q \cdot \frac{1}{2}$
<br/>$\Rightarrow \quad(p+p q)=1$
<br/>$\Rightarrow \quad p(1+q)=1$</div>


tags: ['Mathematics', 'Probability', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch1_P1.db
title:
a-survey-of-people-in-a-given-region-showed-that-20-were-smokers-the-probability-of-death-due-to-lung-cancer-given-that-a-person-smoked-was-10-times-t

slug:
a-survey-of-people-in-a-given-region-showed-that-20-were-smokers-the-probability-of-death-due-to-lung-cancer-given-that-a-person-smoked-was-10-times-t-24214

question:
<div class="question">A survey of people in a given region showed that $20 \%$ were smokers. The probability of death due to lung cancer given that a person smoked was 10 times the probability of death due to lung cancer, given that a person did not smoke. If the probability of death due to lung cancer in the region is 0.006 . What is the probability of death due to lung cancer given that a person is a smoker?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 / 140$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1 / 70$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$3 / 140$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$1 / 10$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3 / 140$</span> </div>

answer:
<div class="solution">Let $S=$ Event that person is smoker
<br/>$\mathrm{NS}=$ Event that person is non-smoker
<br/>$D=$ Event that death is due to lung cancer. 
<br/>Now, probability of death due to cancer that a person is a smoker, $P(D)=P(S) \cdot P\left(\frac{D}{S}\right)+P(N S) \cdot P\left(\frac{D}{N S}\right)$
<br/>$\Rightarrow 0.006=\frac{20}{100} \times P\left(\frac{D}{S}\right)+\frac{80}{100} \times \frac{1}{10} \times P\left(\frac{D}{S}\right)$
<br/>$\Rightarrow \frac{6}{1000}=\frac{2}{10} P\left(\frac{D}{S}\right)+\frac{8}{100} P\left(\frac{D}{S}\right)$
<br/>$\Rightarrow \quad P\left(\frac{D}{S}\right)\left[\frac{2}{10}+\frac{8}{100}\right]=\frac{6}{1000}$
<br/>$\Rightarrow \quad P\left(\frac{D}{S}\right)\left[\frac{20+8}{100}\right]=\frac{6}{1000}$
<br/>$\therefore \quad P\left(\frac{D}{S}\right)=\frac{6}{1000} \times \frac{100}{28}$
<br/>$=\frac{3}{140}$</div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'JEE Main']
source_db: db\MarksBatch1_P1.db
title:
a-tennis-ball-hits-the-floor-with-a-speed-v-at-an-angle-with-the-normal-to-the-floor-if-the-collision-is-inelastic-and-the-coefficient-of-restitution--1

slug:
a-tennis-ball-hits-the-floor-with-a-speed-v-at-an-angle-with-the-normal-to-the-floor-if-the-collision-is-inelastic-and-the-coefficient-of-restitution-1-94736

question:
<div class="question">A tennis ball hits the floor with a speed $v$ at an angle $\theta$ with the normal to the floor. If the collision is inelastic and the co-efficient of restitution is $\varepsilon$, what will be the angle of reflection?</div>

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

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

answer:
<div class="solution">Hint:
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/pOnd9c6nLaNmaZfDKfKxgkIFvSsVCvKSqfsOv43k0dc.original.fullsize.png"/><br/> <br/>$\tan \theta^{\prime}=\frac{\operatorname{usin} \theta}{\operatorname{eucos} \theta} \quad \tan \theta^{\prime}=\frac{1}{\mathrm{e}} \tan \theta$
<br/>Since the floor is smooth. Hence tangential component of velocity remains unchanged.</div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P1.db
title:
a-tennis-ball-hits-the-floor-with-a-speed-v-at-an-angle-with-the-normal-to-the-floor-if-the-collision-is-inelastic-and-the-coefficient-of-restitution-

slug:
a-tennis-ball-hits-the-floor-with-a-speed-v-at-an-angle-with-the-normal-to-the-floor-if-the-collision-is-inelastic-and-the-coefficient-of-restitution-45513

question:
<div class="question">A tennis ball hits the floor with a speed $v$ at an angle $\theta$ with the normal to the floor. If the collision is inelastic and the co-efficient of restitution is $\varepsilon$, what will be the angle of reflection?</div>

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

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

answer:
<div class="solution">Hint:
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/pOnd9c6nLaNmaZfDKfKxgkIFvSsVCvKSqfsOv43k0dc.original.fullsize.png"/><br/> <br/>$\tan \theta^{\prime}=\frac{\operatorname{usin} \theta}{\operatorname{eucos} \theta} \quad \tan \theta^{\prime}=\frac{1}{\mathrm{e}} \tan \theta$
<br/>Since the floor is smooth. Hence tangential component of velocity remains unchanged.</div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Main']
source_db: db\MarksBatch1_P1.db
title:
a-thin-charged-rod-is-bent-into-the-shape-of-a-small-circle-of-radius-r-the-charge-per-unit-length-of-the-rod-being-the-circle-is-rotated-about-its-ax-1

slug:
a-thin-charged-rod-is-bent-into-the-shape-of-a-small-circle-of-radius-r-the-charge-per-unit-length-of-the-rod-being-the-circle-is-rotated-about-its-ax-1-71993

question:
<div class="question">A thin charged rod is bent into the shape of a small circle of radius $\mathrm{R}$ the charge per unit length of the rod being $\lambda$. The circle is rotated about its axis with a time period $T$ and it is found that the magnetic field at a distance ' $d$ ' away $(d&gt;&gt;R)$ from the center and on the axis, varies as $\frac{\mathrm{R}^{\mathrm{m}}}{\mathrm{d}^{\mathrm{n}}} .$ The values of $\mathrm{m}$ and $\mathrm{n}$ respectively are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$m=2, n=2$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$m=2, n=3$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$m=3, n=2$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$m=3, n=3$</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">$m=3, n=3$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/ygUtZVg5dOUpNj8-0dTvdfFZgq8-O2T5LDWtz713d8U.original.fullsize.png"/><br/> <br/>$\mathrm{B}=\frac{\mu_{0}}{4 \pi} \frac{2 \pi \mathrm{R}^{2} \mathrm{I}}{\left(\mathrm{R}^{2}+\mathrm{d}^{2}\right)^{3 / 2}} \quad \mathrm{I}=\frac{\mathrm{q}}{\mathrm{T}}$
<br/>$=\frac{2 \pi \mathrm{R} \lambda}{\mathrm{T}}$
<br/>$=\frac{\mu_{0}}{4 \pi} \frac{2 \pi \mathrm{R}^{2} \mathrm{I}}{\mathrm{d}^{3}}(\mathrm{~d}&gt;&gt;\mathrm{R})$
<br/>$\frac{\mu_{0}}{2} \frac{\mathrm{R}^{2}}{\mathrm{~d}^{3}} \times \frac{2 \pi \mathrm{R} \lambda}{\mathrm{T}}$
<br/>$\mathrm{B} \propto \frac{\mathrm{R}^{3}}{\mathrm{~d}^{3}}$
<br/>$\therefore \mathrm{m}=\mathrm{n}=3$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch1_P1.db
title:
a-thin-charged-rod-is-bent-into-the-shape-of-a-small-circle-of-radius-r-the-charge-per-unit-length-of-the-rod-being-the-circle-is-rotated-about-its-ax

slug:
a-thin-charged-rod-is-bent-into-the-shape-of-a-small-circle-of-radius-r-the-charge-per-unit-length-of-the-rod-being-the-circle-is-rotated-about-its-ax-94219

question:
<div class="question">A thin charged rod is bent into the shape of a small circle of radius $\mathrm{R}$ the charge per unit length of the rod being $\lambda$. The circle is rotated about its axis with a time period $T$ and it is found that the magnetic field at a distance ' $d$ ' away $(d&gt;&gt;R)$ from the center and on the axis, varies as $\frac{\mathrm{R}^{\mathrm{m}}}{\mathrm{d}^{\mathrm{n}}} .$ The values of $\mathrm{m}$ and $\mathrm{n}$ respectively are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$m=2, n=2$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$m=2, n=3$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$m=3, n=2$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$m=3, n=3$</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">$m=3, n=3$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/ygUtZVg5dOUpNj8-0dTvdfFZgq8-O2T5LDWtz713d8U.original.fullsize.png"/><br/> <br/>$\mathrm{B}=\frac{\mu_{0}}{4 \pi} \frac{2 \pi \mathrm{R}^{2} \mathrm{I}}{\left(\mathrm{R}^{2}+\mathrm{d}^{2}\right)^{3 / 2}} \quad \mathrm{I}=\frac{\mathrm{q}}{\mathrm{T}}$
<br/>$=\frac{2 \pi \mathrm{R} \lambda}{\mathrm{T}}$
<br/>$=\frac{\mu_{0}}{4 \pi} \frac{2 \pi \mathrm{R}^{2} \mathrm{I}}{\mathrm{d}^{3}}(\mathrm{~d}&gt;&gt;\mathrm{R})$
<br/>$\frac{\mu_{0}}{2} \frac{\mathrm{R}^{2}}{\mathrm{~d}^{3}} \times \frac{2 \pi \mathrm{R} \lambda}{\mathrm{T}}$
<br/>$\mathrm{B} \propto \frac{\mathrm{R}^{3}}{\mathrm{~d}^{3}}$
<br/>$\therefore \mathrm{m}=\mathrm{n}=3$</div>


tags: ['Physics', 'Ray Optics', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P1.db
title:
a-thin-convex-lens-is-placed-just-above-an-empty-vessel-of-depth-80-cm-the-image-of-a-coin-kept-at-the-bottom-of-the-vessel-is-thus-formed-20-cm-above

slug:
a-thin-convex-lens-is-placed-just-above-an-empty-vessel-of-depth-80-cm-the-image-of-a-coin-kept-at-the-bottom-of-the-vessel-is-thus-formed-20-cm-above-66681

question:
<div class="question">A thin convex lens is placed just above an empty vessel of depth $80 \mathrm{~cm}$. The image of a coin kept at the bottom of the vessel is thus formed $20 \mathrm{~cm}$ above the lens. If now water is poured in the vessel up to a height of $64 \mathrm{~cm}$, what will be the approximate new position of the image. Assume that refractive index of water is $4 / 3$.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$21.33 \mathrm{~cm}$ above the lens</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$6.67 \mathrm{~cm}$ below the lens</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$33.67 \mathrm{~cm}$ above the lens</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$24 \mathrm{~cm}$ above the lens</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$21.33 \mathrm{~cm}$ above the lens</span> </div>

answer:
<div class="solution">Hint: 
<br/>$\mathrm{u}=-80 \mathrm{~cm} \quad \mathrm{v}=+20 \mathrm{~cm}$
<br/>$\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{1}{20}+\frac{1}{80}=\frac{5}{80}$
<br/>$f=16 \mathrm{~cm}$
<br/>$\mathrm{u}^{\prime}=16+\frac{64 \times 3}{4}=64 \mathrm{~cm}$
<br/>$\frac{1}{16}=\frac{1}{v}+\frac{1}{64} \quad \therefore \frac{1}{v}=\frac{1}{16}-\frac{1}{64}=\frac{3}{64}$
<br/>$v=21.33$ above the lens
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/wWvSiRxqb37vSqr-EwBryKodqsZrEEsQlra4EwdCv1w.original.fullsize.png"/></div>


tags: ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P1.db
title:
a-thin-glass-rod-is-bent-in-a-semicircle-of-radius-mathrmr-a-change-is-nonuniformly-distributed-along-the-rod-with-a-linear-charge-density-lambdalambd

slug:
a-thin-glass-rod-is-bent-in-a-semicircle-of-radius-mathrmr-a-change-is-nonuniformly-distributed-along-the-rod-with-a-linear-charge-density-lambdalambd-68331

question:
<div class="question">A thin glass rod is bent in a semicircle of radius \(\mathrm{R}\). A change is non-uniformly distributed along the rod with a linear charge density \(\lambda=\lambda_0 \sin \left(\lambda_0\right.\) is a positive constant). The electric field at the centre \(P\) of the semicircle is,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/MlujJvxjH1OFoYR8t5A2VtxMwvmiiR9c3E_ulA7lWvA.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(-\frac{\lambda_0}{8 \pi \varepsilon_0 R} \hat{j}\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(\frac{\lambda_0}{8 \pi \varepsilon_0 R} \hat{j}\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(\frac{\lambda_0}{8 \pi \varepsilon_0 R} \hat{i}\)</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">None of these</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">None of these</span> </div>

answer:
<div class="solution">Hint : <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/DgZwWf0j3UB8KTHg9XlUFIne3KWNXepqPnRwa0b1C2s.original.fullsize.png"/><br/><br/>\(\begin{aligned}<br/>&amp; \lambda=\lambda_0 \sin \theta \\<br/>&amp; \mathrm{dE}_{\mathrm{y}}=\frac{\mathrm{k} \lambda}{\mathrm{R}} \sin \theta \mathrm{d} \theta \\<br/>&amp; =\frac{\mathrm{k} \lambda_0}{\mathrm{R}} \int_{-\pi / 2}^{+\pi / 2} \sin ^2 \theta \mathrm{d} \theta=\frac{\mathrm{k} \lambda_0}{2 \mathrm{R}} \int_{-\pi / 2}^{+\pi / 2}(1-\cos 2 \theta) \mathrm{d} \theta \\<br/>&amp; \therefore \overrightarrow{\mathrm{E}}=-\frac{\lambda_0}{8 \varepsilon_0 \mathrm{R}} \hat{\mathrm{j}}<br/>\end{aligned}\)</div>


tags: ['Physics', 'Wave Optics', 'WBJEE', 'WBJEE 2015']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: db\MarksBatch1_P1.db
title:
a-thin-plastic-sheet-of-refractive-index-16-is-used-to-cover-one-of-the-slits-of-a-clouble-slit-arrangement-the-central-point-on-the-scireen-is-now-oc

slug:
a-thin-plastic-sheet-of-refractive-index-16-is-used-to-cover-one-of-the-slits-of-a-clouble-slit-arrangement-the-central-point-on-the-scireen-is-now-oc-96059

question:
<div class="question">A thin plastic sheet of refractive index 1.6 is used to cover one of the slits of a clouble slit arrangement. The central point on the scireen is now occupied by what would have been the 7th bright fringo before the plastic was used. If the wavelength of light is $600 \mathrm{nm}$, what is the thickness (in $\mu \mathrm{m}$ ) of the plastic sheet?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">7</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">4</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">8</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">6</span> </li> </ul>

answer:
<div class="solution">The change in path length $=(\mu-1) t$ This path length change the position of bright fringe upto seventh bright fringe. The thickness of plastic substance inserted in the path of rays will must be 7 (on assuming fringe width to be units).</div>


tags: ['Physics', 'Rotational Motion', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
title:
a-thin-rod-a-b-is-held-horizontally-so-that-it-can-freely-rotate-in-a-vertical-plane-about-the-end-a-as-shown-in-the-figure-the-potential-energy-of-th

slug:
a-thin-rod-a-b-is-held-horizontally-so-that-it-can-freely-rotate-in-a-vertical-plane-about-the-end-a-as-shown-in-the-figure-the-potential-energy-of-th-36146

question:
<div class="question">A thin rod $A B$ is held horizontally so that it can freely rotate in a vertical plane about the end $A$ as shown in the figure. The potential energy of the rod when it hangs vertically is taken to be zero. The end $B$ of the rod is released from rest from a horizontal position. At the instant the rod makes an angle $\theta$ with the horizontal</div>

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

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">the speed of end $B$ is proportional to $\sqrt{\sin \theta}$, the angular acceleration is proportional to $\cos \theta$</span> </div>

answer:
<div class="solution">Loss in potential energy = gain in kinetic energy
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_phy_a57.png"/> <br/> <br/>$\Rightarrow \quad m g \frac{L}{2} \sin \theta=\frac{1}{2} I \omega^{2}$
<br/>So $\omega \propto \sqrt{\sin \theta}$
<br/>and $\quad v \propto \sqrt{\sin \theta} \quad\left(\because K=\frac{1}{2} \mathrm{H} \omega^{2}\right)$
<br/>The speed of end $B$ is proportional to $\sqrt{\sin \theta}$
<br/>and
<br/>$$
<br/>U=m g h=m g \frac{L}{2}(1-\sin \theta) \quad(\because \tau=l \alpha)
<br/>$$
<br/>$\Rightarrow \quad m g \frac{L}{2} \cos \theta=\frac{m I^{2}}{3} \times \boldsymbol{\alpha}$
<br/>$$
<br/>\alpha \propto \cos \theta
<br/>$$
<br/>The angular acceleration is proportional to cos $\theta$</div>


tags: ['Physics', 'Waves and Sound', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch1_P1.db
title:
a-train-approaching-a-railway-platform-with-a-speed-of-20-ms-1-starts-blowing-the-whistle-speed-of-sound-in-air-is-340-ms-1-if-the-frequency-of-the-em

slug:
a-train-approaching-a-railway-platform-with-a-speed-of-20-ms-1-starts-blowing-the-whistle-speed-of-sound-in-air-is-340-ms-1-if-the-frequency-of-the-em-80339

question:
<div class="question">A train approaching a railway platform with a speed of $20 \mathrm{ms}^{-1}$ starts blowing the whistle. Speed of sound in air is $340 \mathrm{ms}^{-1}$. If the frequency of the emitted sound from the whistle is $640 \mathrm{Hz}$, the frequency of sound to a person standing on the platform will appear to be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$600 \mathrm{Hz}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$640 \mathrm{Hz}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$680 \mathrm{Hz}$</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">D</span> <span class="option-data">$720 \mathrm{Hz}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$680 \mathrm{Hz}$</span> </div>

answer:
<div class="solution">Given $\quad v=340 \mathrm{ms}^{-1}, \quad u_{5}=20 \mathrm{ms}^{-1} \quad$ and
<br/>$v_{0}=640 \mathrm{Hz}$
<br/>From Doppler's law,
<br/>$$
<br/>\begin{array}{l}
<br/>v=\left(\frac{340}{340-20}\right) 640 \\
<br/>v=680 \mathrm{Hz}
<br/>\end{array}
<br/>$$</div>


tags: ['Physics', 'Work Power Energy', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P1.db
title:
a-train-is-moving-along-the-tracks-at-a-constant-speed-mathrmu-a-girl-on-the-train-throws-a-ball-of-mass-m-straight-ahead-along-the-direction-of-motio

slug:
a-train-is-moving-along-the-tracks-at-a-constant-speed-mathrmu-a-girl-on-the-train-throws-a-ball-of-mass-m-straight-ahead-along-the-direction-of-motio-12257

question:
<div class="question">A train is moving along the tracks at a constant speed \(\mathrm{u}\). A girl on the train throws a ball of mass \(m\) straight ahead along the direction of motion of the train with speed \(v\) with respect to herself. Then</div>

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

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">Kinetic energy of the ball as measured by the girl on the train is \(\mathrm{mv}^2 / 2\), Work done by the girl in throwing the ball is \(\mathrm{mv}^2 / 2\), Work done by the train is mvu</span> </div>

answer:
<div class="solution">Hint : w.r.t. the girl \(E_k=\frac{1}{2} m v^2\)<br/>\(\therefore \mathrm{W}=\Delta \mathrm{E}_{\mathrm{k}}=1 / 2 \mathrm{mv}^2\)<br/>Work by the train \(=\left\{\frac{1}{2}(v+u)^2-\frac{1}{2} m u^2\right\}-\frac{1}{2} m v^2\)<br/>\(\begin{aligned}<br/>&amp; =\frac{1}{2} m\left(v^2+u^2+2 v u\right)-\frac{1}{2} m\left(v^2+u^2\right) \\<br/>&amp; =m v u<br/>\end{aligned}\)<br/>Gain in \(E_k=\frac{1}{2} m(v+u)^2-\frac{1}{2} m u^2=\frac{1}{2} m v^2+m v u\)<br/>measured from rail track</div>


tags: ['Physics', 'Waves and Sound', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch1_P1.db
title:
a-train-is-moving-with-a-uniform-speed-c-2-33-m-s-and-an-observer-is-approaching-the-train-with-the-same-speed-if-the-train-blows-a-whistle-of-frequen

slug:
a-train-is-moving-with-a-uniform-speed-c-2-33-m-s-and-an-observer-is-approaching-the-train-with-the-same-speed-if-the-train-blows-a-whistle-of-frequen-94912

question:
<div class="question">$A$ train is moving with a uniform speed $c^{2}$ $33 \mathrm{m} / \mathrm{s}$ and an observer is approaching the train with the same speed. If the train blows a whistle of frequency $1000 \mathrm{Hz}$ and the velocity of sound is $333 \mathrm{m} / \mathrm{s},$ then the apparent frequency of the sound that the observer hears is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$1220 \mathrm{Hz}$</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">$1099 \mathrm{Hz}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1110 \mathrm{Hz}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1200 \mathrm{Hi}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1220 \mathrm{Hz}$</span> </div>

answer:
<div class="solution">We have,
<br/>Apparent frequency,
<br/>$\mathrm{v}  =\left(\frac{v+u_{0}}{v-u_{s}}\right)\mathrm{v}_{0}=\left(\frac{333+33}{333-33}\right) \times 1000 \\=\frac{366}{300} \times 1000=1220 \mathrm{Hz}$</div>


tags: ['Physics', 'Motion In One Dimension', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch1_P1.db
title:
a-train-moves-from-rest-with-acceleration-and-in-time-t-1-covers-a-distance-x-it-then-decelerates-to-rest-at-constant-retardation-for-distance-y-in-ti

slug:
a-train-moves-from-rest-with-acceleration-and-in-time-t-1-covers-a-distance-x-it-then-decelerates-to-rest-at-constant-retardation-for-distance-y-in-ti-45193

question:
<div class="question">A train moves from rest with acceleration and in time $t_{1}$ covers a distance $x$. It then decelerates to rest at constant retardation $\beta$ for distance $y$ in time $t_{2}$. Then,</div>

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

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">$\frac{x}{y}=\frac{\beta}{\alpha}$, $\frac{\beta}{\alpha}=\frac{t_{1}}{t_{2}}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_phy_a38.png"/> <br/> <br/>Shape of the graph $\mathrm{OP}$ shows the acceleration in train
<br/>$\therefore \tan \theta=$ acceleration.
<br/>$$
<br/>\boldsymbol{\alpha}=\frac{V_{0}}{t_{1}}
<br/>$$
<br/>Shape of the graph pt shows the deceleration in train.
<br/>$\therefore$ Similarly. $\quad \beta=\frac{v_{0}}{t_{2}}$
<br/>$\therefore \quad \frac{\boldsymbol{\beta}}{\boldsymbol{\alpha}}=\frac{\boldsymbol{v}_{0} / \boldsymbol{t}_{\boldsymbol{2}}}{\mathrm{v}_{0} / t_{1}}=\frac{t_{1}}{t_{2}}$
<br/>Displacement = area of graph obtained between v-t
<br/>$$
<br/>\begin{array}{l}
<br/>x=\frac{1}{2} t_{1}, v_{0} \\
<br/>y=\frac{1}{2} t_{2}, v_{0}
<br/>\end{array}
<br/>$$
<br/>$\therefore \frac{x}{y}=\frac{t_{1}}{t_{2}}
<br/>\Rightarrow \quad \frac{x}{y}=\frac{t_{1}}{t_{2}}=\frac{\beta}{a}$</div>


tags: ['Physics', 'Waves and Sound', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P1.db
title:
a-travelling-acoustic-wave-frequency-500-hz-is-moving-along-the-positive-x-direction-with-a-velocity-of-300-ms-1-the-phase-difference-between-two-poin

slug:
a-travelling-acoustic-wave-frequency-500-hz-is-moving-along-the-positive-x-direction-with-a-velocity-of-300-ms-1-the-phase-difference-between-two-poin-68396

question:
<div class="question">A travelling acoustic wave frequency $500 \mathrm{Hz}$ is moving along the positive $x$ -direction with a velocity of $300 \mathrm{ms}^{-1}$. The phase difference between two points $x_{1}$ and $x_{2}$ is $60^{\circ} .$ Then the minimum separation between the two points is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 \mathrm{mm}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1 \mathrm{cm}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$10 \mathrm{cm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$10 \mathrm{mm}$</span> </li> </ul>

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

answer:
<div class="solution">By using the relation, $v=v \lambda$
<br/>We have, $\quad \lambda=\frac{V}{v}=\frac{300}{500}=\frac{3}{5} \mathrm{m}$
<br/>The phase difference, $\phi=\frac{2 \pi}{\lambda}(\Delta x)$ $\Rightarrow \quad \frac{\pi}{3}=\frac{2 \pi \times 5}{3}(\Delta x) \Rightarrow \Delta x=\frac{1}{10} m=10 \mathrm{cm}$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch1_P1.db
title:
a-uniform-capillary-tube-of-length-l-and-inner-radius-r-with-its-upper-end-sealed-is-submerged-vertically-into-water-the-outside-pressure-is-p-0-and-s

slug:
a-uniform-capillary-tube-of-length-l-and-inner-radius-r-with-its-upper-end-sealed-is-submerged-vertically-into-water-the-outside-pressure-is-p-0-and-s-48824

question:
<div class="question">A uniform capillary tube of length $l$ and inner radius $r$ with its upper end sealed is submerged vertically into water. The outside pressure is $p_{0}$ and surface tension of water is $\gamma$. When a length $x$ of the capillary is submerged into water, it is found that water levels inside and outside the capillary coincide. The value of $x$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{l}{\left(1+\frac{p_{0} r}{4 \gamma}\right)}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$l\left(1-\frac{p_{0} r}{4 \gamma}\right)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$l\left(1-\frac{p_{0} r}{2 \gamma}\right)$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{l}{\left(1+\frac{p_{0} r}{2 \gamma}\right)}$</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 answer is:
<span class="option-value">$\frac{l}{\left(1+\frac{p_{0} r}{2 \gamma}\right)}$</span> </div>

answer:
<div class="solution">When the sealed capillary tube is submerged vertically into water, the pressure inside the tube changes
<br/>For the inside capillary,
<br/>$$
<br/>p_{1} V_{1}=p_{2} v_{2}
<br/>$$
<br/>$\therefore \quad P_{0}(l A)=p^{\prime}(l-x) A$
<br/>where $p^{\prime}$ is pressure in capillary after being submerged
<br/>$\therefore$
<br/>$$
<br/>p^{\prime}=\frac{p_{0}l}{l-x}
<br/>$$
<br/>According to question, since level of water inside capillary coincides with outside.
<br/>$$
<br/>\begin{array}{l}
<br/>\therefore \quad p^{\prime}-p_{0}=\frac{2 \gamma}{r} \\
<br/>\therefore \quad \frac{p_{d}}{l-x}-p_{0}=\frac{2 \gamma}{r}=\frac{l}{\left(1+\frac{p_{0} r}{2 \gamma}\right)}
<br/>\end{array}
<br/>$$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Main']
source_db: db\MarksBatch1_P1.db
title:
a-uniform-current-is-flowing-along-the-length-dinfinite-straight-thin-hollow-cylinder-dradius-r-the-magnetic-field-b-produced-at-perpendicular-distanc-1

slug:
a-uniform-current-is-flowing-along-the-length-dinfinite-straight-thin-hollow-cylinder-dradius-r-the-magnetic-field-b-produced-at-perpendicular-distanc-1-33232

question:
<div class="question">A uniform current is flowing along the length dinfinite, straight. thin. hollow cylinder dradius $R$ The magnetic field $B$ produced at perpendicular distance $d$ from the axis of the cylinder is plotied in a graph. Which of the following figures looks like the plot?</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/2018_phy_q27_opta.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_q27_optb.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/2018_phy_q27_optc.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/2018_phy_q27_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/2018_phy_q27_optc.png"/></span> </div>

answer:
<div class="solution">$\because$ Magnetic field due to a hollow cylinder of radius $r$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_a27.png"/> <br/> <br/>$$
<br/>\begin{aligned}
<br/>B_{\text {inside }} &amp;=0(\text { for } d &lt; r) \\
<br/>B_{\text {outside }} &amp;=\frac{\mu_{0}}{2 \pi} \cdot \frac{i}{d}(\text { for } d \geq r)
<br/>\end{aligned}
<br/>$$
<br/>So, graph between $B$ and $d$.<img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_a27a.png"/></div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch1_P1.db
title:
a-uniform-current-is-flowing-along-the-length-dinfinite-straight-thin-hollow-cylinder-dradius-r-the-magnetic-field-b-produced-at-perpendicular-distanc

slug:
a-uniform-current-is-flowing-along-the-length-dinfinite-straight-thin-hollow-cylinder-dradius-r-the-magnetic-field-b-produced-at-perpendicular-distanc-75684

question:
<div class="question">A uniform current is flowing along the length dinfinite, straight. thin. hollow cylinder dradius $R$ The magnetic field $B$ produced at perpendicular distance $d$ from the axis of the cylinder is plotied in a graph. Which of the following figures looks like the plot?</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/2018_phy_q27_opta.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_q27_optb.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/2018_phy_q27_optc.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/2018_phy_q27_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/2018_phy_q27_optc.png"/></span> </div>

answer:
<div class="solution">$\because$ Magnetic field due to a hollow cylinder of radius $r$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_a27.png"/> <br/> <br/>$$
<br/>\begin{aligned}
<br/>B_{\text {inside }} &amp;=0(\text { for } d &lt; r) \\
<br/>B_{\text {outside }} &amp;=\frac{\mu_{0}}{2 \pi} \cdot \frac{i}{d}(\text { for } d \geq r)
<br/>\end{aligned}
<br/>$$
<br/>So, graph between $B$ and $d$.<img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_a27a.png"/></div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2010']
source_db: db\MarksBatch1_P1.db
title:
a-uniform-long-tube-is-bent-into-a-circle-of-radius-r-and-it-lies-in-vertical-plane-two-liquids-of-same-volume-but-densities-and-fill-half-the-tube-th

slug:
a-uniform-long-tube-is-bent-into-a-circle-of-radius-r-and-it-lies-in-vertical-plane-two-liquids-of-same-volume-but-densities-and-fill-half-the-tube-th-81042

question:
<div class="question">A uniform long tube is bent into a circle of radius $\mathrm{R}$ and it lies in vertical plane. Two liquids of same volume but densities $\rho$ and $\delta$ fill half the tube. The angle $\theta$ is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/mYpgkigHCPKfG3PgHWoUOVNJNqfKPU9PqzkMoFNYFSc.original.fullsize.png"/><br/></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\tan ^{-1}\left(\frac{\rho-\delta}{\rho+\delta}\right)$</span> </div>

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>&amp; \text { Hints: } \delta g R(\cos \theta+\sin \theta)=\rho g R(\cos \theta-\sin \theta) \\<br/>&amp; \delta \cos \theta+\delta \sin \theta=\rho \cos \theta-\rho \sin \theta \\<br/>&amp; \sin \theta(\delta+\rho)=\cos \theta(\rho-\delta) \\<br/>&amp; \tan \theta=\frac{\rho-\delta}{\rho+\delta}<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P1.db
title:
a-uniform-magnetic-field-b-exists-in-a-region-an-electron-of-charge-q-and-mass-m-moving-with-velocity-v-enters-the-region-in-a-direction-perpendicular

slug:
a-uniform-magnetic-field-b-exists-in-a-region-an-electron-of-charge-q-and-mass-m-moving-with-velocity-v-enters-the-region-in-a-direction-perpendicular-99153

question:
<div class="question">A uniform magnetic field \(B\) exists in a region. An electron of charge \(q\) and mass \(m\) moving with velocity \(v\) enters the region in a direction perpendicular to the magnetic field. Considering Bohr angular momentum quantization, 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 radius of \(\mathrm{n}^{\text {th }}\) orbit \(\mathrm{r}_{\mathrm{n}} \propto \sqrt{\mathrm{n}}\)</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="correct"> <span class="option-label">B</span> <span class="option-data">The maximum velocity of the electron is \(\frac{\sqrt{\mathrm{qB} \hbar}}{\mathrm{m}}\)</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="correct"> <span class="option-label">C</span> <span class="option-data">Energy of the \(n^{\text {th }}\) level \(E_n \propto n\)</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="correct"> <span class="option-label">D</span> <span class="option-data">Transition frequency \(\omega\) between two successive levels is independent of \(n\)</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> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">The radius of \(\mathrm{n}^{\text {th }}\) orbit \(\mathrm{r}_{\mathrm{n}} \propto \sqrt{\mathrm{n}}\), The maximum velocity of the electron is \(\frac{\sqrt{\mathrm{qB} \hbar}}{\mathrm{m}}\), Energy of the \(n^{\text {th }}\) level \(E_n \propto n\), Transition frequency \(\omega\) between two successive levels is independent of \(n\)</span> </div>

answer:
<div class="solution">Hint: \(r=\frac{m v}{q B}\)<br/>\(m v r=\frac{n h}{2 \pi}\)<br/>\(m v=\frac{n h}{2 \pi r}\)<br/>\(r=\frac{n h}{2 \pi r q B}\)<br/>\(\begin{aligned} &amp; r^2=\frac{n h}{2 \pi q B} \Rightarrow r=\sqrt{\frac{n h}{2 \pi q B}} \\ &amp; r \propto \sqrt{n} \\ &amp; v=\frac{q B r}{m}=\frac{q B}{m} \sqrt{\frac{n h}{2 \pi q B}} \\ &amp; \underset{m i n}{v}=\sqrt{\frac{q^2 B^2}{m^2} \times \frac{n h}{2 \pi q B}}=\sqrt{\frac{n \mathrm{qBh}}{2 \pi m^2}}=\frac{1}{m} \sqrt{q B} \hbar\end{aligned}\)<br/>\(\begin{aligned} E &amp; =\frac{1}{2} m v^2 \\ &amp; =\frac{1}{2} m\left[\frac{n q B h}{2 \pi m^2}\right]\end{aligned}\)<br/>\(E \propto n\)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/0GvPdfaj6UI240P5YCvSdBmEVFHr42bHO6m-vDKIYmw.original.fullsize.png"/><br/><br/>\(\begin{aligned} &amp; \mathrm{E}_2-\mathrm{E}_1=\left(\mathrm{n}_2-\mathrm{n}_1\right) \frac{\mathrm{qBh}}{4 \pi \mathrm{m}} \\ &amp; \mathrm{hf}=\left(\mathrm{n}_2-\mathrm{n}_1\right) \frac{\mathrm{qBh}}{4 \pi \mathrm{m}} \\ &amp; \mathrm{n}_2-\mathrm{n}_1=1 \text { for successive levels }\end{aligned}\)</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
title:
a-uniform-rod-is-suspended-horizontally-from-its-midpoint-a-piece-of-metal-whose-weight-is-w-is-suspended-at-a-distance-l-from-the-midpoint-another-we

slug:
a-uniform-rod-is-suspended-horizontally-from-its-midpoint-a-piece-of-metal-whose-weight-is-w-is-suspended-at-a-distance-l-from-the-midpoint-another-we-34215

question:
<div class="question">A uniform rod is suspended horizontally from its mid-point. A piece of metal whose weight is $w$ is suspended at a distance $l$ from the mid-point. Another weight $W_{1}$ is suspended on the other side at a distance $l_{1}$ from the mid-point to bring the rod to a horizontal position. Wben $w$ is completely immersed in water, $w_{1}$ needs to be kept at a distance $l_{2}$ from the mid-point to get the rod back into horizontal position. The specific gravity of the metal piece is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{w}{w_{1}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{w l_{1}}{w l-w_{1} l_{2}}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{L_{1}}{l_{1}-l_{2}}$</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">D</span> <span class="option-data">$\frac{l_{1}}{l_{2}}$</span> </li> </ul>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_phy_a20.png"/> <br/> <br/>$$
<br/>W-F_{B}=W\left(1-\frac{1}{\rho}\right)
<br/>$$
<br/>where $\rho=$ specific gravity $W\left(1-\frac{1}{\rho}\right)=W_{1} b$
<br/>$\left(1-\frac{1}{\rho}\right)=\frac{W_{1} L_{2}}{W}$
<br/>$\left(1-\frac{1}{\rho}\right)=\frac{W_{1} b_{2}}{W_{1} L_{1}}$
<br/>$1-\frac{1}{\rho}=\frac{L_{2}}{L_{1}} \Rightarrow \frac{1}{\rho}=1-\frac{b}{L_{1}}$
<br/>$\frac{1}{\rho}=\frac{l_{1}-L_{2}}{l_{1}}$ or $\rho=\frac{l_{1}}{l_{1}-L_{2}}$</div>


tags: ['Physics', 'Rotational Motion', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch1_P1.db
title:
a-uniform-rod-of-length-l-pivoted-at-one-end-p-is-freely-rotated-in-a-horizontal-plane-with-an-angular-velocity-about-a-vertical-axis-passing-through-

slug:
a-uniform-rod-of-length-l-pivoted-at-one-end-p-is-freely-rotated-in-a-horizontal-plane-with-an-angular-velocity-about-a-vertical-axis-passing-through-30124

question:
<div class="question">A uniform rod of length $L$ pivoted at one end $P$ is freely rotated in a horizontal plane with an angular velocity $\omega$ about a vertical axis passing through $\mathrm{P}$. If the temperature of the system is increased by $\Delta \mathrm{T}$, angular velocity becomes $\frac{\omega}{2}$. If coefficient of linear expansion of the rod is $\alpha(\alpha&lt; &lt; 1)$, then $\Delta \mathrm{T}$ will be</div>

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

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

answer:
<div class="solution">$\mathrm{I} \omega=\mathrm{I}_{1} \frac{\omega}{2}$
<br/>$\quad \mathrm{I}_{1}=2 \mathrm{I}$
<br/>$\quad \frac{\mathrm{ml}_{1}^{2}}{3}=2 \frac{\mathrm{ml}_{0}^{2}}{3}$
<br/>$\left\{\mathrm{I}_{0}^{2}(1+\alpha \Delta \mathrm{T})\right\}^{2}=2 \mathrm{I}_{0}^{2}, \therefore 1+2 \alpha \Delta \mathrm{T}=2 \therefore \Delta \mathrm{T}=\frac{1}{2 \alpha}$</div>


tags: ['Physics', 'Work Power Energy', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P1.db
title:
a-uniform-rope-of-length-4-mathrmm-and-mass-04-mathrmkg-is-held-on-a-frictionless-table-in-such-a-way-that-06-mathrmm-of-the-rope-is-hanging-over-the-

slug:
a-uniform-rope-of-length-4-mathrmm-and-mass-04-mathrmkg-is-held-on-a-frictionless-table-in-such-a-way-that-06-mathrmm-of-the-rope-is-hanging-over-the-97730

question:
<div class="question">A uniform rope of length \(4 \mathrm{~m}\) and mass \(0.4 \mathrm{~kg}\) is held on a frictionless table in such a way that \(0.6 \mathrm{~m}\) of the rope is hanging over the edge. The work done to pull the hanging part of the rope on the to the table is, (Assume \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(0.36 \mathrm{~J}\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(0.24 \mathrm{~J}\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(0.12 \mathrm{~J}\)</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">\(0.18 \mathrm{~J}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(0.18 \mathrm{~J}\)</span> </div>

answer:
<div class="solution">\(\begin{aligned}<br/>&amp; \text {Hint : } W=\frac{\mathrm{mgL}}{2}=\frac{0.4}{4} \times 0.6 \times 10 \times \frac{0.6}{2} \\<br/>&amp; =0.1 \times 0.6 \times 10 \times 0.3 \\<br/>&amp; =0.18 \mathrm{~J}<br/>\end{aligned}\)</div>


tags: ['Physics', 'Rotational Motion', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
title:
a-uniform-solid-spherical-ball-is-rolling-down-a-smooth-inclined-plane-from-a-height-h-the-velocity-attained-by-the-ball-when-it-reaches-the-bottom-of

slug:
a-uniform-solid-spherical-ball-is-rolling-down-a-smooth-inclined-plane-from-a-height-h-the-velocity-attained-by-the-ball-when-it-reaches-the-bottom-of-55811

question:
<div class="question">A uniform solid spherical ball is rolling down a smooth inclined plane from a height $h$. The velocity attained by the ball when it reaches the bottom of the inclined plane is v. If the ball is now thrown vertically upwards with the same velocity $v$, the maximum height to which the ball will rise is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{5 h}{8}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{3 h}{5}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{5 h}{7}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{7 h}{9}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{5 h}{7}$</span> </div>

answer:
<div class="solution">We know that total kinetic energy of a body rolling without slipping
<br/>$K_{\text {total }}=K_{\text {rot }}+K_{\text {trans }}$ For solid spherical ball, $I=\frac{2}{5} m R^{2}$ (along to diameter) and $v=R \omega$ where $R$ is radius of spherical ball
<br/>So.
<br/>$$
<br/>K_{\text {total }}=\frac{1}{2}\left(\frac{2}{5} m R^{2}\right) \omega^{2}+\frac{1}{2} m R^{2} \omega^{2}
<br/>$$
<br/>$$
<br/>\begin{array}{l}
<br/>=\frac{7}{10} m R^{2} \omega^{2} \\
<br/>K=\frac{7}{10} m v^{2}
<br/>\end{array}
<br/>$$
<br/>Potential energy = Kinetic energy
<br/>$$
<br/>\begin{aligned}
<br/>m g h &amp;=\frac{7}{10} m v^{2} \\
<br/>v^{2} &amp;=\frac{10}{7} g h
<br/>\end{aligned}
<br/>$$
<br/>For vertical projection,
<br/>$$
<br/>\begin{array}{c}
<br/>v^{2}=u^{2}+2 g h^{\prime} \\
<br/>\frac{10}{7} g h=0+2 g h^{\prime} \Rightarrow h^{\prime}=\frac{5}{7} h
<br/>\end{array}
<br/>$$</div>


tags: ['Physics', 'Waves and Sound', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch1_P1.db
title:
a-uniform-string-of-length-l-and-mass-m-is-fixed-at-both-ends-while-it-is-subject-to-a-tension-t-it-can-vibrate-at-frequencies-v-given-by-the-formula-

slug:
a-uniform-string-of-length-l-and-mass-m-is-fixed-at-both-ends-while-it-is-subject-to-a-tension-t-it-can-vibrate-at-frequencies-v-given-by-the-formula-34164

question:
<div class="question">A uniform string of length $L$ and mass $M$ is fixed at both ends while it is subject to a
<br/>tension $T$. It can vibrate at frequencies $(v)$ given by the formula (where $n=1,2,3, \ldots)$</div>

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

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

answer:
<div class="solution">The formula of frequency of 3 vibrations produced in tensed wire is
<br/>$$
<br/>v=\frac{n}{2} \sqrt{\frac{T}{m}}
<br/>$$
<br/>$m=$ Mass per unit length of the wire $=\frac{M}{L}$
<br/>$M=$ Mass of wire
<br/>$L=$ Length of wire $n=$ Number of loops produced in wire $v=\frac{n}{2 L} \sqrt{\frac{T}{M / L}}=\frac{n}{2} \sqrt{\frac{T}{M L}}$</div>


tags: ['Physics', 'Rotational Motion', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch1_P1.db
title:
a-uniform-thin-rod-of-length-l-mass-m-is-lying-on-a-smooth-horizontal-table-a-horizontal-impulse-p-is-suddenly-applied-perpendicular-to-the-rod-at-one

slug:
a-uniform-thin-rod-of-length-l-mass-m-is-lying-on-a-smooth-horizontal-table-a-horizontal-impulse-p-is-suddenly-applied-perpendicular-to-the-rod-at-one-38025

question:
<div class="question">A uniform thin rod of length $L$, mass $m$ is lying on a smooth horizontal table. A horizontal impulse $P$ is suddenly applied perpendicular to the rod at one end. The total energy of the rod after the impulse is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\mathrm{P}^{2}}{\mathrm{M}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{7 \mathrm{P}^{2}}{8 \mathrm{M}}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{13 \mathrm{P}^{2}}{2 \mathrm{M}}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{2 P^{2}}{M}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/WS9WFkG-BtGi3MlQoa9YXZHufnsDFUZ1hIq6U4L0JoQ.original.fullsize.png"/> <br/>$\mathrm{P}=(\mathrm{mv}-0)$
<br/>angular impulse $\mathrm{J}=\mathrm{P} \times \frac{\mathrm{L}}{2}=\mathrm{L}_{\mathrm{f}}-0$
<br/>$\mathrm{LE}_{\mathrm{f}}=\frac{\mathrm{PL}}{2}$
<br/>$=\frac{\mathrm{K}_{\mathrm{r}}}{2 \mathrm{~m}}+\mathrm{K}_{\mathrm{t}}=\frac{\mathrm{P}^{2}}{2 \mathrm{~m}}+\frac{\mathrm{L}_{\mathrm{f}}^{2}}{2 \mathrm{I}}$
<br/>$=\frac{(\mathrm{PL} / 2)^{2}}{2 \times \frac{\mathrm{mL}^{2}}{12}}$
<br/>$=\frac{\mathrm{P}^{2}}{2 \mathrm{~m}}+\frac{\mathrm{P}^{2} \mathrm{~L}^{2}}{4 \times \frac{\mathrm{mL}^{2}}{6}}=\frac{\mathrm{P}}{2 \mathrm{~m}}+\frac{3 \mathrm{P}^{2}}{2 \mathrm{~m}}=\frac{2 \mathrm{P}^{2}}{\mathrm{~m}}$</div>


tags: ['Physics', 'Oscillations', 'JEE Main']
source_db: db\MarksBatch1_P1.db
title:
a-unit-negative-charge-with-mass-m-resides-at-the-midpoint-of-the-straight-line-of-length-2-a-adjoining-two-fixed-charges-of-magnitude-q-each-if-it-is-1

slug:
a-unit-negative-charge-with-mass-m-resides-at-the-midpoint-of-the-straight-line-of-length-2-a-adjoining-two-fixed-charges-of-magnitude-q-each-if-it-is-1-51701

question:
<div class="question">A unit negative charge with mass $M$ resides at the mid-point of the straight line of length $2 a$ adjoining two fixed charges of magnitude $+Q$ each. If it is given a very small displacement $x(x&lt; &lt; a)$ in a direction perpendicular to the straight line, it will</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">come back to its original position and stay there</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">execute oscillations with frequency
<br/>$$
<br/>\frac{1}{2 \pi} \sqrt{\frac{Q}{4 \pi \varepsilon_{0} M a^{3}}}
<br/>$$</span> </li><li class="correct"> <span class="option-label">C</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><li class=""> <span class="option-label">D</span> <span class="option-data">execute oscillations with frequency
<br/>$$
<br/>\frac{1}{2 \pi} \sqrt{\frac{Q}{4 \pi \varepsilon_{0} M a^{2}}}
<br/>$$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">None of the above</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_phy_a34.png"/> <br/> <br/>From figure the net force
<br/>$\begin{aligned} F_{\text {bet }} &amp;=-F \cos \theta+(-F \cos \theta) \\ &amp;=-2 F \cos \theta \\ &amp;=-2 \times \frac{k Q \times 1}{\left(x^{2}+a^{2}\right)} \times \frac{x}{\sqrt{x^{2}+a^{2}}} \\ &amp;=-\frac{2 k Q}{\left(x^{2}+a^{2}\right)^{3 / 2}} \cdot x \\ F_{\text {net }} &amp;=-\left(\frac{2 k Q}{a^{3}}\right) \cdot x \end{aligned}$
<br/>Frequency of oscillation $=\frac{1}{2 \pi} \sqrt{\frac{2 k Q}{M a^{3}}}$
<br/>$=\frac{1}{2 \pi} \sqrt{\frac{2 \times \frac{1}{4 \pi \varepsilon_{0}} \cdot Q}{M a^{3}}}$
<br/>$=\frac{1}{2 \pi} \sqrt{\frac{Q}{2 \pi e_{0} M a^{3}}}$
<br/>$\Rightarrow\left(^{*}\right.$ None of the option matches)</div>


tags: ['Physics', 'Oscillations', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch1_P1.db
title:
a-unit-negative-charge-with-mass-m-resides-at-the-midpoint-of-the-straight-line-of-length-2-a-adjoining-two-fixed-charges-of-magnitude-q-each-if-it-is

slug:
a-unit-negative-charge-with-mass-m-resides-at-the-midpoint-of-the-straight-line-of-length-2-a-adjoining-two-fixed-charges-of-magnitude-q-each-if-it-is-37138

question:
<div class="question">A unit negative charge with mass $M$ resides at the mid-point of the straight line of length $2 a$ adjoining two fixed charges of magnitude $+Q$ each. If it is given a very small displacement $x(x&lt; &lt; a)$ in a direction perpendicular to the straight line, it will</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">come back to its original position and stay there</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">execute oscillations with frequency
<br/>$$
<br/>\frac{1}{2 \pi} \sqrt{\frac{Q}{4 \pi \varepsilon_{0} M a^{3}}}
<br/>$$</span> </li><li class="correct"> <span class="option-label">C</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><li class=""> <span class="option-label">D</span> <span class="option-data">execute oscillations with frequency
<br/>$$
<br/>\frac{1}{2 \pi} \sqrt{\frac{Q}{4 \pi \varepsilon_{0} M a^{2}}}
<br/>$$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">None of the above</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_phy_a34.png"/> <br/> <br/>From figure the net force
<br/>$\begin{aligned} F_{\text {bet }} &amp;=-F \cos \theta+(-F \cos \theta) \\ &amp;=-2 F \cos \theta \\ &amp;=-2 \times \frac{k Q \times 1}{\left(x^{2}+a^{2}\right)} \times \frac{x}{\sqrt{x^{2}+a^{2}}} \\ &amp;=-\frac{2 k Q}{\left(x^{2}+a^{2}\right)^{3 / 2}} \cdot x \\ F_{\text {net }} &amp;=-\left(\frac{2 k Q}{a^{3}}\right) \cdot x \end{aligned}$
<br/>Frequency of oscillation $=\frac{1}{2 \pi} \sqrt{\frac{2 k Q}{M a^{3}}}$
<br/>$=\frac{1}{2 \pi} \sqrt{\frac{2 \times \frac{1}{4 \pi \varepsilon_{0}} \cdot Q}{M a^{3}}}$
<br/>$=\frac{1}{2 \pi} \sqrt{\frac{Q}{2 \pi e_{0} M a^{3}}}$
<br/>$\Rightarrow\left(^{*}\right.$ None of the option matches)</div>


title: a-van-der-waals-gas-may-behave-ideally-when
slug: a-van-der-waals-gas-may-behave-ideally-when-61002
question: <div class="question">A van der Waals' gas may behave ideally when</div>
tags: ['Chemistry', 'States of Matter', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">the volume is very low</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">the temperature is very high</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">the pressure is very low</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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 temperature, pressure and volume all are very high</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">the pressure is very low</span> </div>

answer:
<div class="solution">At very low pressure, compressibility factor, $Z$ is approximatedly one.
<br/>$\therefore$ van der Waals' gas may behave ideally</div>


tags: ['Mathematics', 'Circle', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch1_P1.db
title:
a-variable-circle-passes-through-the-fixed-point-a-p-q-and-touches-x-axis-the-locus-of-the-other-end-of-the-diameter-through-a-is-1

slug:
a-variable-circle-passes-through-the-fixed-point-a-p-q-and-touches-x-axis-the-locus-of-the-other-end-of-the-diameter-through-a-is-1-91112

question:
<div class="question">A variable circle passes through the fixed point $A(p, q)$ and touches $X$ -axis. The locus of the other end of the diameter through $A$ is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(x-p)^{2}=4 q y$</span> </div>

answer:
<div class="solution">In a circle, $A B$ is a diameter where the coordinate of $A$ is $(p, q)$ and let the coordinate of $B\left(x_{1}, y_{1}\right)$
<br/>Equation of circle in diameter form is
<br/>$$
<br/>(x-p)\left(x-x_{1}\right)+(y-q)\left(y-y_{1}\right)=0
<br/>$$
<br/>$\Rightarrow x^{2}-\left(p+x_{1}\right) x+p x_{1}+y^{2}-\left(y_{1}+q\right) y+q y_{1}=0$
<br/>$\Rightarrow x^{2}-\left(p+x_{1}\right) x+y^{2}-\left(y_{1}+q\right) y+p x_{1}+q y_{1}=0$
<br/>Since, this circle touches $X$ -axis
<br/>$\therefore$
<br/>$$
<br/>y=0
<br/>$$
<br/>$\Rightarrow \quad x^{2}-\left(p+x_{1}\right) x+p x_{1}+q y_{1}=0$
<br/>Also, the discriminant of above equation will be equal to zero because circle touches $X$ -axis.
<br/>$\therefore \quad\left(p+x_{1}\right)^{2}=4\left(p x_{1}+q y_{1}\right)$
<br/>$\Rightarrow p^{2}+x_{1}^{2}+2 p x_{1}=4 p x_{1}+4 q y_{1}$
<br/>$\Rightarrow x_{1}^{2}-2 p x_{1}+p^{2}=4 q y_{1}$
<br/>$\Rightarrow \quad\left(x_{1}-p\right)^{2}=4 q y_{1}$
<br/>Therefore, the locus of point $B$ is
<br/>$$
<br/>(x-p)^{2}=4 q y
<br/>$$</div>


tags: ['Mathematics', 'Straight Lines', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch1_P1.db
title:
a-variable-line-passes-through-a-fixed-point-x-1-y-1-and-meets-the-axes-at-a-and-b-if-the-rectangle-o-a-pb-be-completed-the-locus-of-p-is-o-being-the-

slug:
a-variable-line-passes-through-a-fixed-point-x-1-y-1-and-meets-the-axes-at-a-and-b-if-the-rectangle-o-a-pb-be-completed-the-locus-of-p-is-o-being-the-97567

question:
<div class="question">A variable line passes through a fixed point $\left(x_{1}, y_{1}\right)$ and meets the axes at $A$ and $B$. If the rectangle $O A P B$ be completed, the locus of $P$ is, $(O$ being the origin of the system of axes).</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left(y-y_{1}\right)^{2}=4\left(x-x_{1}\right)$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{x_{1}}{x}+\frac{y_{1}}{y}=1$</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">$x^{2}+y^{2}=x_{1}^{2}+y_{1}^{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{x^{2}}{2 x_{1}^{2}}+\frac{y^{2}}{y_{1}^{2}}=1$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{x_{1}}{x}+\frac{y_{1}}{y}=1$</span> </div>

answer:
<div class="solution">Let the equation of line be $\frac{x}{a}+\frac{y}{b}=1$ since, the line passing through a fixed point $\left(x_{1}, y_{1}\right)$.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2019_mat_a33.png"/> <br/>$\therefore \quad \frac{x_{1}}{a}+\frac{y_{1}}{b}=1$
<br/>since, $O A P B$ is a rectangle, therefore the coordinate of $P$ will be $(a, b)$
<br/>Hence, locus of $P$ is
<br/>$\frac{x_{1}}{x}+\frac{y_{1}}{y}=1$</div>


tags: ['Mathematics', 'Straight Lines', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch1_P1.db
title:
a-variable-line-passes-through-the-fixed-point-the-locus-of-the-foot-of-the-perpendicular-from-the-origin-on-the-line-is

slug:
a-variable-line-passes-through-the-fixed-point-the-locus-of-the-foot-of-the-perpendicular-from-the-origin-on-the-line-is-65023

question:
<div class="question">A variable line passes through the fixed point $(\alpha, \beta) .$ The locus of the foot of the perpendicular from the origin on the line is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$x^{2}+y^{2}-\alpha x-\beta y=0$</span> </div>

answer:
<div class="solution">Let $(\alpha, \beta)$ be the given point, let $Q(x, y)$ be the foot of the perpendicular, and let $O$ be the origin. The line can have any direction
<br/>$$
<br/>\angle P Q O=90^{\circ}
<br/>$$
<br/>Point $Q$ lies on the circle having diameter $O P$.
<br/>The locus of point $Q$.
<br/>$$
<br/>(x-0)(x-\alpha)+(y-0)(y-\beta)=0
<br/>$$
<br/>$\Rightarrow \quad x^{2}-x \alpha+y^{2}-y \beta=0$
<br/>$$
<br/>\Rightarrow \quad x^{2}+y^{2}-\alpha x-\beta y=0
<br/>$$</div>


tags: ['Mathematics', 'Permutation Combination', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch1_P1.db
title:
a-vehicle-registration-number-consists-of-2-letters-of-english-alphabet-followed-by-4-digits-where-the-first-digit-is-not-zero-then-the-total-number-o

slug:
a-vehicle-registration-number-consists-of-2-letters-of-english-alphabet-followed-by-4-digits-where-the-first-digit-is-not-zero-then-the-total-number-o-81732

question:
<div class="question">A vehicle registration number consists of 2 letters of English alphabet followed by 4 digits, where the first digit is not zero. Then, the total number of vehicles with distinct registration numbers is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$26^{2} \times 10^{4}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">${ }^{26} \mathrm{P}_{2} \times{ }^{10} \mathrm{P}_{4}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">${ }^{26} \mathrm{P}_{2} \times 9 \times{ }^{10} \mathrm{P}_{3}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$26^{2} \times 9 \times 10^{3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$26^{2} \times 9 \times 10^{3}$</span> </div>

answer:
<div class="solution">The total number of arrangements of 2 letters of English alphabet
<br/>$$
<br/>=26 \times 26
<br/>$$
<br/>The total number of arrangements of 4 digits number in which first digit is not zero
<br/>$$
<br/>=9 \times 10 \times 10 \times 10
<br/>$$
<br/>$\therefore$ The total number of vehicles with distinct registration number
<br/>$$
<br/>\begin{array}{l}
<br/>=26 \times 26 \times 9 \times 10 \times 10 \times 10 \\
<br/>=26^{2} \times 9 \times 10^{3}
<br/>\end{array}
<br/>$$</div>


tags: ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P1.db
title:
a-very-long-charged-solid-cylinder-of-radius-a-contains-a-uniform-charge-density-dielectric-constant-of-the-material-of-the-cylinder-is-k-what-will-be

slug:
a-very-long-charged-solid-cylinder-of-radius-a-contains-a-uniform-charge-density-dielectric-constant-of-the-material-of-the-cylinder-is-k-what-will-be-49348

question:
<div class="question">A very long charged solid cylinder of radius 'a' contains a uniform charge density $\rho$. Dielectric constant of the material of the cylinder is $\mathrm{k}$. What will be the magnitude of electric field at a radial distance ' $x^{\prime}(x    &lt; a)$ from the axis of the cylinder?</div>

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

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

answer:
<div class="solution">Hint: 
<br/>Using Gauss's Law
<br/>$\mathrm{E}(2 \pi \times \ell)=\frac{\rho\left(\pi \mathrm{X}^{2} \ell\right)}{\mathrm{k} \varepsilon_{0}} \quad \therefore \mathrm{E}=\frac{\rho \mathrm{x}}{2 \mathrm{k} \varepsilon_{0}}$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/NvlHRetdyeAQk4ZzU57frqGksj8P7zgKO1rDS-cCUt0.original.fullsize.png"/></div>


tags: ['Physics', 'Electromagnetic Induction', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
title:
a-very-small-circular-loop-of-radius-a-is-initially-at-t-0-coplanar-and-concentric-with-a-much-larger-fixed-circular-loop-of-radius-b-a-constant-curre

slug:
a-very-small-circular-loop-of-radius-a-is-initially-at-t-0-coplanar-and-concentric-with-a-much-larger-fixed-circular-loop-of-radius-b-a-constant-curre-19829

question:
<div class="question">A very small circular loop of radius $a$ is initially (at $t=0$ ) coplanar and concentric with a much larger fixed circular loop of radius b. A constant current $I$ flows in the larger loop. The smaller loop is rotated with a constant angular speed $\omega$ about the common diameter. The emf induced in the smaller loop as a function of time $t$ is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\pi a^{2} \mu_{0} l}{2 b}$ $\omega sin$ $(\omega t)$</span> </div>

answer:
<div class="solution">We know that $\tau=$ NBAosin $\omega t$
<br/>where $N=$ number of loops $=1$
<br/>$$
<br/>\begin{aligned}
<br/>B &amp;=\frac{\mu_{0} I}{2 b} \text { newton/amp-m } \\
<br/>A &amp;=\pi a^{2} \text { metre }^{2} \\
<br/>\begin{aligned}
<br/>\therefore &amp;=\frac{\mu_{0} I}{2 b}\left(\pi a^{2}\right) \omega \sin \omega t \\
<br/>&amp;=\frac{\pi a^{2} \mu_{0} I}{2 b} \cdot \omega \sin \omega t
<br/>\end{aligned}
<br/>\end{aligned}
<br/>$$</div>


tags: ['Chemistry', 'Ionic Equilibrium', 'WBJEE', 'WBJEE 2010']
source_db: db\MarksBatch1_P1.db
title:
a-weak-acid-of-dissociation-constant-1-0-5-is-being-titrated-with-aqueous-naoh-solution-the-ph-at-the-point-of-onethird-neutralisation-of-the-acid-wil

slug:
a-weak-acid-of-dissociation-constant-1-0-5-is-being-titrated-with-aqueous-naoh-solution-the-ph-at-the-point-of-onethird-neutralisation-of-the-acid-wil-90181

question:
<div class="question">A weak acid of dissociation constant $10^{-5}$ is being titrated with aqueous $\mathrm{NaOH}$ solution. The $\mathrm{pH}$ at the point of one-third neutralisation of the acid will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5+\log 2-\log 3$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$5-\log 2$</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">$5-\log 3$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$5-\log 6$</span> </li> </ul>

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

answer:
<div class="solution">Hints: $\mathrm{K}_{\mathrm{a}}=10^{-5} \Rightarrow \mathrm{pK}_{\mathrm{a}}=-\log \mathrm{K}_{\mathrm{a}}=-\log 10^{-5}=5$<br/>$$<br/>\begin{array}{llcc} <br/>&amp; \mathrm{HA}+\mathrm{NaOH} \longrightarrow \mathrm{NaA}+\mathrm{H}_2 \mathrm{O} \\<br/>\text { Initial } &amp; 1 \mathrm{~mole} 0 &amp; 0 &amp; 0 \\<br/>\text { Final } &amp; (1-1 / 3) \mathrm{mole} &amp; 1 / 3 \mathrm{~mole} &amp; 1 / 3 \mathrm{~mole} \\<br/>&amp; =2 / 3 \mathrm{~mole} &amp; 1 / 3 \mathrm{~mole}<br/>\end{array}<br/>$$<br/>(Assumed weak acid to be monoprotic, since only one dissociation constant value is provided)<br/>Final solution acts as an acidic buffer.<br/>$$<br/>\Rightarrow \mathrm{pH}=\mathrm{pK}_{\mathrm{a}}+\log \frac{[\text { salt }]}{[\text { Acid }]} \Rightarrow \mathrm{pH}=5+\log \frac{\frac{1}{3}}{\frac{2}{3}}=5+\log \frac{1}{2} \Rightarrow \mathrm{pH}=5-\log 2<br/>$$</div>


tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch1_P1.db
title:
a-wheatstone-bridge-has-the-resistances-10-10-10-and-30-in-its-four-arms-what-resistance-joined-in-parallel-to-the-30-resistance-will-bring-it-to-the-

slug:
a-wheatstone-bridge-has-the-resistances-10-10-10-and-30-in-its-four-arms-what-resistance-joined-in-parallel-to-the-30-resistance-will-bring-it-to-the-38045

question:
<div class="question">A Wheatstone bridge has the resistances $10 \Omega$. $10 \Omega, 10 \Omega$ and $30 \Omega$ in its four arms. What resistance joined in parallel to the $30 \Omega$ resistance will bring it to the balanced condition?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \Omega$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$5 \Omega$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$10 \Omega$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$15 \Omega$</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">$15 \Omega$</span> </div>

answer:
<div class="solution">In balanced Wheatstone bridge,
<br/>$$
<br/>\begin{array}{l}
<br/>\frac{1}{10}=\frac{1}{x}+\frac{1}{30} \\
<br/>x=15 \Omega
<br/>\end{array}
<br/>$$</div>


tags: ['Physics', 'Waves and Sound', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
title:
a-whistle-whose-air-column-is-open-at-both-ends-has-a-fundamental-frequency-of-5100-hz-if-the-speed-of-sound-in-air-is-340-ms-1-the-length-of-the-whis

slug:
a-whistle-whose-air-column-is-open-at-both-ends-has-a-fundamental-frequency-of-5100-hz-if-the-speed-of-sound-in-air-is-340-ms-1-the-length-of-the-whis-59840

question:
<div class="question">$A$ whistle whose air column is open at both ends has a fundamental frequency of $5100 \mathrm{Hz}$. If the speed of sound in air is $340 \mathrm{ms}^{-1}$, the length of the whistle, in $\mathrm{cm}$, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5 / 3$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$10 / 3$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">5</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$20 / 3$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$10 / 3$</span> </div>

answer:
<div class="solution">For an open pipe, the frequency
<br/>$$
<br/>\begin{array}{l}
<br/>f=\frac{v}{2 l} \Rightarrow 5100=\frac{340}{2 \times 1} \\
<br/>l=\frac{340}{5100 \times 2} \Rightarrow l=\frac{2}{30 \times 2}=\frac{1}{30} \mathrm{m} \\
<br/>l=\frac{100}{30}=\frac{10}{3} \mathrm{cm}
<br/>\end{array}
<br/>$$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P1.db
title:
a-wire-carrying-a-steady-current-i-is-kept-in-the-xy-plane-along-the-curve-ya-sin-leftfrac2-pilambda-xright-a-magnetic-field-b-exists-in-the-zdirectio

slug:
a-wire-carrying-a-steady-current-i-is-kept-in-the-xy-plane-along-the-curve-ya-sin-leftfrac2-pilambda-xright-a-magnetic-field-b-exists-in-the-zdirectio-53508

question:
<div class="question">A wire carrying a steady current \(I\) is kept in the \(x\)-y plane along the curve \(y=A \sin \left(\frac{2 \pi}{\lambda} x\right)\). A magnetic field \(B\) exists in the \(z\)-direction. The magnitude of the magnetic force in the portion of the wire between \(x=0\) and \(x=\lambda\) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(2 \mathrm{I} \lambda \mathrm{B}\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(\mathrm{I} \lambda \mathrm{B}\)</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">D</span> <span class="option-data">\(\mathrm{I} \lambda \mathrm{B} / 2\)</span> </li> </ul>

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

answer:
<div class="solution">Hint : <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/D1gfYa6J9ynKmFKuqdAqbykySlwN_5YYokqCI2rqZ2M.original.fullsize.png"/><br/><br/>Magnetic force \(=\mathrm{I} \lambda \mathrm{B}\)</div>


tags: ['Physics', 'Mechanical Properties of Solids', 'WBJEE', 'WBJEE 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$1: 1$</span> </div>
source_db: db\MarksBatch1_P1.db
title:
a-wire-of-initial-length-l-and-raidus-r-is-stretched-by-a-length-l-another-wire-of-same-material-but-with-initial-length-2-l-and-radius-2-r-is-stretch

slug:
a-wire-of-initial-length-l-and-raidus-r-is-stretched-by-a-length-l-another-wire-of-same-material-but-with-initial-length-2-l-and-radius-2-r-is-stretch-66467

question:
<div class="question">A wire of initial length $L$ and raidus $r$ is stretched by a length $l$. Another wire of same material but with initial length $2 L$ and radius $2 r$ is stretched by a length $2 l$. The ratio of stored elastic energy per unit volume in the first and second wire is</div>

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

answer:
<div class="solution">Elastic energy per unit volume of wire. $\mu=\frac{1}{2} \times$ Young's modulus $\times(\text { Strain })^{2}$
<br/>$\therefore \quad \frac{u_{1}}{u_{2}}=\left\{\frac{(\text { Strain })_{1}}{(\text { Strain })_{2}}\right\}^{2}=\frac{l^{2}}{L^{2}} \times \frac{4 L^{2}}{4 l^{2}}=1: 1$</div>


tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2009']
source_db: db\MarksBatch1_P1.db
title:
a-wire-of-resistance-5-is-drawn-out-so-that-its-new-length-is-3-times-its-original-length-what-is-the-reistance-of-the-new-wire

slug:
a-wire-of-resistance-5-is-drawn-out-so-that-its-new-length-is-3-times-its-original-length-what-is-the-reistance-of-the-new-wire-90446

question:
<div class="question">A wire of resistance $5 \Omega$ is drawn out so that its new length is 3 times its original length. What is the reistance of the new wire?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$45 \Omega$</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><li class=""> <span class="option-label">B</span> <span class="option-data">$15 \Omega$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$5 / 3 \Omega$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$5 \Omega$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$45 \Omega$</span> </div>

answer:
<div class="solution">$\left(\frac{r_1}{r_2}\right)^2=\left(\frac{\ell_2}{\ell_1}\right)=\frac{3 \ell}{\ell}=3$<br/>$\left(\frac{R_2}{R_1}\right)=\frac{\ell_2}{\ell_1} \times \frac{A_1}{A_2}=3 \times\left(\frac{r_1}{r_2}\right)^2=3 \times 3 \Rightarrow R_2=45$</div>


title: a-wire-of-resistance-r-is-elongated-n-fold-to-make-a-new-uniform-wire-the-resistance-of-new-wire
tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2010']
answer: <div class="solution">Hints : $\mathrm{R}^{\prime}=n^2 \mathrm{R}$</div>
source_db: db\MarksBatch1_P1.db
slug:
a-wire-of-resistance-r-is-elongated-n-fold-to-make-a-new-uniform-wire-the-resistance-of-new-wire-56579

question:
<div class="question">A wire of resistance $\mathrm{R}$ is elongated $n$-fold to make a new uniform wire. The resistance of new wire</div>

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

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


tags: ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
title:
a-wooden-block-is-floating-on-water-kept-in-a-beaker-40-of-the-block-is-above-the-water-surface-now-the-beaker-is-kept-inside-a-lift-that-starts-going

slug:
a-wooden-block-is-floating-on-water-kept-in-a-beaker-40-of-the-block-is-above-the-water-surface-now-the-beaker-is-kept-inside-a-lift-that-starts-going-60217

question:
<div class="question">A wooden block is floating on water kept in a beaker. $40 \%$ of the block is above the water surface. Now the beaker is kept inside a lift that starts going upward with acceleration equal to $g / 2$. The block will then</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">fioat with $40 \%$ above the water surface</span> </div>

answer:
<div class="solution">The buoyant force acting on an immersed body is equal to the weight of the fluid displaced by it, if the fluid is in rest. In this case, the fluid is accelerating upwards so the buoyant force must also provide the displaced fluid force to accelerate.
<br/>Therefore, buoyant force will be \(\mathrm{fV} \rho \mathrm{g}_{\text {eff }}\) where \(\mathrm{V}=\) volume of body and \(\mathrm{f}=\) fraction of volume of body immersed in fluid and \(\mathrm{g}_{\text {eff }}=\mathrm{g}+\mathrm{a}=1.5 \mathrm{~g}\).
<br/>When fluid is at rest: \(\mathrm{f}=1-0.4=0.6\), 
<br/>so \(0.6 \mathrm{~V} \rho \mathrm{g}=\mathrm{V} \rho_{\mathrm{b}} \mathrm{g}\) 
<br/>where \(\rho_{\mathrm{b}}\) is the density of the block. \(\Rightarrow \rho_{\mathrm{b}}=0.6 \rho .\)
<br/>In the second case: \(1.5 \mathrm{fV} \rho \mathrm{g}=\mathrm{V} \rho_{\mathrm{b}} \mathrm{g}+\mathrm{V} \rho_{\mathrm{b}} \mathrm{a}=1.5 \mathrm{~V} \rho_{\mathrm{b}} \mathrm{g} \Rightarrow \mathrm{f} \rho=\rho_{\mathrm{b}} \Rightarrow \mathrm{f}=0.6\) Thus, the fraction of immersed volume remains the same.
<br/>Body will float with \(40 \%\) of the volume above water surface.</div>


tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch1_P1.db
title:
a-zener-diode-having-break-down-voltage-vz-6-v-is-used-in-a-voltage-regulator-circuit-as-shown-in-the-figure-the-minimum-current-required-to-pass-thro

slug:
a-zener-diode-having-break-down-voltage-vz-6-v-is-used-in-a-voltage-regulator-circuit-as-shown-in-the-figure-the-minimum-current-required-to-pass-thro-84566

question:
<div class="question">A Zener diode having break down voltage $\mathrm{Vz}=6 \mathrm{~V}$ is used in a voltage regulator circuit as shown in the figure. The minimum current required to pass through the Zener to act as a voltage regulator is $10 \mathrm{~mA}$ and maximum allowed current through Zener is $40 \mathrm{~mA}$. The maximum value of $R_{\mathrm{s}}$ for Zener to act as a voltage regulator is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/LQ4Ex1Lm3fBBtrw0_24bOpfvtHYdA-zy-gcbPNbX72o.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$100 \Omega$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$400 \Omega$</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><li class=""> <span class="option-label">C</span> <span class="option-data">$0.4 \Omega$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$950 \Omega$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$400 \Omega$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/o9QDJD9ptfoSmcd2ezmvfMMhx6PLncvwB9w7hkCdHKI.original.fullsize.png"/><br/><br/>Minimum current $=10 \mathrm{~mA}\left(\mathrm{I}_{\mathrm{L}}=0\right)$<br/>$$<br/>\mathrm{R}_{\mathrm{S}}=\frac{\mathrm{V}}{\mathrm{l}}=\frac{4 \mathrm{~V}}{10 \mathrm{~mA}}=400 \Omega<br/>$$</div>


tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch1_P1.db
title:
a-zener-diode-having-breakdown-voltage-56-v-is-connected-in-reverse-bias-with-a-battery-of-emf-10-v-and-a-resistance-of-100-in-series-the-current-flow

slug:
a-zener-diode-having-breakdown-voltage-56-v-is-connected-in-reverse-bias-with-a-battery-of-emf-10-v-and-a-resistance-of-100-in-series-the-current-flow-56636

question:
<div class="question">A Zener diode having break-down voltage $5.6 \mathrm{V}$ is connected in reverse bias with a battery of emf $10 \mathrm{V}$ and a resistance of $100 \Omega$ in series. The current flowing through the Zener diode is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$88 \mathrm{mA}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.88 \mathrm{mA}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$4.4 \mathrm{mA}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$44 \mathrm{mA}$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$44 \mathrm{mA}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_phy_a24.png"/> <br/> <br/>Breakdown voltage of Zener diode $=5.6 \mathrm{V}$ 
<br/>Voltage of source $=10 \mathrm{V}$ 
<br/>Potential difference $\Delta V=(10-5.6) \mathrm{V}=4.4 \mathrm{V}$
<br/>Resistance of circuit $=100 \Omega$
<br/>The current passing through the Zener diode
<br/>$$
<br/>\begin{aligned}
<br/>l &amp;=\frac{\Delta V}{R} \\
<br/>&amp;=\frac{4.4}{100} \\
<br/>&amp;=4.4 \times 10^{-2} \mathrm{A} \\
<br/>&amp;=44 \times 10^{-3} \mathrm{A} \\
<br/>&amp;=44 \mathrm{mA}
<br/>\end{aligned}
<br/>$$</div>


tags: ['Mathematics', 'Parabola', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch1_P1.db
title:
ab-is-a-chord-of-a-parabola-y-2-4-ax-a-0-with-vertex-a-bc-is-drawn-perpendicular-to-ab-meeting-the-axis-at-c-the-projection-of-bc-on-the-axis-of-the-p

slug:
ab-is-a-chord-of-a-parabola-y-2-4-ax-a-0-with-vertex-a-bc-is-drawn-perpendicular-to-ab-meeting-the-axis-at-c-the-projection-of-bc-on-the-axis-of-the-p-51248

question:
<div class="question">$\mathrm{AB}$ is a chord of a parabola $\mathrm{y}^2=4 \mathrm{ax},(\mathrm{a}&gt;0)$ with vertex $\mathrm{A} . \mathrm{BC}$ is drawn perpendicular to $\mathrm{AB}$ meeting the axis at $\mathrm{C}$. The projection of $\mathrm{BC}$ on the axis of the parabola is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">a unit</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2a unit</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">8a unit</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">4a unit</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">4a unit</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/mcbt6D0w5yDCQ464ywvdMRCjM9dh3oRfii2fRFbkAww.original.fullsize.png"/><br/><br/>$$<br/>\begin{aligned}<br/>&amp;\mathrm{B}\left(a \mathrm{at}^2, 2 a t\right) \therefore \mathrm{D}\left(\mathrm{at}^2, 0\right) \\<br/>&amp;\mathrm{m}_{\mathrm{AB}}=\frac{2 a \mathrm{at}^2}{\mathrm{at}^2}=\frac{2}{\mathrm{t}} \therefore \mathrm{m}_{\mathrm{BC}}=-\frac{\mathrm{t}}{2}<br/>\end{aligned}<br/>$$<br/>$\therefore y-2 a t=-\frac{t}{2}\left(x-a t^2\right)$ [Equation of $B C$ ]<br/>for $y=0,-2 a t=-\frac{t}{2}\left(x-a t^2\right)=-\frac{t}{2} x+\frac{a t^3}{2}$<br/>$$<br/>\begin{aligned}<br/>&amp;\Rightarrow \mathrm{tx}=4 a \mathrm{at}+\mathrm{at}^3 \\<br/>&amp;\Rightarrow \mathrm{x}=4 \mathrm{a}+\mathrm{at}^2 \\<br/>&amp;\therefore \mathrm{c}\left(4 \mathrm{a}+\mathrm{at}^2, 0\right)<br/>\end{aligned}<br/>$$<br/>$\therefore$ Projection of $B C$ on the axis is $D C=A C-A D=4 a+a t^2-a t^2=4 a$</div>


tags: ['Physics', 'Motion In One Dimension', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P1.db
title:
acceleration-due-to-gravity-at-a-height-mathrmh-from-the-surface-of-a-planet-is-the-same-as-that-at-a-depth-of-mathrmh-below-of-surface-if-mathrmr-be-

slug:
acceleration-due-to-gravity-at-a-height-mathrmh-from-the-surface-of-a-planet-is-the-same-as-that-at-a-depth-of-mathrmh-below-of-surface-if-mathrmr-be-74468

question:
<div class="question">Acceleration due to gravity at a height \(\mathrm{H}\) from the surface of a planet is the same as that at a depth of \(\mathrm{H}\) below of surface. If \(\mathrm{R}\) be the radius of the planet, then \(\mathrm{H}\) vs. \(\mathrm{R}\) graph for different planets will be</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/xzRSI0MTQlW-KCVOvtVO0k7sP3UQNrrTWc0FoAIrR6I.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/rs9TKhiPN5lsrwRgVoms4llJ43FfJ8gKeBmiahLa0mk.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/xQ7PeShQ5j19q68q5LtLCcB2mJxUORNBH9dUuI66kn8.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/Nwi-JsgmLaTZVS0qxfqLvKEVe2VaLOBDFIWfaOU0_ow.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/xQ7PeShQ5j19q68q5LtLCcB2mJxUORNBH9dUuI66kn8.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">Hint : <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/RkoPaX07KVUPp91_qyBTcO7oM23FWZumEd6VZ9-tBM0.original.fullsize.png"/><br/><br/>\(\begin{aligned} &amp; \frac{G M}{(R+H)^2}=\frac{G M(R-H)}{R^3} \\ &amp; (R+H)^2(R-H)=R^3 \\ &amp; R^3-R H^2+H R^2-H^3=R^3 \\ &amp; H^2-R^2+R H=0 \\ &amp; H=\frac{(\sqrt{5}-1)}{2} R\end{aligned}\)<img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/kaqX9m3-1sGnPCgQVlGUe49cSsO74doDch9jw7Vwhd8.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Chemical Kinetics', 'WBJEE', 'WBJEE 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: db\MarksBatch1_P1.db
title:
acid-catalysed-hydrolysis-of-ethyl-acetate-follows-a-pseudofirst-order-kinetics-with-respect-to-ester-if-the-reaction-is-carried-out-with-large-excess

slug:
acid-catalysed-hydrolysis-of-ethyl-acetate-follows-a-pseudofirst-order-kinetics-with-respect-to-ester-if-the-reaction-is-carried-out-with-large-excess-50029

question:
<div class="question">Acid catalysed hydrolysis of ethyl acetate follows a pseudo-first order kinetics with respect to ester. If the reaction is carried out with large excess of ester, the order with respect to ester will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1.5</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">0</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">0.5</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1</span> </li> </ul>

answer:
<div class="solution">$\mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{CH}_{3} \mathrm{COOH}$ $+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}$ 
<br/>If above reaction is carried out with large excess of ester, the rate of reaction does not depend upon cencentration of both the reactants. Due to which, the reaction becomes of zero order.</div>


tags: ['Chemistry', 'Coordination Compounds', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P1.db
title:
addition-of-excess-potassium-iodide-solution-to-a-solution-of-mereuric-chloride-gives-the-halide-complex

slug:
addition-of-excess-potassium-iodide-solution-to-a-solution-of-mereuric-chloride-gives-the-halide-complex-52580

question:
<div class="question">Addition of excess potassium iodide solution to a solution of mereuric chloride gives the halide complex</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">tetrahedral $\mathrm{K}_{2}\left[\mathrm{HgI}_{4}\right]$</span> </div>

answer:
<div class="solution">$\mathrm{HgCl}_{2}+4 \mathrm{KI} \longrightarrow \mathrm{K}_{2}\left[\mathrm{Hg} \mathrm{I}_{4}\right]+2 \mathrm{KCl}$
<br/>$\mathrm{Hg}=[\mathrm{Xe}] 4 t^{14}, 5 d^{10} \mathrm{Gs}^{2}$
<br/>$$
<br/>\mathrm{Hg}^{2+}=[\mathrm{Xe}] 4{ }^{14}, 5 d^{10}, 6 \mathrm{s}^{\circ}
<br/>$$ <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_a36.png"/></div>


tags: ['Chemistry', 'Practical Chemistry', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch1_P1.db
title:
addition-of-sodium-thiosulphate-solution-to-a-solution-of-silver-nitrate-gives-x-as-white-precipitate-insoluble-in-water-but-soluble-in-excess-thiosul

slug:
addition-of-sodium-thiosulphate-solution-to-a-solution-of-silver-nitrate-gives-x-as-white-precipitate-insoluble-in-water-but-soluble-in-excess-thiosul-48194

question:
<div class="question">Addition of sodium thiosulphate solution to a solution of silver nitrate gives $X$ as white precipitate, insoluble in water but soluble in excess thiosulphate solution to give $Y$. On boiling in water, $Y$ gives $Z . X, Y$ and $Z$ respectively are</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{Ag}_{2} \mathrm{S}_{2} \mathrm{O}_{3} \cdot \mathrm{Na}_{3}\left[\mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{2}\right], \mathrm{Ag}_{2} \mathrm{S}$</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">$\mathrm{Ag}_{2} \mathrm{SO}_{4}, \mathrm{Na}\left[\mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{2}\right], \mathrm{Ag}_{2} \mathrm{S}_{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Ag}_{2} \mathrm{S}_{2} \mathrm{O}_{3} \cdot \mathrm{Na}_{5}\left[\mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{3}\right], \mathrm{AgS}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Ag}_{2} \mathrm{SO}_{3} \cdot \mathrm{Na}_{3}\left[\mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{2}\right], \mathrm{Ag}_{2} \mathrm{O}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Ag}_{2} \mathrm{S}_{2} \mathrm{O}_{3} \cdot \mathrm{Na}_{3}\left[\mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{2}\right], \mathrm{Ag}_{2} \mathrm{S}$</span> </div>

answer:
<div class="solution">The sequence of reactions are
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_che_a71.png"/> <br/>Hence, $X=A g_{2} S_{2} O_{3}$
<br/>$Y=\mathrm{Na}_{3}\left[\mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{2}\right] Z=\mathrm{Ag}_{2} \mathrm{S}$</div>


title: adp-and-atp-differ-in-the-number-of
slug: adp-and-atp-differ-in-the-number-of-88913
question: <div class="question">ADP and ATP differ in the number of</div>
tags: ['Chemistry', 'Biomolecules', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">phosphate 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">ribose units</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">adenine base</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">nitrogen atom</span> </li> </ul>

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

answer:
<div class="solution">$\begin{array}{llll}\text {} &amp; \text { ADP } &amp; \text { is } &amp; \text { adenosine } &amp; \text { diphosphate }\end{array}$
<br/>(2-phosphate groups) and ATP is adenosine triphosphate ( 3 phosphate groups) Thus, they differ in number of phosphate units.</div>


tags: ['Physics', 'Kinetic Theory of Gases', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch1_P1.db
title:
air-inside-a-closed-container-is-saturated-with-water-vapour-the-air-pressure-is-mathrmp-and-the-saturated-vapour-pressure-of-water-is-barp-if-the-mix

slug:
air-inside-a-closed-container-is-saturated-with-water-vapour-the-air-pressure-is-mathrmp-and-the-saturated-vapour-pressure-of-water-is-barp-if-the-mix-97189

question:
<div class="question">Air inside a closed container is saturated with water vapour. The air pressure is \(\mathrm{p}\) and the saturated vapour pressure of water is \(\bar{p}\). If the mixture is compressed to one half of its volume by maintaining temperature constant, the pressure becomes</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(2 \mathrm{p}+\overline{\mathrm{p}}\)</span> </div>

answer:
<div class="solution">Hints: \(P_f=2 P+\bar{P}\)<br/>Saturated vapour pressure will not change if temperature remains constant</div>


tags: ['Mathematics', 'Straight Lines', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P1.db
title:
aline-cuts-the-x-axis-at-a-7-0-and-the-y-axis-at-b-0-5-a-variable-line-pq-is-drawn-perpendicular-to-a-b-cutting-the-x-axis-at-p-a-0-and-the-y-axis-at-

slug:
aline-cuts-the-x-axis-at-a-7-0-and-the-y-axis-at-b-0-5-a-variable-line-pq-is-drawn-perpendicular-to-a-b-cutting-the-x-axis-at-p-a-0-and-the-y-axis-at-36179

question:
<div class="question">Aline cuts the $x$ -axis at $A(7,0)$ and the $y$ -axis at $B(0,-5)$. A variable line $P Q$ is drawn perpendicular to $A B$ cutting the $x$ -axis at $P(a, 0)$ and the $y$ -axis at $Q(0, b)$. If $A Q$ and BP intersect at $R$, the locus of $R$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$x^{2}+y^{2}+7 x+5 y=0$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$x^{2}+y^{2}+7 x-5 y=0$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$x^{2}+y^{2}-7 x+5 y=0$</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">$x^{2}+y^{2}-7 x-5 y=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$x^{2}+y^{2}-7 x+5 y=0$</span> </div>

answer:
<div class="solution">Hint:
<br/>$\mathrm{P}$ is orthocentre of $\triangle \mathrm{ABQ}$
<br/>$\mathrm{m}_{\mathrm{BR}} \times \mathrm{m}_{\mathrm{AR}}=-1$
<br/>$\Rightarrow\left(\frac{\mathrm{k}+5}{\mathrm{~h}}\right) \times\left(\frac{\mathrm{k}}{\mathrm{h}-7}\right)=-1$
<br/>$\Rightarrow x^{2}+y^{2}-7 x+5 y=0$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/iB2dn4rQp5x6VGXc3KnhLhDtCuJTwXxj48h2KBp-l-I.original.fullsize.png"/></div>


title: among-be-b-mg-and-al-the-second-ionisation-potential-is-maximum-for
slug: among-be-b-mg-and-al-the-second-ionisation-potential-is-maximum-for-34084
question: <div class="question">Among Be, B, Mg and Al, the second ionisation potential is maximum for</div>
tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'WBJEE', 'WBJEE 2015']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">B</span> </div>
source_db: db\MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">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">Be</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Ma</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$A$</span> </li> </ul>

answer:
<div class="solution">Group II A Group III A
<br/>$\quad \quad \quad \mathrm{Be} \quad  \quad \quad \mathrm{B}$
<br/>$\quad \quad \quad \mathrm{Mg} \quad  \quad \quad \mathrm{Al}$
<br/>The electronic configuration of boron is $2 s^{2}2p$. And electronic configuration of $\mathrm{B}^{+}$ is $2 \mathrm{s}^{2}$. Hence it is difficult to remove second electron ty $2 s^{2}$ shell because half-filled and fully orbitals are more stable than others.</div>


title: among-me-3-n-c-5-h-5-n-and-mecn-me-methyl-group-the-electronegativity-of-n-is-in-the-order-1
slug: among-me-3-n-c-5-h-5-n-and-mecn-me-methyl-group-the-electronegativity-of-n-is-in-the-order-1-51812
tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'JEE Main']
source_db: db\MarksBatch1_P1.db
question:
<div class="question">Among $\mathrm{Me}_{3}\mathrm{N}, \mathrm{C}_{5} \mathrm{H}_{5} \mathrm{N}$ and MeCN
<br/>(Me $=$ methyl group) the electronegativity of $\mathrm{N}$ is in the order</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{MeCN}&gt;\mathrm{C}_{\mathrm{g}} \mathrm{H}_{\mathrm{s}} \mathrm{N}&gt;\mathrm{Me}_{3} \mathrm{N}$</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">B</span> <span class="option-data">$\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{N}&gt;\mathrm{Me}_{3} \mathrm{N}&gt;\mathrm{MeCN}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Me}_{3} \mathrm{N}&gt;\mathrm{MeCN}&gt;\mathrm{C}_{3} \mathrm{H}_{\mathrm{s}} \mathrm{N}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Electronegativity same in all</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{MeCN}&gt;\mathrm{C}_{\mathrm{g}} \mathrm{H}_{\mathrm{s}} \mathrm{N}&gt;\mathrm{Me}_{3} \mathrm{N}$</span> </div>

answer:
<div class="solution">$\because$ In Me $_{3} \mathrm{N} \rightarrow \mathrm{N}$ is $s p^{3}$ -hybrid
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_che_a49.png"/> <br/> <br/>and in $\mathrm{MeCN} \rightarrow \mathrm{N}$ is $s p$ -hybrid Also electronegativity of any element $\alpha \%$ $s$ -character in hybrid orbitals. Thus, order of electronegativity for nitrogen is
<br/>$$
<br/>\mathrm{MeCN}&gt;\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{N} &lt; \mathrm{Me}_{3} \mathrm{N}
<br/>$$</div>


title: among-the-alkenes-which-one-produces-tertiary-bytyl-alcohol-on-acid-hydration
slug: among-the-alkenes-which-one-produces-tertiary-bytyl-alcohol-on-acid-hydration-25787
tags: ['Chemistry', 'Hydrocarbons', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch1_P1.db
question:
<div class="question">Among the alkenes which one produces tertiary bytyl alcohol on acid hydration</div>

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

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

answer:
<div class="solution">Hints: <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/lz3Wyx-gHco-8-xeUDxDpdlKjB8mUpsMo0wMuD7GvU4.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'General Organic Chemistry', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch1_P1.db
title:
among-the-following-carbocations-i-mathrmph2stackrelmathrmc-mathrmch2-mathrmmemathrmii-mathrmph-mathrmch2-mathrmch2-stackrelmathrmc-mathrmhph-iii-math

slug:
among-the-following-carbocations-i-mathrmph2stackrelmathrmc-mathrmch2-mathrmmemathrmii-mathrmph-mathrmch2-mathrmch2-stackrelmathrmc-mathrmhph-iii-math-78343

question:
<div class="question">Among the following carbocations :
<br/>(I) \(\mathrm{Ph}_{2}\stackrel{+}{\mathrm{C}} \mathrm{CH}_{2} \mathrm{Me}(\mathrm{II}) \mathrm{Ph} \mathrm{CH}_{2} \mathrm{CH}_{2} \stackrel{+}{\mathrm{C}} \mathrm{HPh}\)
<br/>(III) \(\mathrm{Ph}_{2} \mathrm{CH} \stackrel{+}{\mathrm{C}} \mathrm{HMe}\) (IV) \(\mathrm{Ph}_{2} \mathrm{C}(\mathrm{Me}) \stackrel{+}{\mathrm{C}} H_{2}\) the order of stability is :</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$I&gt;\mathrm{II}&gt;\mathrm{III}&gt;\mathrm{IV}$</span> </div>

answer:
<div class="solution">The order of stability of carbocation is $3^{\circ}$ benzylic $&gt;2^{\circ}$ benzylic $&gt;2^{*}&gt;1^{*}$ Thus, the correct order of stability will be
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_a36.png"/></div>


tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch1_P1.db
title:
among-the-following-chlorides-the-compounds-which-will-be-hydrolysed-most-easily-and-most-slowly-in-aqueous-naoh-solution-are-respectively-1methoxymet

slug:
among-the-following-chlorides-the-compounds-which-will-be-hydrolysed-most-easily-and-most-slowly-in-aqueous-naoh-solution-are-respectively-1methoxymet-19044

question:
<div class="question">Among the following chlorides the compounds which will be hydrolysed most easily and most slowly in aqueous $\mathrm{NaOH}$ solution are respectively.
<br/>1.Methoxymethyl chloride
<br/>2.Benzyl chloride
<br/>3.Neopentyl chloride
<br/>4.Propyl chloride</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">1 and 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">2 and 3</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2 and 4</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">3 and 1</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">1 and 3</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/_G0UP1rqYAbnOjubXD6wSOOHrs7yYF9sxXUOKu7FeHQ.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/p99-GA4BMQ3XYP5CGTQiyaYkv4x-GpPORzsSms_PcpQ.original.fullsize.png"/></div>


tags: ['Chemistry', 'Chemical Kinetics', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
title:
among-the-following-compounds-the-onele-that-gives-give-effervescence-with-aqueoug-nahco-3-solution-is-are

slug:
among-the-following-compounds-the-onele-that-gives-give-effervescence-with-aqueoug-nahco-3-solution-is-are-87065

question:
<div class="question">Among the following compounds, the onele that gives (give) effervescence with aqueoug $\mathrm{NaHCO}_{3}$ solution is (are) <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_q21.png"/></div>

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

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

answer:
<div class="solution">Only carboxylic acids and their derivatives like anhydride are capable to give effervescence with aqueous $NaHCO_{3}$ solution, because they are more acidic as compared to $\mathrm{H}_{2} \mathrm{CO}_{3}$ (carbonic acidi-
<br/>$\mathrm{IICH}_{3} \mathrm{COOH}+\mathrm{NaHCO}_{3}$
<br/>$$
<br/>\longrightarrow \mathrm{CH}_{3} \mathrm{COONa}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}
<br/>$$
<br/>$1\left(\mathrm{CH}_{3} \mathrm{CO}\right)_{2} \mathrm{O}+2 \mathrm{NaHCO}_{3}$
<br/>$$
<br/>\longrightarrow 2 \mathrm{CH}_{3} \mathrm{COONa}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}
<br/>$$</div>


title: among-the-following-observations-the-correct-one-that-differentiates-between-so-3-2-and-so-4-2-is
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
slug:
among-the-following-observations-the-correct-one-that-differentiates-between-so-3-2-and-so-4-2-is-26553

question:
<div class="question">Among the following observations, the correct one that differentiates between $\mathrm{SO}_{3}^{2-}$ and $\mathrm{SO}_{4}^{2-}$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">both form precipitate with $\mathrm{BaCl}_{2}, \mathrm{SO}_{3}^{2-}$ dissolves in $\mathrm{HCl}$ but $\mathrm{SO}_{4}^{2-}$ does not</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$\mathrm{SO}_{3}^{2-}$ forms precipitate with $\mathrm{BaCl}_{2}, \mathrm{SO}_{4}^{2-}$ does not</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{SO}_{4}^{2-}$ forms precipitate with $\mathrm{BaCl}_{2}, \mathrm{SO}_{3}^{2-}$ does not</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">both form precipitate with $\mathrm{BaCl}_{2}, \mathrm{SO}_{4}^{2-}$ dissolves in HCl but $S O_{3}^{2-}$ does not</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">both form precipitate with $\mathrm{BaCl}_{2}, \mathrm{SO}_{3}^{2-}$ dissolves in $\mathrm{HCl}$ but $\mathrm{SO}_{4}^{2-}$ does not</span> </div>

answer:
<div class="solution">$\mathrm{SO}_{3}^{2-}$ and $\mathrm{SO}_{4}^{2-}$ when treated with $\mathrm{BaCl}_{2}$, give white ppt of $BaSO_{3}$ and $BaSO_{4}$ respectively.
<br/>$$
<br/>\begin{array}{c}
<br/>\mathrm{BaCl}_{2}+\mathrm{SO}_{3}^{2-} \longrightarrow \mathrm{BaSO}_{3}+2 \mathrm{Cl}^{-} \\
<br/>\text {Barium sulphide} \\
<br/>\mathrm{BaCl}_{2}+\mathrm{SO}_{4}^{2-} \longrightarrow \begin{array}{c}
<br/>\text {  } \\
<br/>\mathrm{BaSO}_{4}+2 \mathrm{Cl}^{-} \\
<br/>\text {Barium sulphate }
<br/>\end{array}
<br/>\end{array}
<br/>$$
<br/>Out of these $\mathrm{two}, \mathrm{SO}_{3}^{2-}$ is soluble in $\mathrm{HCl}$ but $\mathrm{SO}_{4}^{2-}$ does not.</div>


title: among-the-following-statements-about-the-molecules-x-and-y-the-ones-which-correct-is-are
slug: among-the-following-statements-about-the-molecules-x-and-y-the-ones-which-correct-is-are-93713
tags: ['Chemistry', 'General Organic Chemistry', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
question:
<div class="question">Among the following statements about the molecules $X$ and $Y$, the one(s) which correct is (are) <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_q60.png"/></div>

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

answer:
<div class="solution">Both the given molecules contain 6 carbon atoms with an aldehyde group, so these are called aldohexoser, In $X$, the $-O H$ attached to second last carbon in on right hand side while in $Y$ it is on left hand side, so $x_{i j}$ D-sugar and $Y$ is L-sugar, $X$ and $Y$ are the mirror images of each other, i.e., these are enantiomers.</div>


title: among-the-following-structures-the-one-which-is-not-a-resonating-structure-of-others-is
slug: among-the-following-structures-the-one-which-is-not-a-resonating-structure-of-others-is-91897
tags: ['Chemistry', 'General Organic Chemistry', 'WBJEE', 'WBJEE 2014']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">IV</span> </div>
source_db: db\MarksBatch1_P1.db
question:
<div class="question">Among the following structures the one which is not a resonating structure of others is <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_q12.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">I</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">II</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">III</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">IV</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Resonating structures involve movement of electrons, but they do not involve movernent of atom or group of atoms. <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_a12.png"/> <br/> <br/>Thus, structure IV is not a resonating structure of others.</div>


title: among-the-following-the-extensive-variables-are
slug: among-the-following-the-extensive-variables-are-42551
question: <div class="question">Among the following, the extensive variables <br/>are</div>
tags: ['Chemistry', 'Thermodynamics (C)', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{H}$ (Enthalpy)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$p$ (Pressure)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">E (internal energy)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\vee$ (volume)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">$\mathrm{H}$ (Enthalpy), E (internal energy), $\vee$ (volume)</span> </div>

answer:
<div class="solution">Among the given options, the e
<br/>xtensive variables are $H$ (enthalpy), $E$ (internal energy). $V$ (volume).These variables have values that depends upon the quantity or size of matter present in the system. Other examples are heat
<br/>capacity, entropy, free energy, length and mass.</div>


title: among-the-following-the-ion-which-will-be-more-effective-for-flocculation-of-fe-oh-3-sol-is
slug: among-the-following-the-ion-which-will-be-more-effective-for-flocculation-of-fe-oh-3-sol-is-54132
tags: ['Chemistry', 'Surface Chemistry', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P1.db
question:
<div class="question">Among the following, the ion which will be more effective for flocculation of $\mathrm{Fe}(\mathrm{OH})_{3}$ sol. is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{PO}_{4}^{3-}$</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">$\mathrm{SO}_{4}^{2-}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{SO}_{3}^{2-}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{NO}_{3}^{-}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{PO}_{4}^{3-}$</span> </div>

answer:
<div class="solution">Hint: 
<br/>$\mathrm{Fe}(\mathrm{OH})_{3}$ is a positive sol. $\mathrm{PO}_{4}^{3-}$ carrying the highest -ve charge amongst the given ions is most effective</div>


title: among-the-following-the-one-which-is-not-a-green-house-gas-is
slug: among-the-following-the-one-which-is-not-a-green-house-gas-is-87310
question: <div class="question">Among the following, the one which is not a "green house gas", is</div>
tags: ['Chemistry', 'Environmental Chemistry', 'WBJEE', 'WBJEE 2014']
answer: <div class="solution">Oxygen is not a green house gas</div>
source_db: db\MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{N}_{2} \mathrm{O}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{CO}_{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{CH}_{4}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{O}_{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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


title: amongst-ni-h-2-o-6-2-ni-pph-3-2-cl-2-ni-co-4-and-ni-cn-4-2-the-paramagnetic-species-are-1
slug: amongst-ni-h-2-o-6-2-ni-pph-3-2-cl-2-ni-co-4-and-ni-cn-4-2-the-paramagnetic-species-are-1-51651
tags: ['Chemistry', 'Coordination Compounds', 'JEE Main']
source_db: db\MarksBatch1_P1.db
question:
<div class="question">Amongst $\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}, \quad\left[\mathrm{Ni}\left(\mathrm{PPh}_{3}\right)_{2} \mathrm{Cl}_{2} ]\right.$, $\left[\mathrm{Ni}(\mathrm{CO})_{4}\right.]$ and $\left[\mathrm{Ni}\left(\mathrm{CN}_{4}\right)\right]^{2-}$ the paramagnetic species are</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\left[\mathrm{NiCl}_{4}\right]^{2-},\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} \cdot\left[\mathrm{Ni}\left(\mathrm{PPh}_{3}\right)_{2} \mathrm{Cl}_{2}\right]$</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">B</span> <span class="option-data">$\left[\mathrm{Ni}(\mathrm{CO})_{4}\right],\left[\mathrm{Ni}\left(\mathrm{PPh}_{3}\right)_{2} \mathrm{Cl}_{2}\right],\left[\mathrm{NiCl}_{4}\right]^{2-}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-} \cdot\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+},\left[\mathrm{NiCl}_{4}\right]^{2-}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left[\mathrm{Nl}\left(\mathrm{PPh}_{3}\right)_{2} \mathrm{Cl}_{2}\right\}\left[\mathrm{Ni}(\mathrm{CO})_{4}\right\}\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left[\mathrm{NiCl}_{4}\right]^{2-},\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} \cdot\left[\mathrm{Ni}\left(\mathrm{PPh}_{3}\right)_{2} \mathrm{Cl}_{2}\right]$</span> </div>

answer:
<div class="solution">Species having unpaired electrons are paramagnetic
<br/>$$
<br/>\mathrm{Ni}^{2+}=[\mathrm{Ar}] 3 \mathrm{d}^{8}
<br/>$$ <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_a31.png"/> <br/> <br/>(i) In $[\left.\mathrm{NiCl}_{4}\right]^{2-}$ and $[\left.\operatorname{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ ligands $\mathrm{Cl}^{-}$ and
<br/>$\mathrm{H}_{2} \mathrm{O}$ are weak ligands, therefore no pairing will be possible. Thus, there are two unpained electrons.
<br/>(II) In [Ni $\left.\left(P h_{3}\right)_{2} C l_{2}\right\}$. although $P P h_{3}$, has d-acceptance nature but presence of Cl, makes electrons unpaired.</div>


tags: ['Chemistry', 'Aldehydes and Ketones', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch1_P1.db
title:
amongst-the-following-compounds-the-one-that-will-not-respond-to-cannizzaro-reaction-upon-treatment-with-alkali-is

slug:
amongst-the-following-compounds-the-one-that-will-not-respond-to-cannizzaro-reaction-upon-treatment-with-alkali-is-18388

question:
<div class="question">Amongst the following compounds, the one that will not respond to Cannizzaro reaction upon treatment with alkali is</div>

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

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

answer:
<div class="solution">For a carbonyl group to give Cannizaro reaction, it should not have an $\alpha$ -hydrogen atom. Among the given compound $\mathrm{Ne}_{3} \mathrm{CCHO}, \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CHO}$ and HCHO respond
<br/>to Cannizaro reaction but $\mathrm{Cl}_{3} \mathrm{CCHO}$ do not due to the following reason.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_che_a1.png"/> <br/> <br/>When hydroxyl group attacks the carbonyl group a tetrahedral intermediate forms. This tetrahedral intermediate will revert to a carbonyl compound by
<br/>expelling the best leaving group. The CCl $_{3}$ carbonium is resonance stabilised therefore it is better leaving group than OH. These initial products exchange a proton to give ion of carboxylic acid and trichloromethane ($CHCl_{3}$).</div>


title: amongst-the-following-compounds-the-one-which-would-not-respond-to-iodoform-test-is
slug: amongst-the-following-compounds-the-one-which-would-not-respond-to-iodoform-test-is-28065
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch1_P1.db
question:
<div class="question">Amongst the following compounds, the one which would not respond to iodoform test is</div>

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

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

answer:
<div class="solution">Acetic acid, \(\mathrm{CH}_{3} \mathrm{COOH}\) would not respond to iodoform test. In the mechanism of haloform reaction, in the first step, base deprotonates most acidic alpha \(\mathrm{H}\) atom (of methyl keto group).
<br/>In acetic acid, the most acidic proton is attached to \(\mathrm{O}\) atom. So deprotonation of \(\alpha-\) hydrogen does not occur and hence no haloform reaction.</div>


title: amongst-the-following-compounds-the-ones-which-readily-react-with-ethanolic-kcn
slug: amongst-the-following-compounds-the-ones-which-readily-react-with-ethanolic-kcn-57195
tags: ['Chemistry', 'Carboxylic Acid Derivatives', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch1_P1.db
question:
<div class="question">Amongst the following compounds, the one(s) which readily react with ethanolic KCN.</div>

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

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">Ethyl chioride, Benzaldehyde</span> </div>

answer:
<div class="solution">(a) Ethyl chioride gives ethyl cyanide, when it reacts with KCN (ethanolic).
<br/>$$
<br/>\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}+\mathrm{KCN} \stackrel{\text { EThande }}{\longrightarrow} \mathrm{C}_{2}\mathrm{H}_{\mathrm{s}}-\mathrm{CN}
<br/>$$
<br/>(b) It does not react with KCN.
<br/>(c) Benzaldehyde : KCN gives HCN in alcoholic medium and HCN gives cyanohydrin with benzaldehyde.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_che_a40.png"/></div>


title: amongst-the-following-the-one-which-can-exist-in-free-state-as-a-stable-compound-is
slug: amongst-the-following-the-one-which-can-exist-in-free-state-as-a-stable-compound-is-26312
tags: ['Chemistry', 'General Organic Chemistry', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P1.db
question:
<div class="question">Amongst the following, the one which can exist in free state as a stable compound is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$C_{7}H_{9}O$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{C}_{8} \mathrm{H}_{12} \mathrm{O}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{C}_{10} \mathrm{H}_{17} \mathrm{O}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{C}_{8} \mathrm{H}_{12} \mathrm{O}$</span> </div>

answer:
<div class="solution">Molecules having whole number for degree of unsaturation can exist in free state as stable compounds. 
<br/>Degree of unsaturation $=\frac{\Sigma n(v-2)}{2}+1$
<br/>where, $n=$ number of atoms of a particular type $v=$ valency of the atom.
<br/>(a) For $\mathrm{C}_{7} \mathrm{H}_{9} \mathrm{O}$,
<br/>$D U=\frac{7(4-2)+9(1-2)+1(2-2)}{2}+1=3 \cdot 5$
<br/>(b) For $\mathrm{C}_{8} \mathrm{H}_{12} \mathrm{O}$
<br/>$$
<br/>\mathrm{DU}=\frac{8(4-2)+9(1-2)+1(2-2)}{2}+1=3 \cdot 0
<br/>$$
<br/>(c) For $\mathrm{C}_{6} \mathrm{H}_{11} \mathrm{O}$
<br/>$$
<br/>\mathrm{DU}=\frac{6(4-2)+11(1-2)+1(2-2)}{2}+1=1 \cdot 5
<br/>$$
<br/>(d) For $\mathrm{C}_{10} \mathrm{H}_{17} \mathrm{O}_{2}$
<br/>$D U=\frac{10(4-2)+17(1-2)+2(2-2)}{2}+1=2 \cdot 5$
<br/>$\therefore \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}$ will exist in free state or a stable compound.</div>


title: amongst-the-following-which-should-have-the-highest-rms-speed-at-the-same-temperature
slug: amongst-the-following-which-should-have-the-highest-rms-speed-at-the-same-temperature-24517
tags: ['Chemistry', 'States of Matter', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch1_P1.db
question:
<div class="question">Amongst the following, which should have the highest rms speed at the same temperature?</div>

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

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

answer:
<div class="solution">$\because$ rms velocity $(v_{rms}) \propto \sqrt{\frac{1}{M}}$. Thus, smaller the mass, more will be the rms speed. $\mathrm{H}_{2}$ has minimum molar mass, So it has highest value of rms speed.</div>


tags: ['Physics', 'Nuclear Physics', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P1.db
title:
an-alpha-particle-4-he-has-a-mass-of-400300-amu-a-proton-has-a-mass-of-100783-amu-and-a-neutron-has-a-mass-of-100867-amu-respectively-the-binding-ener

slug:
an-alpha-particle-4-he-has-a-mass-of-400300-amu-a-proton-has-a-mass-of-100783-amu-and-a-neutron-has-a-mass-of-100867-amu-respectively-the-binding-ener-23407

question:
<div class="question">An alpha particle $\left({ }^{4} \mathrm{He}\right)$ has a mass of 4.00300 amu. A proton has a mass of 1.00783 amu and a neutron has a mass of 1.00867 amu respectively. The binding energy of alpha estimated from these data is the closest to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$27.9 \mathrm{MeV}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$22.3 \mathrm{MeV}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$35.0 \mathrm{MeV}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$20.4 \mathrm{MeV}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$27.9 \mathrm{MeV}$</span> </div>

answer:
<div class="solution">The mass defect, $\Delta m=2\left(m_{p}+m_{n}\right)-m_{\text {He }}$
<br/>$=2(1.00783+1.00867)-4.00300$
<br/>$=0.0300$ amu
<br/>So, the binding energy, $E=\Delta m c^{2}$
<br/>$=0.03 \times 931 \mathrm{MeV}=27.9 \mathrm{MeV}$</div>


tags: ['Physics', 'Alternating Current', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch1_P1.db
title:
an-altermating-current-is-flowing-through-a-series-l-c-r-circuit-it-is-found-that-the-current-reaches-a-value-of-1-ma-at-both-200-hz-and-800-hz-freque

slug:
an-altermating-current-is-flowing-through-a-series-l-c-r-circuit-it-is-found-that-the-current-reaches-a-value-of-1-ma-at-both-200-hz-and-800-hz-freque-80771

question:
<div class="question">An altermating current is flowing through a series $L-C - R$ circuit. It is found that the current reaches a value of $1 \mathrm{mA}$ at both $200 \mathrm{Hz}$ and $800 \mathrm{Hz}$ frequency. What is the resonance frequency of the circuit?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$600 \mathrm{Hz}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$300 \mathrm{Hz}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$500 \mathrm{Hz}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$400 \mathrm{Hz}$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$400 \mathrm{Hz}$</span> </div>

answer:
<div class="solution">$\because$ Resonance frequency, $f_{0}=\sqrt{f_{1} f_{2}}$
<br/>$$
<br/>=\sqrt{200 \times 800}=400 \mathrm{Hz}
<br/>$$</div>


tags: ['Physics', 'Alternating Current', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P1.db
title:
an-alternating-current-in-a-circuit-is-given-by-i-20-sin-100-t-005-a-the-rms-value-and-the-frequency-of-current-respectively-are

slug:
an-alternating-current-in-a-circuit-is-given-by-i-20-sin-100-t-005-a-the-rms-value-and-the-frequency-of-current-respectively-are-93398

question:
<div class="question">An alternating current in a circuit is given by $I=20 \sin (100 \pi t+0.05 \pi)$ A. The r.m.s. value and the frequency of current respectively are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$10 \mathrm{A}$ and $100 \mathrm{Hz}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$10 \mathrm{A}$ and $50 \mathrm{Hz}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$10 \sqrt{2} \mathrm{A}$ and $50 \mathrm{Hz}$</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">D</span> <span class="option-data">$10 \sqrt{2}$ A and $100 \mathrm{Hz}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$10 \sqrt{2} \mathrm{A}$ and $50 \mathrm{Hz}$</span> </div>

answer:
<div class="solution">Given, $I=20 \sin (100 \pi t+0.05 \pi)$
<br/>The root mean square value of alternating
<br/>$$
<br/>\text { current }=l_{\mathrm{ms}}=\frac{l_{0}}{\sqrt{2}}=\frac{20}{\sqrt{2}}=10 \sqrt{2} \mathrm{A}
<br/>$$
<br/>Also, $\quad \omega=100 \pi$
<br/>$\Rightarrow \quad 2 \pi f=100 \pi$ or $f=50 \mathrm{Hz}$</div>


tags: ['Physics', 'Alternating Current', 'WBJEE', 'WBJEE 2009']
source_db: db\MarksBatch1_P1.db
title:
an-alternating-current-of-rms-value-10-a-is-passed-through-a-12-resistor-the-maximum-potential-difference-across-the-resistor-is

slug:
an-alternating-current-of-rms-value-10-a-is-passed-through-a-12-resistor-the-maximum-potential-difference-across-the-resistor-is-63796

question:
<div class="question">An alternating current of rms value $10 \mathrm{~A}$ is passed through a $12 \Omega$ resistor. The maximum potential difference across the resistor is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$20 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$90 \mathrm{~V}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$1969.68 \mathrm{~V}$</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">D</span> <span class="option-data">none</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1969.68 \mathrm{~V}$</span> </div>

answer:
<div class="solution">$I_{\mathrm{rms}}=10 \mathrm{~A}$<br/>$\begin{aligned} &amp; I_{r m s}=\frac{I_0}{\sqrt{2}} \Rightarrow I_0=\sqrt{2} \times 10=10 \sqrt{2} \\ &amp; \text { Max. P.D. }=\sqrt{2} \times 10 \times 12=120 \times 1.414=169.68 \mathrm{~V}\end{aligned}$</div>


tags: ['Chemistry', 'Amines', 'JEE Main']
source_db: db\MarksBatch1_P1.db
title:
an-amine-c-3-h-9-n-reacts-with-benzene-sulphonyl-chloride-to-form-a-white-precipitate-which-is-insoluble-in-aq-naoh-the-amine-is-1

slug:
an-amine-c-3-h-9-n-reacts-with-benzene-sulphonyl-chloride-to-form-a-white-precipitate-which-is-insoluble-in-aq-naoh-the-amine-is-1-62732

question:
<div class="question">An amine $\mathrm{C}_{3} \mathrm{H}_{9} \mathrm{N}$ reacts with benzene sulphonyl chloride to form a white precipitate which is insoluble in $\mathrm{aq} . \mathrm{NaOH}$. The amine is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_q35_opta.png"/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_q35_optb.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_q35_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_q35_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_q35_optb.png"/></span> </div>

answer:
<div class="solution">Since, the amine gives white precipitate with benzene sulphonyl chloride which is insoluble in aq. $\mathrm{Na} \mathrm{OH},$ so Ti must be a secondary amine lie. amine having RNHR group).
<br/>Among the given compound, only <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_a35.png"/> <br/>is a secondary amine, so it represents the structure of given amine.</div>


tags: ['Chemistry', 'Amines', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
title:
an-amine-c-3-h-9-n-reacts-with-benzene-sulphonyl-chloride-to-form-a-white-precipitate-which-is-insoluble-in-aq-naoh-the-amine-is

slug:
an-amine-c-3-h-9-n-reacts-with-benzene-sulphonyl-chloride-to-form-a-white-precipitate-which-is-insoluble-in-aq-naoh-the-amine-is-76163

question:
<div class="question">An amine $\mathrm{C}_{3} \mathrm{H}_{9} \mathrm{N}$ reacts with benzene sulphonyl chloride to form a white precipitate which is insoluble in $\mathrm{aq} . \mathrm{NaOH}$. The amine is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_q35_opta.png"/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_q35_optb.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_q35_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_q35_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_q35_optb.png"/></span> </div>

answer:
<div class="solution">Since, the amine gives white precipitate with benzene sulphonyl chloride which is insoluble in aq. $\mathrm{Na} \mathrm{OH},$ so Ti must be a secondary amine lie. amine having RNHR group).
<br/>Among the given compound, only <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_a35.png"/> <br/>is a secondary amine, so it represents the structure of given amine.</div>


tags: ['Physics', 'Electromagnetic Induction', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P1.db
title:
an-amount-of-charge-q-passes-through-a-coil-of-resistance-r-if-the-current-in-the-coil-decreases-to-zero-at-a-uniform-rate-during-time-t-then-the-amou

slug:
an-amount-of-charge-q-passes-through-a-coil-of-resistance-r-if-the-current-in-the-coil-decreases-to-zero-at-a-uniform-rate-during-time-t-then-the-amou-24121

question:
<div class="question">An amount of charge Q passes through a coil of resistance R. If the current in the coil decreases to zero at a uniform rate during time \(T\), then the amount of heat generated in the coil will be,</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\frac{4 Q^2 R}{3 T}\)</span> </div>

answer:
<div class="solution">Hint : <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/JeNm1jOnFhnbuqgn_HiCd9J-uKOMt6TEQer7Pab2Nxw.original.fullsize.png"/><br/><br/>Given, \(\frac{1}{2} \mathrm{I}_0 T=Q \Rightarrow \mathrm{I}_0=\frac{2 \mathrm{Q}}{\mathrm{T}}\)<br/>Equation of \(\mathrm{I}(\mathrm{t}) \Rightarrow \frac{\mathrm{I}}{\mathrm{I}_0}+\frac{\mathrm{t}}{\mathrm{T}}=1\)<br/>\(\begin{aligned}<br/>&amp; I=I_0\left(1-\frac{t}{T}\right)=\frac{2 Q}{T}\left(1-\frac{t}{T}\right) \\<br/>&amp; \text { Heat }=\int_0^T I^2 R d f \\<br/>&amp; =R \int_0^T \frac{4 Q^2}{T^2}\left(1-\frac{t}{T}\right)^2 \\<br/>&amp; =\frac{4 Q^2 R}{T^2}\left[\int_0^T d t+\frac{1}{T^2} \int_0^T t^2 d t-\frac{2}{T} \int_0^T t d t\right]=\frac{4 Q^2 R}{T^2}\left[\not T+\frac{T}{3}-\not T\right]=\frac{4 Q^2 R}{3 T}<br/>\end{aligned}\)</div>


tags: ['Physics', 'Gravitation', 'WBJEE', 'WBJEE 2014']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$-2 E$</span> </div>
source_db: db\MarksBatch1_P1.db
title:
an-artificial-satellite-moves-in-a-circular-orbit-around-the-earth-total-energy-of-the-satellite-is-given-by-e-the-potential-energy-of-the-satellite-i

slug:
an-artificial-satellite-moves-in-a-circular-orbit-around-the-earth-total-energy-of-the-satellite-is-given-by-e-the-potential-energy-of-the-satellite-i-97254

question:
<div class="question">An artificial satellite moves in a circular orbit around the earth. Total energy of the satellite is given by $E$. The potential energy of the satellite is</div>

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

answer:
<div class="solution">We know that
<br/>The potential energy of the satellite
<br/>$$
<br/>U=-\frac{G M_{e} m}{R_{0}}
<br/>$$
<br/>The kinetic energy of the satellite
<br/>$$
<br/>K=\frac{1}{2} \frac{G M_{e} m}{R_{e}}
<br/>$$
<br/>The total energy
<br/>$$
<br/>\begin{aligned}
<br/>E=U+K &amp;=-\frac{G M_{e} m}{R}+\frac{1}{2} \frac{G M_{e} m}{R_{0}} \\
<br/>E &amp;=-\frac{1}{2} \frac{G M_{e} m}{R} \\
<br/>2 E &amp;=-\frac{G M_{e} m}{R_{0}} \Rightarrow-2 E=U
<br/>\end{aligned}
<br/>$$
<br/>So. $\mathrm{PE}=-2(\mathrm{TE})$
<br/>$$
<br/>\mathrm{PE}=-2 E
<br/>$$</div>


title: an-atomic-nucleus-having-low-n-p-ratio-tries-to-find-stability-by
slug: an-atomic-nucleus-having-low-n-p-ratio-tries-to-find-stability-by-73448
question: <div class="question">An atomic nucleus having low $n / p$ ratio tries to find stability by</div>
tags: ['Chemistry', 'Chemical Kinetics', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">the emission of an $\alpha$ -particle</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">the emission of a positron</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">capturing an orbital electron (K-electron capture)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">emission of a $\beta$ -particle</span> </li> </ul>

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

answer:
<div class="solution">Emission of a positron results in the conversion of a proton into neutron, along with the release of neutrino. Thus, the number of protons decreases and of neutron increases, i.e. $n / p$ ratio increases and the nuclei becomes stable.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_a15.png"/></div>


tags: ['Physics', 'Gravitation', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P1.db
title:
an-earths-satellite-nejar-the-surface-of-the-earth-takes-about-90-min-per-revolution-a-satellite-orbiting-the-moon-also-takes-about-90-min-per-revolut

slug:
an-earths-satellite-nejar-the-surface-of-the-earth-takes-about-90-min-per-revolution-a-satellite-orbiting-the-moon-also-takes-about-90-min-per-revolut-30439

question:
<div class="question">An earth's satellite nejar the surface of the earth takes about 90 min per revolution. A satellite orbiting the moon also takes about 90 min per revolution. Then which of the following is true?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(\rho_m  &lt; \rho_e\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(\rho_m &gt; \rho_e\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(\rho_{\mathrm{m}}=\rho_{\mathrm{e}}\)</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">D</span> <span class="option-data">No conclusion can be made about the densities</span> </li> </ul>

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

answer:
<div class="solution">Hint : <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/4JOL9GSH1VW6kAhZ4UuQQUW5jjxhBpv0oLMl1jD6y9I.original.fullsize.png"/><br/><br/>\(m\left(E_g\right)=m \omega^2 R\)<br/>\(\begin{aligned}<br/>&amp; m \cdot 4 \pi \frac{G \rho R}{3}=m \omega^2 R \\<br/>&amp; \Rightarrow \omega^2 \propto \rho \\<br/>&amp; \Rightarrow T \propto \frac{1}{\sqrt{\rho}}<br/>\end{aligned}\)<br/>If \(\mathrm{T}\) are equal, so will be \(\rho\)</div>


tags: ['Physics', 'Capacitance', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch1_P1.db
title:
an-electric-bulb-a-capacitor-a-battery-and-a-switch-are-all-in-series-in-a-circuit-how-does-the-intensity-of-light-vary-when-the-switch-is-turn-on

slug:
an-electric-bulb-a-capacitor-a-battery-and-a-switch-are-all-in-series-in-a-circuit-how-does-the-intensity-of-light-vary-when-the-switch-is-turn-on-61102

question:
<div class="question">An electric bulb, a capacitor, a battery and a switch are all in series in a circuit. How does the intensity of light vary when the switch is
<br/>turn on?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Continues to increase gradually</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Gradually increases for sometime and then becomes steady</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Sharply rises initially and then gradually 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">D</span> <span class="option-data">Gradually increases for sometime and then gradually decreases</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Sharply rises initially and then gradually decreases</span> </div>

answer:
<div class="solution">Initially, there will be no voltage drop across capacitor, so intensity of bulb will rise sharply and gradually voltage drop across capacitor will increase as a result voltage drop across bulb decreases, so intensity of bulb will decreases.</div>


tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch1_P1.db
title:
an-electric-bulb-marked-as-50w200v-is-connected-across-a-100-v-supply-the-present-power-of-the-bulb-is

slug:
an-electric-bulb-marked-as-50w200v-is-connected-across-a-100-v-supply-the-present-power-of-the-bulb-is-49101

question:
<div class="question">An electric bulb marked as 50W-200V is connected across a $100 \mathrm{V}$ supply. The present power of the bulb is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$37.5 \mathrm{W}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$25 \mathrm{W}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$12.5 \mathrm{W}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$10 \mathrm{W}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$12.5 \mathrm{W}$</span> </div>

answer:
<div class="solution">We know that
<br/>$$
<br/>R=\frac{V^{2}}{P}
<br/>$$
<br/>Given $\quad V=200 \mathrm{V}, P=40 \mathrm{W}$
<br/>and $\quad V=100 \mathrm{V}$
<br/>Hence, $\quad R=\frac{V^{2}}{P}=\frac{200 \times 200}{50}$
<br/>$$
<br/>\begin{array}{l}
<br/>P=\frac{V^{2}}{R}=\frac{100 \times 100 \times 50}{200 \times 200} \\
<br/>P^{\prime}=12.5 \mathrm{W}
<br/>\end{array}
<br/>$$</div>


tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P1.db
title:
an-electric-cell-of-emf-e-is-connected-across-a-copper-wire-of-diameter-d-and-length-l-the-drift-velocity-of-electrons-in-the-wire-is-v-d-if-the-lengt

slug:
an-electric-cell-of-emf-e-is-connected-across-a-copper-wire-of-diameter-d-and-length-l-the-drift-velocity-of-electrons-in-the-wire-is-v-d-if-the-lengt-37837

question:
<div class="question">An electric cell of emf $E$ is connected across a copper wire of diameter $d$ and length $l$. The drift velocity of electrons in the wire is $v_{d}$. If the length of the wire is changed to $2 l,$ the new drift velocity of electrons in the copper wire will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$v_{d}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 v_{d}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$v_{d} / 2$</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">$v_{d} / 4$</span> </li> </ul>

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

answer:
<div class="solution">The drift velocity is given as
<br/>$$
<br/>\begin{aligned}
<br/>v_{d} &amp;=\frac{i}{n e A}=\frac{E}{R \times n e A} \\
<br/>&amp;=\frac{E \times A}{\rho l \times n e A}=\frac{E}{ln e}
<br/>\end{aligned}
<br/>$$
<br/>When length of wire changed to 2l , the new drift velocity.
<br/>$$
<br/>\begin{aligned}
<br/>v_{d}^{\prime} &amp;=\frac{E}{\rho \times 2 l \times n e} \\
<br/>\therefore \quad &amp; \frac{v_{d}^{\prime}}{v_{d}}=\frac{E / \rho 2 \text { lne }}{E / \rho \text { lne }}=\frac{1}{2} \\
<br/>\Rightarrow \quad v_{d}^{\prime} &amp;=\frac{v_{d}}{2}
<br/>\end{aligned}
<br/>$$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2019']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Zero</span> </div>
source_db: db\MarksBatch1_P1.db
title:
an-electric-current-i-enters-and-leaves-a-uniform-circular-wire-of-radius-r-through-diametrically-opposite-points-a-particle-carrying-a-charge-q-moves

slug:
an-electric-current-i-enters-and-leaves-a-uniform-circular-wire-of-radius-r-through-diametrically-opposite-points-a-particle-carrying-a-charge-q-moves-49484

question:
<div class="question">An electric current $^{\prime} I^{\prime}$ enters and leaves a uniform circular wire of radius $r$ through diametrically opposite points. A particle carrying a charge $q$ moves along the axis of the circular wire with speed $v$. What is the magnetic force experienced by the particle when it passes through the centre of the circle?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$q v \frac{\mu_{0} i}{a}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$q v \frac{\mu_{0} i}{2 a}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$q v \frac{\mu_{0} i}{2 \pi a}$</span> </li><li class="correct"> <span class="option-label">D</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> </ul>

answer:
<div class="solution">Given, electric current in circular wire $=I$ 
<br/>Radius of wire $=r$
<br/>Charge on particle $=q$ 
<br/>Speed of the particle $=v$
<br/>The given loop can be as shown in the figure below. $1 / 2$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2019_phy_a22.png"/> <br/>$\because$ Net magnetic field at the centre $=0$
<br/>So, magnetic force $\mathbf{F}_{\text {magnetic }}=q(\mathbf{v} \times \mathbf{B})=0$ So, the magnetic force experienced by the particle when it passes through the centre is $F=0$</div>


tags: ['Chemistry', 'Biomolecules', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch1_P1.db
title:
an-electric-current-is-passed-through-an-aqueous-solution-of-a-mixture-of-alanine-isoelectric-point-60-glutamic-acid-32-and-arginine-107-buffered-at-m

slug:
an-electric-current-is-passed-through-an-aqueous-solution-of-a-mixture-of-alanine-isoelectric-point-60-glutamic-acid-32-and-arginine-107-buffered-at-m-90434

question:
<div class="question">An electric current is passed through an aqueous solution of a mixture of alanine (isoelectric point 6.0) glutamic acid (3.2) and arginine (10.7) buffered at \(\mathrm{pH}\) 6. What is the fate of the three acids?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Glutamic acid migrates to anode at \(\mathrm{pH}\) 6. Arginine is present as a cation and migrates to the cathode. Alanine in a dipolar ion remains uniformly distributed in solution.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Glutamic acid migrates to cathode and others remain uniformly distributed in solution.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">All three remain uniformly distributed in solution.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">All three move to cathode</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Glutamic acid migrates to anode at \(\mathrm{pH}\) 6. Arginine is present as a cation and migrates to the cathode. Alanine in a dipolar ion remains uniformly distributed in solution.</span> </div>

answer:
<div class="solution">Hints : At \(\mathrm{pH}=6\), glutamic acid exists as a dianionic species &amp; migrates to anode while arginine exists as cationic species &amp; moves to cathode. Alanine does not migrate to any electrode at its isoelectric point .</div>


tags: ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P1.db
title:
an-electric-dipole-of-dipole-moment-vecp-is-placed-at-the-origin-of-the-coordinate-system-along-the-zaxis-the-amount-of-work-required-to-move-a-charge

slug:
an-electric-dipole-of-dipole-moment-vecp-is-placed-at-the-origin-of-the-coordinate-system-along-the-zaxis-the-amount-of-work-required-to-move-a-charge-52236

question:
<div class="question">An electric dipole of dipole moment \(\vec{p}\) is placed at the origin of the co-ordinate system along the \(z\)-axis. The amount of work required to move a charge ' \(q\) ' from the point \((a, 0,0)\) to the point \((0,0, a)\) is,</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\frac{p q}{4 \pi \varepsilon_0 a^2}\)</span> </div>

answer:
<div class="solution">Hint : <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/UFEJVOC7663RHmfChhV7XYrzDy3PX60FhKeDS_GaBhw.original.fullsize.png"/><br/><br/>\(\begin{aligned} W &amp; =q\left(V_B-V_A\right) \\ &amp; =q\left(\frac{p}{4 \pi \epsilon_0} \cdot \frac{\cos 0}{a^2}-\frac{p \cos 90^{\circ}}{4 \pi \epsilon_0 a^2}\right) \\ &amp; =\frac{p q}{4 \pi \varepsilon_0 a^2}\end{aligned}\)</div>


tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2009']
source_db: db\MarksBatch1_P1.db
title:
an-electrical-cable-having-a-resistance-of-02-delivers-10-kw-at-200-v-dc-to-a-factory-what-is-the-efficiency-of-transmission

slug:
an-electrical-cable-having-a-resistance-of-02-delivers-10-kw-at-200-v-dc-to-a-factory-what-is-the-efficiency-of-transmission-43242

question:
<div class="question">An electrical cable having a resistance of $0.2 \Omega$ delivers $10 \mathrm{kw}$ at $200 \mathrm{~V}$ D.C. to a factory. What is the efficiency of transmission?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$65 \%$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$75 \%$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$85 \%$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$95 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$95 \%$</span> </div>

answer:
<div class="solution">$P=V I \Rightarrow I=\frac{10 \times 10^3}{200}=50 A$, Power loss $=(50)^2(0.2)=500 \mathrm{~W}$<br/>Efficiency $=\frac{10000 \times 100}{10000+500}=95.23 \%$</div>


tags: ['Physics', 'Dual Nature of Matter', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch1_P1.db
title:
an-electron-accelerated-through-a-potential-of-10000-v-from-rest-has-a-debroglie-wave-length-what-should-be-the-accelerating-potential-so-that-the-wav

slug:
an-electron-accelerated-through-a-potential-of-10000-v-from-rest-has-a-debroglie-wave-length-what-should-be-the-accelerating-potential-so-that-the-wav-28138

question:
<div class="question">An electron accelerated through a potential of $10000 \mathrm{V}$ from rest has a de-Broglie wave length $\lambda$. What should be the accelerating potential, so that the wavelength is doubled?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$20000 \mathrm{V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$40000 \mathrm{V}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$5000 \mathrm{V}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$2500 \mathrm{V}$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2500 \mathrm{V}$</span> </div>

answer:
<div class="solution">$\because$ Kinetic energy of a electron due to accelerated by a potential $V, \mathrm{KE}=e V$
<br/>$$
<br/>\frac{1}{2} m_{r} v^{2}=c V
<br/>$$
<br/>$\Rightarrow \quad \frac{1 \times p^{2}}{2 m_{e}}=e V \quad[\because p=m v]$
<br/>$\therefore$
<br/>$$
<br/>p=\sqrt{2 e V m_{e}}
<br/>$$
<br/>$\because$ de-Broglie wavelength of a particle having momentum $p$
<br/>$$
<br/>\lambda=\frac{h}{p}
<br/>$$
<br/>According to question, $\frac{\lambda_{1}}{\lambda_{2}}=\frac{p_{2}}{p_{1}}=\frac{\sqrt{2 e V_{2} m_{c}}}{\sqrt{2 e V_{1} m_{e}}}=\sqrt{\frac{V_{2}}{V_{1}}}$
<br/>$\because$
<br/>$$
<br/>\lambda_{2}=2 \lambda_{1}
<br/>$$
<br/>$\Rightarrow \quad \frac{\lambda_{1}}{2 \lambda_{1}}=\sqrt{\frac{V_{2}}{10000}}$
<br/>$\therefore \quad$ Potential $V_{2}=\frac{10^{4}}{4}=2500 \mathrm{V}$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch1_P1.db
title:
an-electron-enters-an-electric-field-having-intensity-e-3-i-6-j-2-k-v-m-1-and-magnetic-field-having-induction-b-2-i-3-j-t-with-a-velocity-v-2-i-3-j-ms

slug:
an-electron-enters-an-electric-field-having-intensity-e-3-i-6-j-2-k-v-m-1-and-magnetic-field-having-induction-b-2-i-3-j-t-with-a-velocity-v-2-i-3-j-ms-33563

question:
<div class="question">An electron enters an electric field having
<br/>intensity $\mathbf{E}=3 \overrightarrow{\mathbf{i}}+6 \hat{\mathbf{j}}+2 \hat{\mathbf{k}} \cdot \mathbf{V} \mathbf{m}^{-1}$ and magnetic
<br/>field having induction $\mathrm{B}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}$ T with a velocity $\mathbf{v}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}$ ms $^{-1}$. The magnitude of the force acting on the electron is (Given, $\left.e=-1.6 \times 10^{-19} \mathrm{C}\right)$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2.02 \times 10^{-18} \mathrm{N}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$5.16 \times 10^{-16} \mathrm{N}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3.72 \times 10^{-17} \mathrm{N}$</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>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">None of the above</span> </div>

answer:
<div class="solution">Given, $E=3 i+6 j+2 \hat{k} \vee / m$
<br/>$$
<br/>\begin{array}{l}
<br/>B=2 \hat{i}+3 \hat{j} T \\
<br/>v=2 \hat{i}+3 \hat{j} m / s \\
<br/>e=-1.6 \times 10^{-10} C
<br/>\end{array}
<br/>$$
<br/>The magnitude of electric field
<br/>$$
<br/>\begin{aligned}
<br/>|E| &amp;=\sqrt{(3)^{2}+(6)^{2}+(2)^{2}} \\
<br/>&amp;=\sqrt{9+36+4} \\
<br/>&amp;=\sqrt{49}=7
<br/>\end{aligned}
<br/>$$
<br/>The force acting on electron due to electric field
<br/>$$
<br/>F=q E
<br/>$$
<br/>$$
<br/>\begin{aligned}
<br/>|F| &amp;=|q||\mathbf{E}| \\
<br/>&amp;=1.6 \times 10^{-19} \times 7 \mathrm{N} \\
<br/>&amp;=11.2 \times 10^{-19} \mathrm{N} \\
<br/>&amp;=1.12 \times 10^{-18} \mathrm{N}
<br/>\end{aligned}
<br/>$$
<br/>Alternate Method
<br/>B $\|$ v Magnetic field is parallel to velocily of electron. $\mathrm{v} \| \mathrm{B}$ Magnetic force
<br/>$$
<br/>\begin{aligned}
<br/>F_{m} &amp;=q(\mathbf{v} \times \mathbf{B}) \\
<br/>&amp;=q v B \sin \theta \\
<br/>&amp;=q v B \sin 0 \\
<br/>&amp;=0
<br/>\end{aligned}
<br/>$$
<br/>$\therefore$ Net force $\quad F=F_{e}+F_{m}$
<br/>$$
<br/>\begin{array}{l}
<br/>=\left(1.12 \times 10^{-18}+0\right) \mathrm{N} \\
<br/>=1.12 \times 10^{-18} \mathrm{N}
<br/>\end{array}
<br/>$$
<br/>Hence, none of the given options is correct.</div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
title:
an-electron-in-a-circular-orbit-of-radius-005-nm-performs-1-0-16-revolutions-per-second-the-maghetic-moment-due-to-this-rotation-of-electron-is-in-am-

slug:
an-electron-in-a-circular-orbit-of-radius-005-nm-performs-1-0-16-revolutions-per-second-the-maghetic-moment-due-to-this-rotation-of-electron-is-in-am-98734

question:
<div class="question">An electron in a circular orbit of radius $0.05 \mathrm{nm}$ performs $10^{16}$ revolutions per second. The maghetic moment due to this rotation of electron is (in $\mathrm{Am}^{2}$ )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2.16 \times 10^{-23}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3.21 \times 10^{-22}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3.21 \times 10^{-24}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$1.26 \times 10^{-23}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$1.26 \times 10^{-23}$</span> </div>

answer:
<div class="solution">Given, $r=0.05 \mathrm{nm}=0.05 \times 10^{-9} \mathrm{m}$
<br/>$$
<br/>\begin{array}{l}
<br/>\qquad\left(\because 1 \mathrm{nm}=10^{-9} \mathrm{m}\right) \\
<br/>n=10^{16} \text { revolutions } \\
<br/>e=1.6 \times 10^{-19} \mathrm{C}
<br/>\end{array}
<br/>$$
<br/>We know that
<br/>The magnetic moment $M=A L$
<br/>$$
<br/>\begin{aligned}
<br/>M &amp;=\pi r^{2} \times n e \\
<br/>M &amp;=3.14 \times\left(0.05 \times 10^{-9}\right)^{2} \times 10^{16} \times 1.6 \times 10^{-19} \\
<br/>M &amp;=0.1256 \times 10^{-18} \times 10^{16} \times 10^{-19} \\
<br/>\text {or } M &amp;=1.26 \times 10^{-23} \mathrm{Am}^{2}
<br/>\end{aligned}
<br/>$$</div>


title: an-electron-in-the-5-mathrmd-orbital-can-be-represented-by-the-following-leftn-1-m0right-values
tags: ['Chemistry', 'Structure of Atom', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P1.db
slug:
an-electron-in-the-5-mathrmd-orbital-can-be-represented-by-the-following-leftn-1-m0right-values-14076

question:
<div class="question">An electron in the \(5 \mathrm{~d}\) orbital can be represented by the following \(\left(n, 1, m_0\right)\) values</div>

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

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">\((5,2,1)\), \((5,2,-1)\)</span> </div>

answer:
<div class="solution">Hint: \(5 \mathrm{~d} \quad \therefore \mathrm{n}=5 \quad \mathrm{I}=2\)<br/>and \(m\) can be -2 to 2</div>


tags: ['Physics', 'Rotational Motion', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P1.db
title:
an-electron-of-charge-e-and-mass-m-is-moving-in-a-circular-of-radius-r-with-a-uniform-angular-speed-then-which-of-the-following-statements-are-correct

slug:
an-electron-of-charge-e-and-mass-m-is-moving-in-a-circular-of-radius-r-with-a-uniform-angular-speed-then-which-of-the-following-statements-are-correct-54909

question:
<div class="question">An electron of charge $e$ and mass $m$ is moving in a circular of radius $r$ with a uniform angular speed $\omega .$ Then which of the following statements are correct?</div>

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

answer:
<div class="solution">Magnetic moment, $m=IA$ $=\frac{e v}{2 \pi f} \times \pi r^{2}=\frac{e v r}{2}$
<br/>Angular momentum $=2 m \frac{d A}{d t}$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch1_P1.db
title:
an-electron-revolves-around-the-nucleus-in-a-circular-path-with-angular-momentum-l-a-uniform-magnetic-field-b-is-applied-perpendicular-to-the-plane-of

slug:
an-electron-revolves-around-the-nucleus-in-a-circular-path-with-angular-momentum-l-a-uniform-magnetic-field-b-is-applied-perpendicular-to-the-plane-of-66468

question:
<div class="question">An electron revolves around the nucleus in a circular path with angular momentum $\overrightarrow{\mathrm{L}} . \mathrm{A}$ uniform magnetic field $\overrightarrow{\mathrm{B}}$ is applied perpendicular to the plane of its orbit. If the electron experiences a torque $\overrightarrow{\mathrm{T}}$, then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\overrightarrow{\mathrm{T}} \| \overrightarrow{\mathrm{L}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\overrightarrow{\mathrm{T}}$ is anti-parallel to $\overrightarrow{\mathrm{L}}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\overrightarrow{\mathrm{T}} \cdot \overrightarrow{\mathrm{L}}=0$</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">Angle between $\vec{T}$ and $\vec{L}$ is $45^{\circ}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\overrightarrow{\mathrm{T}} \cdot \overrightarrow{\mathrm{L}}=0$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/aaJemW6eTzYjEoAGpGSi3P1KpfMpQMY3CUc84-fhRYk.original.fullsize.png"/><br/><br/>$\vec{\tau}=0 \Rightarrow \vec{\tau} \cdot \vec{L}=0$</div>


tags: ['Chemistry', 'Structure of Atom', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch1_P1.db
title:
an-element-belongs-to-group-15-and-third-period-of-the-periodic-table-its-electonic-configuration-will-be

slug:
an-element-belongs-to-group-15-and-third-period-of-the-periodic-table-its-electonic-configuration-will-be-49654

question:
<div class="question">An element belongs to Group 15 and third period of the periodic table. Its electonic configuration will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(1 \mathrm{~s}^2 2 \mathrm{~s}^2 2 \mathrm{p}^3\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(1 \mathrm{~s}^2 2 \mathrm{~s}^2 2 \mathrm{p}^4\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(1 s^2 2 s^2 2 p^6 3 s^2 3 p^3\)</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">\(1 \mathrm{~s}^2 2 \mathrm{~s}^2 2 \mathrm{p}^6 3 \mathrm{~s}^2 3 \mathrm{p}^2\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(1 s^2 2 s^2 2 p^6 3 s^2 3 p^3\)</span> </div>

answer:
<div class="solution">Hints: General valence shell electronic configuration of 15 group elements is \(n s^2 n p^3\). where \(n=\) period number.</div>


tags: ['Chemistry', 'Solid State', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch1_P1.db
title:
an-element-crystallizes-in-a-body-centred-cubic-lattice-the-edge-length-of-the-unit-cell-is-200-pm-and-the-density-of-the-element-is-50-g-cm-3-calcula

slug:
an-element-crystallizes-in-a-body-centred-cubic-lattice-the-edge-length-of-the-unit-cell-is-200-pm-and-the-density-of-the-element-is-50-g-cm-3-calcula-78975

question:
<div class="question">An element crystallizes in a body centred cubic lattice. The edge length of the unit cell is $200 \mathrm{pm}$ and the density of the element is $5.0 \mathrm{~g} \mathrm{~cm}^{-3}$. Calculate the number of atoms in $100 \mathrm{~g}$ of this element.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2.5 \times 10^{23}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2.5 \times 10^{24}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$5.0 \times 10^{23}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$5.0 \times 10^{24}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$5.0 \times 10^{24}$</span> </div>

answer:
<div class="solution">$\rho_{\text {unit cell }}(\mathrm{g} / \mathrm{cc})=\frac{\mathrm{Z} \times \mathrm{M} \cdot \mathrm{Mass}(\mathrm{g} / \mathrm{mol})}{\mathrm{N}_{\mathrm{A}}\left(\mathrm{mol}^{-1}\right) \times(\mathrm{a} \mathrm{pm})^{3} \times 10^{-30}} \quad \mathrm{Z}_{\text {B.c.c }}=2$
<br/>or $5=\frac{2 \times \text { M.Mass }}{\mathrm{N}_{\mathrm{A}} \times(200)^{3} \times 10^{-30}}$
<br/>or M.Mass $=\frac{5 \times 8 \times \mathrm{N}_{\mathrm{A}} \times 10^{-24}}{2}=2 \mathrm{~N}_{\mathrm{A}} \times 10^{-23}$
<br/>Now, no. of moles in $100 \mathrm{~g}=\frac{100}{2 \mathrm{~N}_{\mathrm{A}} \times 10^{-23}}$
<br/>$\therefore$ no. of atoms $=\frac{100}{2 \mathrm{~N}_{\mathrm{A}} \times 10^{-23}} \times \mathrm{N}_{\mathrm{A}}=50 \times 10^{23}=5.0 \times 10^{24}$</div>


title: an-element-e-loses-one-and-two-particle-in-three-successive-stages-the-resultibg-element-will-be
tags: ['Chemistry', 'Chemical Kinetics', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch1_P1.db
slug:
an-element-e-loses-one-and-two-particle-in-three-successive-stages-the-resultibg-element-will-be-30588

question:
<div class="question">An element $E$ loses one $\alpha$ and two $\beta$ particle in three successive stages. The resultibg element will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">an isobar of $E$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">an isotone of $E$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">an isotope of $E$</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">D</span> <span class="option-data">$E$ itself</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">an isotope of $E$</span> </div>

answer:
<div class="solution">Let $Z$ = atomic number 
<br/>$M=$ atornic mass
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_che_a21.png"/> <br/> <br/>Hence, ${ }_{Z} E^{M}$ and ${ }_{2} E^{M-4}$ has same atomic number with different atomic mass thus, they are isotopes.</div>


tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch1_P1.db
title:
an-element-x-belongs-to-fourth-period-and-fifteenth-group-of-the-periodic-table-which-of-the-following-statements-is-true

slug:
an-element-x-belongs-to-fourth-period-and-fifteenth-group-of-the-periodic-table-which-of-the-following-statements-is-true-33803

question:
<div class="question">An element $X$ belongs to fourth period and fifteenth group of the periodic table. Which of the following statements is true?</div>

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

answer:
<div class="solution">The element belonging to 4 th period and 15 th group is arsenic (As). The outer electronic configuration of 15 th group element is $n s^{2} n \rho^{3}$. Since arsenic belongs to 4 th period, therefore it has filled 'd' orbital too. Thus, the electronic configuration of As is $[A r] 4 s^{2} 3 d^{10} 4 \rho^{3} .$
<br/>So, it has filled's' and'd orbital and half-fliled porbital.</div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">zero</span> </div>
source_db: db\MarksBatch1_P1.db
title:
an-equilateral-triangle-is-made-by-uniform-wires-a-b-bc-c-a-a-current-i-enters-at-a-and-leaves-from-the-mid-point-of-bc-if-the-lengths-of-each-side-of-1

slug:
an-equilateral-triangle-is-made-by-uniform-wires-a-b-bc-c-a-a-current-i-enters-at-a-and-leaves-from-the-mid-point-of-bc-if-the-lengths-of-each-side-of-1-33224

question:
<div class="question">An equilateral triangle is made by uniform wires $A B, B C, C A .$ A current $I$ enters at $A$ and leaves from the mid point of $B C$. If the lengths of each side of the triangle is $L,$ the magnetic field $B$ at the centroid $O$ of the triangle is <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_phy_q22.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\mu_{0}}{4 \pi}\left(\frac{4 L}{L}\right)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\mu_{0}}{2 \pi}\left(\frac{4 L}{L}\right)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mu_{0}}{4 \pi}\left(\frac{2 L}{L}\right)$</span> </li><li class="correct"> <span class="option-label">D</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> </ul>

answer:
<div class="solution">The given situation can be shown as
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_phy_a22.png"/> <br/> <br/>The magnetic field at centroid $O$ = Magnetic field due to left part + Magnetic field due to right part
<br/>$\therefore$
<br/>$$
<br/>\mathrm{B}=\mathrm{B}_{1}+\mathrm{B}_{2}=0
<br/>$$
<br/>(: direction of $B$ due to both parts is different of $O$ )</div>


tags: ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">zero</span> </div>
source_db: db\MarksBatch1_P1.db
title:
an-equilateral-triangle-is-made-by-uniform-wires-a-b-bc-c-a-a-current-i-enters-at-a-and-leaves-from-the-mid-point-of-bc-if-the-lengths-of-each-side-of

slug:
an-equilateral-triangle-is-made-by-uniform-wires-a-b-bc-c-a-a-current-i-enters-at-a-and-leaves-from-the-mid-point-of-bc-if-the-lengths-of-each-side-of-96383

question:
<div class="question">An equilateral triangle is made by uniform wires $A B, B C, C A .$ A current $I$ enters at $A$ and leaves from the mid point of $B C$. If the lengths of each side of the triangle is $L,$ the magnetic field $B$ at the centroid $O$ of the triangle is <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_phy_q22.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\mu_{0}}{4 \pi}\left(\frac{4 L}{L}\right)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\mu_{0}}{2 \pi}\left(\frac{4 L}{L}\right)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mu_{0}}{4 \pi}\left(\frac{2 L}{L}\right)$</span> </li><li class="correct"> <span class="option-label">D</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> </ul>

answer:
<div class="solution">The given situation can be shown as
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_phy_a22.png"/> <br/> <br/>The magnetic field at centroid $O$ = Magnetic field due to left part + Magnetic field due to right part
<br/>$\therefore$
<br/>$$
<br/>\mathrm{B}=\mathrm{B}_{1}+\mathrm{B}_{2}=0
<br/>$$
<br/>(: direction of $B$ due to both parts is different of $O$ )</div>


tags: ['Chemistry', 'Hydrocarbons', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch1_P1.db
title:
an-equimolar-mixture-of-toluene-and-chlorobenzene-is-treated-with-a-mixture-of-conc-h-2-so-4-and-conc-hno-3-indicate-the-correct-statement-from-the-fo

slug:
an-equimolar-mixture-of-toluene-and-chlorobenzene-is-treated-with-a-mixture-of-conc-h-2-so-4-and-conc-hno-3-indicate-the-correct-statement-from-the-fo-68032

question:
<div class="question">An equimolar mixture of toluene and chlorobenzene is treated with a mixture of conc. $\mathrm{H}_{2} \mathrm{SO}_{4}$ and conc. $\mathrm{HNO}_{3}$. Indicate the correct statement from the following.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$p$ -nitrotoluene is formed in excess</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_a35.png"/> <br/> <br/>As toluene and chlorobenzene, both can react with mixture of conc. $\mathrm{H}_{2} \mathrm{SO}_{4}$ and conc. HNO $_{3}$. but being more reactive, toluene will yield p-nitrotoluene in excess.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P1.db
title:
an-ideal-gas-expands-adiabatically-against-vaccum-which-of-the-following-is-correct-for-the-given-process

slug:
an-ideal-gas-expands-adiabatically-against-vaccum-which-of-the-following-is-correct-for-the-given-process-97333

question:
<div class="question">An ideal gas expands adiabatically against vaccum. Which of the following is correct for the given process?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\Delta S=0$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\Delta \mathrm{T}=-\mathrm{ve}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\Delta \mathrm{U}=0$</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">$\Delta \mathrm{P}=0$</span> </li> </ul>

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

answer:
<div class="solution">Hint: 
<br/>For adiabatic free expansion of an ideal gas
<br/>$\mathrm{dq}=0$
<br/>$\mathrm{dU}=0$
<br/>$\mathrm{dH}=0$
<br/>$\mathrm{dT}=0$</div>


tags: ['Physics', 'Thermodynamics', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch1_P1.db
title:
an-ideal-gas-is-compressed-isothermally-until-its-pressure-is-doubled-and-then-allowed-to-expand-adiabatically-to-regain-its-original-volume-leftgamma

slug:
an-ideal-gas-is-compressed-isothermally-until-its-pressure-is-doubled-and-then-allowed-to-expand-adiabatically-to-regain-its-original-volume-leftgamma-66502

question:
<div class="question">An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume \(\left(\gamma=1.4\right.\) and \(\left.2^{-14}=0.38\right)\). The ratio of the final to initial pressure is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(0.76: 1\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(1: 1\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(0.66: 1\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(0.86: 1\)</span> </li> </ul>

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

answer:
<div class="solution">Hints: <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/WBDmK1PFDhgf7WOSS1BrWlc-ypJcgkwoAYntKCEMbgY.original.fullsize.png"/><br/><br/>\(\begin{aligned}<br/>&amp; \mathrm{P}_{\mathrm{f}} \mathrm{V}^\gamma=\left(2 \mathrm{P}_{\mathrm{i}}\right)\left(\frac{\mathrm{V}}{2}\right)^\gamma \\<br/>&amp; \frac{\mathrm{P}_{\mathrm{f}}}{\mathrm{P}_{\mathrm{i}}}=2\left(\frac{\gamma}{2 \gamma}\right)^\gamma=2(2)^{-\gamma} \\<br/>&amp; =2 \times 0.38=0.76 \\<br/>&amp;<br/>\end{aligned}\)</div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch1_P1.db
title:
an-ideal-gas-of-molar-mass-m-is-contained-in-a-very-tall-vertical-cylindrical-column-in-the-uniform-gravitational-field-assuming-the-gas-temperature-t

slug:
an-ideal-gas-of-molar-mass-m-is-contained-in-a-very-tall-vertical-cylindrical-column-in-the-uniform-gravitational-field-assuming-the-gas-temperature-t-75677

question:
<div class="question">An ideal gas of molar mass $\mathrm{M}$ is contained in a very tall vertical cylindrical column in the uniform gravitational field. Assuming the gas temperature to be $\mathrm{T}$, the height at which the centre of gravity of the gas is located is (R: universal gas constant)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\mathrm{RT}}{\mathrm{g}}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{\mathrm{RT}}{\mathrm{Mg}}$</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><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{MgR}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">RTg</span> </li> </ul>

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

answer:
<div class="solution">$\because$ field is uniform COM and COG coincides.
<br/>$$
<br/>\text { So } \mathrm{y}_{\mathrm{cem}}=\frac{\int_{0}^{\infty} \mathrm{ydm}}{\int_{0}^{\infty} \mathrm{dm}}=\frac{\int_{0}^{\infty} \mathrm{y} \mathrm{Ady} \rho}{\int_{0}^{\infty} \mathrm{Ady} \rho}=\frac{\int_{0}^{\infty} \mathrm{y} \rho \mathrm{dy}}{\int_{0}^{\infty} \rho \mathrm{dy}}
<br/>$$
<br/>From Barometric formula :- $\rho=\rho_{0} \mathrm{e}^{-\mathrm{Mgy} / \mathrm{RT}}$
<br/>So $y_{\text {cen }}=\frac{\int_{0}^{\infty} y e^{-M g y / R T}}{\int_{0}^{\infty} e^{-M g y / R T}}=\frac{R T}{M g}$</div>


tags: ['Physics', 'Thermodynamics', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch1_P1.db
title:
an-ideal-gas-undergoes-the-cyclic-process-abca-as-shown-in-the-given-p-v-diagram-it-rejects-50-j-of-heat-during-ab-and-absorbs-80-j-of-heat-during-ca-

slug:
an-ideal-gas-undergoes-the-cyclic-process-abca-as-shown-in-the-given-p-v-diagram-it-rejects-50-j-of-heat-during-ab-and-absorbs-80-j-of-heat-during-ca-98949

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/ooubpT6rFhYuTZYpoItdA8hbcJsRI4PHb5nf3an7Ps8.original.fullsize.png"/><br/> <br/>An ideal gas undergoes the cyclic process abca as shown in the given $\mathrm{P}-\mathrm{V}$ diagram. It rejects $50 \mathrm{~J}$ of heat during $a b$ and absorbs $80 \mathrm{~J}$ of heat during ca. During $b c$, there is no transfer of heat and $40 \mathrm{~J}$ of work is done by the gas. What should be the area of the closed curve abca?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$30 \mathrm{~J}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$40 \mathrm{~J}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$10 \mathrm{~J}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$90 \mathrm{~J}$</span> </li> </ul>

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

answer:
<div class="solution">Hint:
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/btzDCl7YkQMelde_kwnUYmz-kLzAAlX1D3xdPnzdBlM.original.fullsize.png"/><br/> <br/>Area of cycle $=\mathrm{W}_{\text {total }}$
<br/>$=\Delta Q_{\text {net }}=\Delta Q_{A B}+\Delta Q_{B C}+\Delta Q_{C A}=-50+0+80=30 \mathrm{~J}$
<br/>NOTE: In process $\mathrm{BC}, \mathrm{W}_{\mathrm{BC}}&gt;0$ and $\Delta \mathrm{U}_{\mathrm{BC}}&gt;0$
<br/>$\therefore \Delta \mathrm{Q}_{\mathrm{BC}}=\Delta \mathrm{U}_{\mathrm{BC}}+\mathrm{W}_{\mathrm{BC}}&gt;0$
<br/>Thus $\Delta \mathrm{Q}_{\mathrm{eC}}=0$ as given in question isn't possible. But we have neglected this technical mistake while answering.</div>


tags: ['Physics', 'Thermodynamics', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch1_P1.db
title:
an-ideal-monoatomic-gas-of-given-mass-is-heated-at-constant-pressure-in-this-process-the-fraction-of-supplied-heat-energy-used-for-the-increase-of-the

slug:
an-ideal-monoatomic-gas-of-given-mass-is-heated-at-constant-pressure-in-this-process-the-fraction-of-supplied-heat-energy-used-for-the-increase-of-the-48737

question:
<div class="question">An ideal mono-atomic gas of given mass is heated at constant pressure. In this process, the fraction of supplied heat energy used for the increase of the internal energy of the gas is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$3 / 8$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$3 / 5$</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">C</span> <span class="option-data">$3 / 4$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 / 5$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3 / 5$</span> </div>

answer:
<div class="solution">Fraction $=\frac{\Delta U}{\Delta Q}=\frac{C_{Y}}{C_{p}}$
<br/>For monoatomic gas $\frac{C_{p}}{C_{\gamma}}=\gamma=\frac{5}{3}$
<br/>So, $\quad \frac{C_{\gamma}}{C_{p}}=\frac{1}{\gamma}=\frac{3}{5}$</div>


tags: ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch1_P1.db
title:
an-infinite-sheet-carrying-a-uniform-surface-charge-density-lies-on-the-x-y-plane-the-work-done-to-carry-a-charge-q-from-the-point-a-a-i-2-j-3-k-to-th

slug:
an-infinite-sheet-carrying-a-uniform-surface-charge-density-lies-on-the-x-y-plane-the-work-done-to-carry-a-charge-q-from-the-point-a-a-i-2-j-3-k-to-th-43228

question:
<div class="question">An infinite sheet carrying a uniform surface charge density $\sigma$ lies on the $x y$ -plane. The work done to carry a charge $q$ from the point $\mathbf{A}=a(\mathbf{i}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})$ to the point $\mathbf{B}=a(\mathbf{i}-2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}})$
<br/>(where $a$ is a constant with the dimension of length and $\varepsilon_{0}$ is the permittivity of free space) is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{3 \sigma a q}{2 \varepsilon_{0}}$</span> </div>

answer:
<div class="solution">The given
<br/>$$
<br/>\begin{aligned}
<br/>\mathbf{A} &amp;=a(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \\
<br/>\mathbf{B} &amp;=a(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}) \\
<br/>\mathbf{A B} &amp;=\mathbf{O B}-\mathbf{O A} \\
<br/>&amp;=a(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}})-a(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \\
<br/>\mathbf{A B} &amp;=a(-4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})
<br/>\end{aligned}
<br/>$$
<br/>Work done $=q\left(\frac{\sigma}{2 \varepsilon_{0}}\right) \hat{\mathbf{k}} \cdot \mathbf{A B} \quad$ (along to $Z$ -axisi
<br/>$$
<br/>\begin{array}{r}
<br/>=q\left(\frac{\sigma}{2 \varepsilon_{0}}\right) \hat{\mathbf{k}} \cdot a(-4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})=\frac{3 q \sigma a}{2 \varepsilon_{0}} \\
<br/>(\because \mathbf{i} \cdot \mathbf{i}=\mathbf{j} \cdot \mathbf{j}=\mathbf{i} \cdot \mathbf{k}=1 \text { and } \mathbf{i} \cdot \mathbf{j}=\mathbf{j} \cdot \hat{\mathbf{k}}=\hat{\mathbf{k}} \cdot \hat{\mathbf{i}}=0)
<br/>\end{array}
<br/>$$</div>


tags: ['Physics', 'Wave Optics', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch1_P1.db
title:
an-interference-pattern-is-obtained-with-two-coherent-sources-of-intensity-ratio-mathrmn-1-the-ratio-fracmathrmitext-max-mathrmitext-min-mathrmitext-m

slug:
an-interference-pattern-is-obtained-with-two-coherent-sources-of-intensity-ratio-mathrmn-1-the-ratio-fracmathrmitext-max-mathrmitext-min-mathrmitext-m-67666

question:
<div class="question">An interference pattern is obtained with two coherent sources of intensity ratio \(\mathrm{n}: 1\). The ratio \(\frac{\mathrm{I}_{\text {Max }}-\mathrm{I}_{\text {Min }}}{\mathrm{I}_{\text {Max }}+\mathrm{I}_{\text {Min }}}\) will be maximum if</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(n=1\)</span> </div>

answer:
<div class="solution">Hint: \(\frac{I_1}{I_2}=n\)<br/>\(\begin{aligned}<br/>&amp; \mathrm{I}_1=\mathrm{nI}_2 \\<br/>&amp; \mathrm{I}_{\max }=\left(\sqrt{\mathrm{I}_1}+\sqrt{\mathrm{I}_2}\right)^2=\left(\sqrt{\mathrm{nI}} 2+\sqrt{\mathrm{I}_2}\right)^2=(\sqrt{\mathrm{n}}+1)^2\left(\sqrt{\mathrm{I}_2}\right)^2<br/>\end{aligned}\)<br/>\(\begin{aligned}<br/>&amp; I_{\min }=\left(\sqrt{I_1}-\sqrt{I_2}\right)^2=\left(\sqrt{n I_2}-\sqrt{I_2}\right)^2=(\sqrt{n}-1)^2\left(\sqrt{I_2}\right)^2 \\<br/>&amp; \frac{I_{\max }-I_{\min }}{I_{\max }+I_{\min }}=\frac{(\sqrt{n}+1)^2\left(I_2\right)-(\sqrt{n}-1)^2 I_2}{(\sqrt{n}+1)^2 I_2+(\sqrt{n}-1)^2 I_2}=\frac{(\sqrt{n}+1)^2-(\sqrt{n}-1)^2}{(\sqrt{n}+1)^2+(\sqrt{n}-1)^2} \\<br/>&amp; =\frac{(n+1+2 \sqrt{n})-(n+1-2 \sqrt{n})}{n+1+2 \sqrt{n}+n+1-2 \sqrt{n}}=\frac{4 \sqrt{n}}{2(n+1)}=\frac{2 \sqrt{n}}{n+1}<br/>\end{aligned}\)<br/>\(\therefore\) decreases with increasing \(\mathrm{n}\).<br/>\(\therefore\) It will be maximum if \(n=1\)</div>


tags: ['Physics', 'Ray Optics', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch1_P1.db
title:
an-object-is-located-4-m-from-the-first-of-two-thin-converging-lenses-of-focal-lengths-2-m-and-1-m-respectively-the-lenses-are-separated-by-3-m-the-fi

slug:
an-object-is-located-4-m-from-the-first-of-two-thin-converging-lenses-of-focal-lengths-2-m-and-1-m-respectively-the-lenses-are-separated-by-3-m-the-fi-91649

question:
<div class="question">An object is located $4 \mathrm{m}$ from the first of two thin converging lenses of focal lengths $2 \mathrm{m}$ and $1 \mathrm{m},$ respectively. The lenses are separated by $3 \mathrm{m}$. The final image formed by the second lens is located from the source at a distance of
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_q4.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$8.0 \mathrm{m}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$5.5 \mathrm{m}$</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">C</span> <span class="option-data">$6.0 \mathrm{m}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$6.5 \mathrm{m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$5.5 \mathrm{m}$</span> </div>

answer:
<div class="solution">From the lens formula (for first lens)
<br/>$$
<br/>\begin{aligned}
<br/>\frac{1}{f_{1}} &amp;=\frac{1}{v_{1}}-\frac{1}{u_{1}} \Rightarrow \frac{1}{2}=\frac{1}{v_{1}}-\frac{1}{(-4)} \\
<br/>\Rightarrow \quad \frac{1}{2}+\frac{1}{4} &amp;=\frac{1}{v_{1}}=\frac{3}{4} \\
<br/>\Rightarrow \quad v_{1} &amp;=\frac{4}{3}, u_{2}=3-\frac{4}{3}=5 / 3
<br/>\end{aligned}
<br/>$$
<br/>This image will be treated as the source for second lens, then again from lens formula, we have
<br/>$\frac{1}{f_{2}}=\frac{1}{v_{2}}-\frac{1}{u_{2}}4$
<br/>$\Rightarrow \quad \frac{1}{1}=\frac{1}{v_{2}}+5 / 3$
<br/>$\Rightarrow \quad 1-5 / 3=\frac{1}{v_{2}} \Rightarrow v_{2}=-3 / 2$
<br/>[By Eq. (i)]
<br/>This is the final image distance from 2 nd lens. So, the overall distance of image from the primary source(or object)
<br/>Let $d=4+3-1.5=5.5$</div>


tags: ['Physics', 'Ray Optics', 'WBJEE', 'WBJEE 2014']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">20</span> </div>
source_db: db\MarksBatch1_P1.db
title:
an-object-is-placed-30-cm-away-from-a-convex-lens-of-focal-length-10-cm-and-a-sharp-image-is-formed-on-a-screen-now-a-concave-lens-is-placed-in-contac

slug:
an-object-is-placed-30-cm-away-from-a-convex-lens-of-focal-length-10-cm-and-a-sharp-image-is-formed-on-a-screen-now-a-concave-lens-is-placed-in-contac-72697

question:
<div class="question">An object is placed $30 \mathrm{cm}$ away from a convex lens of focal length $10 \mathrm{cm}$ and a sharp image is formed on a screen. Now a concave lens is placed in contact with the convex lens. The screen now has to be moved by $45 \mathrm{cm}$ to get $\underline{a}$ sharp image again. The magnitude of focal length of the concave lens is (in $\mathrm{cm}$ )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">72</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">60</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">36</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">20</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">For the first condition
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_phy_a54.png"/> <br/> <br/>$$
<br/>\frac{1}{f_{1}}=\frac{1}{v}-\frac{1}{u} \Rightarrow \frac{1}{10}=\frac{1}{v}+\frac{1}{30}
<br/>$$
<br/>$\frac{1}{v}=\frac{1}{10}-\frac{1}{30}$
<br/>$v=\frac{30}{2}=15 \mathrm{cm}$
<br/>$$
<br/>\begin{aligned}
<br/>\text { where } f_{1}=10 \mathrm{cm} &amp; \begin{array}{l}
<br/>u=-30 \mathrm{cm} \\
<br/>v &amp; =?
<br/>\end{array}
<br/>\end{aligned}
<br/>$$
<br/>For the first condition<img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_phy_a54a.png"/> <br/> <br/>For the second condition when concave lens is placed
<br/>$$
<br/>\begin{array}{l}
<br/>v^{\prime}=(15+45) \mathrm{cm}=60 \mathrm{cm} \\
<br/>\frac{1}{F}=\frac{1}{v^{\prime}}-\frac{1}{u}
<br/>\end{array}
<br/>$$
<br/>(where $F=$ focal length of combination)
<br/>$\therefore$
<br/>$$
<br/>\begin{array}{l}
<br/>\frac{1}{F}=\frac{1}{60}+\frac{1}{30} \\
<br/>F=\frac{60}{3} \mathrm{cm}=20 \mathrm{cm}
<br/>\end{array}
<br/>$$
<br/>The magnitude of focal length of concave lens $\frac{1}{F}=\frac{1}{f_{1}}+\frac{1}{f_{2}} \Rightarrow \frac{1}{20}=\frac{1}{10}+\frac{1}{f_{2}} \Rightarrow f_{2}=-20 \mathrm{cm}$
<br/>(Negative sign for concave lens)</div>


