# questions

tags: ['Physics', 'Alternating Current', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
paragraph-the-capacitor-of-capacitance-c-can-be-charged-with-the-help-of-a-resistance-r-by-a-voltage-source-v-by-closing-switch-s-1-while-keeping-swit-1

slug:
paragraph-the-capacitor-of-capacitance-c-can-be-charged-with-the-help-of-a-resistance-r-by-a-voltage-source-v-by-closing-switch-s-1-while-keeping-swit-1-96412

question:
<div class="question"><strong>Paragraph:</strong><br/>The capacitor of capacitance $C$ can be charged (with the help of a resistance $R$ ) by a voltage source $V$, by closing switch $S_1$ while keeping switch $S_2$ open. The capacitor can be connected in series with an inductor $L$ by closing switch $S_2$ and opening $S_1$.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0Y1I8mvhYVnowTpUifCLeg2xPE10yRn1Ap7tEzxaL24.original.fullsize.png"/><br/><strong>Question:</strong><br/>Initially, the capacitor was uncharged. Now, switch $S_1$ is closed and $S_2$ is kept open. If time constant of this circuit is $\tau$, then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>after time interval $\tau$, charge on the capacitor is $C V / 2$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>after time interval $2 \tau$, charge on the capacitor is $C V /\left(1-e^{-2}\right)$<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">C</span> <span class="option-data"><br/>the work done by the voltage source will be half on the heat dissipated when the capacitor is fully charged<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>after time interval $2 \tau$, charge on the capacitor is $C V\left(1-e^{-1}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>after time interval $2 \tau$, charge on the capacitor is $C V /\left(1-e^{-2}\right)$<br/></span> </div>

answer:
<div class="solution">Charge on capacitor at time $t$ is $q=q_0\left(1-e^{-t / \tau}\right)$<br/>$\begin{array}{ll}\text { Here, } &amp; q_0=C V \text { and } t=2 \tau \\ \therefore &amp; q=C V\left(1-e^{-2 \tau / \tau}\right)=C V\left(1-e^{-2}\right)\end{array}$</div>


tags: ['Physics', 'Alternating Current', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
paragraph-the-capacitor-of-capacitance-c-can-be-charged-with-the-help-of-a-resistance-r-by-a-voltage-source-v-by-closing-switch-s-1-while-keeping-swit-2

slug:
paragraph-the-capacitor-of-capacitance-c-can-be-charged-with-the-help-of-a-resistance-r-by-a-voltage-source-v-by-closing-switch-s-1-while-keeping-swit-2-15669

question:
<div class="question"><strong>Paragraph:</strong><br/>The capacitor of capacitance $C$ can be charged (with the help of a resistance $R$ ) by a voltage source $V$, by closing switch $S_1$ while keeping switch $S_2$ open. The capacitor can be connected in series with an inductor $L$ by closing switch $S_2$ and opening $S_1$.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0Y1I8mvhYVnowTpUifCLeg2xPE10yRn1Ap7tEzxaL24.original.fullsize.png"/><br/><strong>Question:</strong><br/>After the capacitor gets fully charged, $S_1$ is opened and $S_2$ is closed so that the inductor is connected in series with the capacitor. Then,</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>at $t=0$, energy stored in the circuit is purely in the form of magnetic energy<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>at any time $t&gt;0$, current in the circuit is in the same direction<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>at $t&gt;0$, there is no exchange of energy between the inductor and capacitor<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>at any time $t&gt;0$, maximum instantaneous current in the circuit may $V \sqrt{\frac{C}{L}}$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>at any time $t&gt;0$, maximum instantaneous current in the circuit may $V \sqrt{\frac{C}{L}}$</span> </div>

answer:
<div class="solution">From conservation of energy, $\frac{1}{2} L I_{\max }^2=\frac{1}{2} C V^2$<br/>$$<br/>\therefore \quad I_{\max }=V \sqrt{\frac{C}{L}}<br/>$$</div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
paragraph-the-capacitor-of-capacitance-c-can-be-charged-with-the-help-of-a-resistance-r-by-a-voltage-source-v-by-closing-switch-s-1-while-keeping-swit-3

slug:
paragraph-the-capacitor-of-capacitance-c-can-be-charged-with-the-help-of-a-resistance-r-by-a-voltage-source-v-by-closing-switch-s-1-while-keeping-swit-3-91957

question:
<div class="question"><strong>Paragraph:</strong><br/>The capacitor of capacitance $C$ can be charged (with the help of a resistance $R$ ) by a voltage source $V$, by closing switch $S_1$ while keeping switch $S_2$ open. The capacitor can be connected in series with an inductor $L$ by closing switch $S_2$ and opening $S_1$.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0Y1I8mvhYVnowTpUifCLeg2xPE10yRn1Ap7tEzxaL24.original.fullsize.png"/><br/><strong>Question:</strong><br/>Initially, the capacitor was uncharged. Now, switch $S_1$ is closed and $S_2$ is kept open. If time constant of this circuit is $\tau$, then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>after time interval $\tau$, charge on the capacitor is $C V / 2$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>after time interval $2 \tau$, charge on the capacitor is $C V /\left(1-e^{-2}\right)$<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">C</span> <span class="option-data"><br/>the work done by the voltage source will be half on the heat dissipated when the capacitor is fully charged<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>after time interval $2 \tau$, charge on the capacitor is $C V\left(1-e^{-1}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>after time interval $2 \tau$, charge on the capacitor is $C V /\left(1-e^{-2}\right)$<br/></span> </div>

answer:
<div class="solution">Charge on capacitor at time $t$ is $q=q_0\left(1-e^{-t / \tau}\right)$<br/>$\begin{array}{ll}\text { Here, } &amp; q_0=C V \text { and } t=2 \tau \\ \therefore &amp; q=C V\left(1-e^{-2 \tau / \tau}\right)=C V\left(1-e^{-2}\right)\end{array}$</div>


tags: ['Physics', 'Alternating Current', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
paragraph-the-capacitor-of-capacitance-c-can-be-charged-with-the-help-of-a-resistance-r-by-a-voltage-source-v-by-closing-switch-s-1-while-keeping-swit

slug:
paragraph-the-capacitor-of-capacitance-c-can-be-charged-with-the-help-of-a-resistance-r-by-a-voltage-source-v-by-closing-switch-s-1-while-keeping-swit-55687

question:
<div class="question"><strong>Paragraph:</strong><br/>The capacitor of capacitance $C$ can be charged (with the help of a resistance $R$ ) by a voltage source $V$, by closing switch $S_1$ while keeping switch $S_2$ open. The capacitor can be connected in series with an inductor $L$ by closing switch $S_2$ and opening $S_1$.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0Y1I8mvhYVnowTpUifCLeg2xPE10yRn1Ap7tEzxaL24.original.fullsize.png"/><br/><strong>Question:</strong><br/>If the total charge stored in the $L C$ circuit is $Q_0$, then for $t \geq 0$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>the charge on the capacitor is $Q=Q_0 \cos \left(\frac{\pi}{2}+\frac{t}{\sqrt{L C}}\right)$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>the charge on the capacitor is $Q=Q_0 \cos \left(\frac{\pi}{2}-\frac{t}{\sqrt{L C}}\right)$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>the charge on the capacitor is $Q=-L C \frac{d^2 Q}{d t^2}$<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"><br/>the charge on the capacitor is $Q=-\frac{1}{\sqrt{L C}} \frac{d^2 Q}{d t^2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>the charge on the capacitor is $Q=-L C \frac{d^2 Q}{d t^2}$<br/></span> </div>

answer:
<div class="solution">Comparing the LC oscillations with normal SHM, we get<br/>$$<br/>\frac{d^2 Q}{d t^2}=-\omega^2 Q<br/>$$<br/>Here,<br/>$$<br/>\begin{aligned}<br/>\omega^2 &amp; =\frac{1}{L C} \\<br/>Q &amp; =-L C \frac{d^2 Q}{d t^2}<br/>\end{aligned}<br/>$$<br/>$$<br/>\therefore \quad Q=-L C \frac{d^2 Q}{d t^2}<br/>$$</div>


tags: ['Mathematics', 'Hyperbola', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
paragraph-the-circle-x-2-y-2-8-x-0-and-hyperbola-9-x-2-4-y-2-1-intersect-at-the-points-a-and-b-question-equation-of-a-common-tangent-with-positive-slo

slug:
paragraph-the-circle-x-2-y-2-8-x-0-and-hyperbola-9-x-2-4-y-2-1-intersect-at-the-points-a-and-b-question-equation-of-a-common-tangent-with-positive-slo-19992

question:
<div class="question"><strong>Paragraph:</strong><br/>The circle $x^2+y^2-8 x=0$ and hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ intersect at the points $A$ and $B$.<strong>Question:</strong><br/>Equation of a common tangent with positive slope to the circle as well as to the hyperbola is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$2 x-\sqrt{5} y-20=0$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$2 x-\sqrt{5} y+4=0$<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">C</span> <span class="option-data"><br/>$3 x-4 y+8=0$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$4 x-3 y+4=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$2 x-\sqrt{5} y+4=0$<br/></span> </div>

answer:
<div class="solution">Equation of tangent to hyperbola having slope $m$ is<br/>$$<br/>y=m x+\sqrt{9 m^2-4}<br/>$$<br/>Equation of tangent to circle is<br/>$$<br/>y=m(x-4)+\sqrt{16 m^2+16}<br/>$$<br/>Eqs. (i) and (ii) will be identical for $m=\frac{2}{\sqrt{5}}$ satisfy.<br/>$\therefore$ Equation of common tangent is $2 x-\sqrt{5} y+4=0$</div>


tags: ['Mathematics', 'Circle', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
paragraph-the-circle-x-2-y-2-8-x-0-and-hyperbola-9-x-2-4-y-2-1-intersect-at-the-points-a-and-b-question-equation-of-the-circle-with-a-b-as-its-diamete

slug:
paragraph-the-circle-x-2-y-2-8-x-0-and-hyperbola-9-x-2-4-y-2-1-intersect-at-the-points-a-and-b-question-equation-of-the-circle-with-a-b-as-its-diamete-85278

question:
<div class="question"><strong>Paragraph:</strong><br/>The circle $x^2+y^2-8 x=0$ and hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ intersect at the points $A$ and $B$.<strong>Question:</strong><br/>Equation of the circle with $A B$ as its diameter is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$x^2+y^2-12 x+24=0$<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">B</span> <span class="option-data"><br/>$x^2+y^2+12 x+24=0$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$x^2+y^2+24 x-12=0$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$x^2+y^2-24 x-12=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$x^2+y^2-12 x+24=0$<br/></span> </div>

answer:
<div class="solution">The equation of the hyperbola is $\frac{x^2}{9}-\frac{y^2}{4}=1$ and that of circle is<br/>$$<br/>x^2+y^2-8 x=0<br/>$$<br/>For their points of intersection<br/>$$<br/>\frac{x^2}{9}+\frac{x^2-8 x}{4}=1<br/>$$<br/><br/>$$<br/>\begin{array}{ll}<br/>\Rightarrow &amp; 4 x^2+9 x^2-72 x=36 \\<br/>\Rightarrow &amp; 13 x^2-72 x-36=0<br/>\end{array}<br/>$$<br/><br/>$$<br/>\begin{aligned}<br/>&amp; \Rightarrow \quad 13 x^2-78 x+6 x-36=0 \\<br/>&amp; \Rightarrow \quad 13 x(x-6)+6(x-6)=0 \\<br/>&amp; \Rightarrow \quad x=6, x=-\frac{13}{6} \\<br/>&amp; x=-\frac{13}{6} \text { not acceptable } \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/>Now, for $x=6, y=\pm 2 \sqrt{3}$<br/>Required equation is<br/>$$<br/>\begin{aligned}<br/>&amp; (x-6)^2+(y+2 \sqrt{3})(y-2 \sqrt{3})=0 \\<br/>&amp; \Rightarrow \quad x^2-12 x+y^2+24=0 \\<br/>&amp; \Rightarrow \quad x^2+y^2-12 x+24=0<br/>\end{aligned}<br/>$$</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
paragraph-the-concentration-of-potassium-ions-inside-a-biological-cell-is-at-least-twenty-times-higher-than-the-outside-the-resulting-potential-differ-1

slug:
paragraph-the-concentration-of-potassium-ions-inside-a-biological-cell-is-at-least-twenty-times-higher-than-the-outside-the-resulting-potential-differ-1-56820

question:
<div class="question"><strong>Paragraph:</strong><br/>The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in several processes such as transmission of nerve impulses and maintaining the ion balance. A simple model for such a concentration cell involving a metal $\mathrm{M}$ is :<br/>$$<br/>M(s) \mid M^{+}(\alpha q ; 0.05 \text { molar }) \| M^{+}(a q ; 1 \text { molar }) \mid M(s)<br/>$$<br/>For the above electrolytic cell the magnitude of the cell potential $\left|E_{\text {cell }}\right|=70 \mathrm{mV}$.<strong>Question:</strong><br/>For the above cell</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$E_{\text {cell }} &lt; 0 ; \Delta G&gt;0$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$E_{\text {cell }}&gt;0 ; \Delta G &lt; 0$</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"><br/>$E_{\text {cell }} &lt; 0 ; \Delta G^{\circ}&gt;0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$E_{\text {cell }}&gt;0 ; \Delta G^{\circ} &lt; 0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$E_{\text {cell }}&gt;0 ; \Delta G &lt; 0$</span> </div>

answer:
<div class="solution">The given cell is electrolytic concentration cell, So $E_{\text {cell }}^{\circ}=0$<br/>Anode :<br/>$$<br/>\begin{gathered}<br/>M(s) \longrightarrow M^{+}(a q)+e^{-} \\<br/>\text {Cathode }: \quad M^{+}(a q)+e^{-} \longrightarrow M(s) \\<br/>\hline M^{+}(a q) \text { cathode } \rightleftharpoons M^{+}(a q) \text { anode } \\<br/>E_{\text {cell }}=E_{\text {cell }}^{\circ}-\frac{0.0591}{1} \log \frac{\left[M^{+}\right]_{\text {anodic }}}{\left[M^{+}\right]_{\text {cathodic }}} \\<br/>=0-\frac{0.0591}{1} \log \frac{0.05}{1} \\<br/>E_{\text {cell }}=70 \mathrm{mV}(+\text { ve }) \\<br/>\text { Hence, } \Delta G=-n F E_{\text {cell }}=-\text { ve }<br/>\end{gathered}<br/>$$</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
paragraph-the-concentration-of-potassium-ions-inside-a-biological-cell-is-at-least-twenty-times-higher-than-the-outside-the-resulting-potential-differ

slug:
paragraph-the-concentration-of-potassium-ions-inside-a-biological-cell-is-at-least-twenty-times-higher-than-the-outside-the-resulting-potential-differ-54443

question:
<div class="question"><strong>Paragraph:</strong><br/>The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in several processes such as transmission of nerve impulses and maintaining the ion balance. A simple model for such a concentration cell involving a metal $\mathrm{M}$ is :<br/>$$<br/>M(s) \mid M^{+}(\alpha q ; 0.05 \text { molar }) \| M^{+}(a q ; 1 \text { molar }) \mid M(s)<br/>$$<br/>For the above electrolytic cell the magnitude of the cell potential $\left|E_{\text {cell }}\right|=70 \mathrm{mV}$.<strong>Question:</strong><br/>If the $0.05$ molar solution of $M^{+}$is replaced by a $0.0025$ molar $M^{+}$ solution, then the magnitude of the cell potential would be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$35 \mathrm{mV}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$70 \mathrm{mV}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$140 \mathrm{mV}$<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"><br/>$700 \mathrm{mV}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$140 \mathrm{mV}$<br/></span> </div>

answer:
<div class="solution">$E_{\text {cell }}=E_{\text {cell }}^{\circ}-\frac{0.0591}{1} \log \frac{0.0025}{1}$ $E_{\text {cell }}=140 \mathrm{mV}$ Electrochemistry Straight conceptual III</div>


tags: ['Chemistry', 'Coordination Compounds', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-predict-the-magnetic-1

slug:
paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-predict-the-magnetic-1-50011

question:
<div class="question"><strong>Paragraph:</strong><br/>The coordination number of $\mathrm{Ni}^{2+}$ is 4 .<br/>$\mathrm{NiCl}_2+\mathrm{KCN}$ (excess) $\rightarrow A$ (cyano complex)<br/>$\mathrm{NiCl}_2+$ conc. $\mathrm{HCl}$ (excess) $\rightarrow B$ (chloro complex)<strong>Question:</strong><br/>Predict the magnetic nature of $A$ and $B$ are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>both are diamagnetic<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$A$ is diamagnetic and $B$ is paramagnetic with one unpaired electron<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$A$ is diamagnetic and $B$ is paramagnetic with two unpaired electrons<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"><br/>both are paramagnetic</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$A$ is diamagnetic and $B$ is paramagnetic with two unpaired electrons<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/bxniP2faO05oymhcV10_WdIk3gLHeD2fmQyg8NeBIyg.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tnP_t0NK4QmcgilDBfKM3tt5vf6rtViHlqmfSkxpHDE.original.fullsize.png"/><br/><br/>In it unpaired orbital is not present, so it is diamagnetic in character (square planar shape) In chloro complex $\mathrm{K}_2\left[\mathrm{Ni}(\mathrm{Cl})_4\right]$, complex ion is $\left[\mathrm{Ni}^2\left(\mathrm{Cl}_4\right)\right]^{2-}$ and $\mathrm{Ni}$ is present $\mathrm{Ni}^{2+}$ or $\mathrm{Ni}(\mathrm{II})$, so<br/>$$<br/>\mathrm{Ni}^2+=1 s^2, 2 s^2 2 p^6, 3 s^2 3 p^6 3 d^8, 4 s^0<br/>$$<br/>In $\left.\left[\mathrm{Ni}_{\left(\mathrm{Cl}_4\right)}\right)\right]^2$ ion, $\mathrm{Ni}^{2+}$ is present as follows due to weaker ligand character is $\mathrm{Cl}^{-}$ion. $\left(\mathrm{Cl}^{-}\right.$is weak field ligand). So, it is unable to pair up the electron and $\mathrm{Ni}^{2+}$ needs four empty orbitals to accommodate four $\mathrm{Cl}^{-}$ligand. Thus, $\left(\mathrm{NiCl}_4\right)^{2-}$ shows $s p^3$-hybridisation (Tetrahedral shapes)<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/VMTOLX6FBBnXc5tD6S5F5HPhSdWbXV3aR3-3XVqDn38.original.fullsize.png"/><br/><br/>Hence, due to presence of unpaired orbitals, it is paramagnetic in character.</div>


tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-predict-the-magnetic

slug:
paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-predict-the-magnetic-49674

question:
<div class="question"><strong>Paragraph:</strong><br/>The coordination number of $\mathrm{Ni}^{2+}$ is 4 .<br/>$\mathrm{NiCl}_2+\mathrm{KCN}$ (excess) $\rightarrow A$ (cyano complex)<br/>$\mathrm{NiCl}_2+$ conc. $\mathrm{HCl}$ (excess) $\rightarrow B$ (chloro complex)<strong>Question:</strong><br/>Predict the magnetic nature of $A$ and $B$ are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>both are diamagnetic<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$A$ is diamagnetic and $B$ is paramagnetic with one unpaired electron<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$A$ is diamagnetic and $B$ is paramagnetic with two unpaired electrons<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"><br/>both are paramagnetic</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$A$ is diamagnetic and $B$ is paramagnetic with two unpaired electrons<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/bxniP2faO05oymhcV10_WdIk3gLHeD2fmQyg8NeBIyg.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tnP_t0NK4QmcgilDBfKM3tt5vf6rtViHlqmfSkxpHDE.original.fullsize.png"/><br/><br/>In it unpaired orbital is not present, so it is diamagnetic in character (square planar shape) In chloro complex $\mathrm{K}_2\left[\mathrm{Ni}(\mathrm{Cl})_4\right]$, complex ion is $\left[\mathrm{Ni}^2\left(\mathrm{Cl}_4\right)\right]^{2-}$ and $\mathrm{Ni}$ is present $\mathrm{Ni}^{2+}$ or $\mathrm{Ni}(\mathrm{II})$, so<br/>$$<br/>\mathrm{Ni}^2+=1 s^2, 2 s^2 2 p^6, 3 s^2 3 p^6 3 d^8, 4 s^0<br/>$$<br/>In $\left.\left[\mathrm{Ni}_{\left(\mathrm{Cl}_4\right)}\right)\right]^2$ ion, $\mathrm{Ni}^{2+}$ is present as follows due to weaker ligand character is $\mathrm{Cl}^{-}$ion. $\left(\mathrm{Cl}^{-}\right.$is weak field ligand). So, it is unable to pair up the electron and $\mathrm{Ni}^{2+}$ needs four empty orbitals to accommodate four $\mathrm{Cl}^{-}$ligand. Thus, $\left(\mathrm{NiCl}_4\right)^{2-}$ shows $s p^3$-hybridisation (Tetrahedral shapes)<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/VMTOLX6FBBnXc5tD6S5F5HPhSdWbXV3aR3-3XVqDn38.original.fullsize.png"/><br/><br/>Hence, due to presence of unpaired orbitals, it is paramagnetic in character.</div>


tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-the-hybridization-of

slug:
paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-the-hybridization-of-12331

question:
<div class="question"><strong>Paragraph:</strong><br/>The coordination number of $\mathrm{Ni}^{2+}$ is 4 .<br/>$\mathrm{NiCl}_2+\mathrm{KCN}$ (excess) $\rightarrow A$ (cyano complex)<br/>$\mathrm{NiCl}_2+$ conc. $\mathrm{HCl}$ (excess) $\rightarrow B$ (chloro complex)<strong>Question:</strong><br/>The hybridization of $A$ and $B$ are</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$d s p^2, s p^3$<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">B</span> <span class="option-data"><br/>$s p^3, s p^3$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$d s p^2, d s p^2$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$s p^3 d^2, d^2 s p^3$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$d s p^2, s p^3$<br/></span> </div>

answer:
<div class="solution">Hybridisation of $\mathrm{Ni}$ in $\mathrm{K}_2\left[\mathrm{Ni}(\mathrm{CN})_4\right]$ is $d s p^2$ and in $\mathrm{K}_2\left[\mathrm{Ni}^2\left(\mathrm{Cl}_4\right)\right]$ is $s p^3$ (Detail see in question no. 25).</div>


tags: ['Chemistry', 'Coordination Compounds', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-the-iupac-name-of-a--1

slug:
paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-the-iupac-name-of-a-1-52023

question:
<div class="question"><strong>Paragraph:</strong><br/>The coordination number of $\mathrm{Ni}^{2+}$ is 4 .<br/>$\mathrm{NiCl}_2+\mathrm{KCN}$ (excess) $\rightarrow A$ (cyano complex)<br/>$\mathrm{NiCl}_2+$ conc. $\mathrm{HCl}$ (excess) $\rightarrow B$ (chloro complex)<strong>Question:</strong><br/>The IUPAC name of $A$ and $B$ are</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Potassium tetracyanonickelate (II), potassium tetrachloronickelate (II)<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">B</span> <span class="option-data"><br/>Tetracyanopotassiumnickelate (II), tetrorachloropotassiumnickelate (II)<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Tetracyanonickel (II), tetrachloronickel (II)<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Potassium tetracyanonickel (II), potassium tetrachloronickel (II)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Potassium tetracyanonickelate (II), potassium tetrachloronickelate (II)<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Bn02GMAdWZA8GFgxTA7dU8trtiKgKX_w7sLhSq02ZGE.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-the-iupac-name-of-a-

slug:
paragraph-the-coordination-number-of-ni-2-is-4-nicl-2-kcn-excess-a-cyano-complex-nicl-2-conc-hcl-excess-b-chloro-complex-question-the-iupac-name-of-a-87176

question:
<div class="question"><strong>Paragraph:</strong><br/>The coordination number of $\mathrm{Ni}^{2+}$ is 4 .<br/>$\mathrm{NiCl}_2+\mathrm{KCN}$ (excess) $\rightarrow A$ (cyano complex)<br/>$\mathrm{NiCl}_2+$ conc. $\mathrm{HCl}$ (excess) $\rightarrow B$ (chloro complex)<strong>Question:</strong><br/>The IUPAC name of $A$ and $B$ are</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Potassium tetracyanonickelate (II), potassium tetrachloronickelate (II)<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">B</span> <span class="option-data"><br/>Tetracyanopotassiumnickelate (II), tetrorachloropotassiumnickelate (II)<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Tetracyanonickel (II), tetrachloronickel (II)<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Potassium tetracyanonickel (II), potassium tetrachloronickel (II)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Potassium tetracyanonickelate (II), potassium tetrachloronickelate (II)<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Bn02GMAdWZA8GFgxTA7dU8trtiKgKX_w7sLhSq02ZGE.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Ray Optics', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-the-figure-shows-a-surface-x-y-separating-two-transparent-media-medium1-and-medium2-the-lines-ab-and-c-d-represent-wavefronts-of-a-light-wav-1

slug:
paragraph-the-figure-shows-a-surface-x-y-separating-two-transparent-media-medium1-and-medium2-the-lines-ab-and-c-d-represent-wavefronts-of-a-light-wav-1-93050

question:
<div class="question"><strong>Paragraph:</strong><br/>The figure shows a surface $X Y$ separating two transparent media, medium-1 and medium-2. The lines $a b$ and $c d$ represent wavefronts of a light wave travelling in medium-1 and incident on $X Y$. The lines ef and $g h$ represent wavefronts of the light wave in medium-2 after refraction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tm_QoNKNACdV0vkT1URUx9Z9uiV2_apI_Zxl1TkT2TA.original.fullsize.png"/><br/><strong>Question:</strong><br/>Light travels as a</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>parallel beam in each medium<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">B</span> <span class="option-data"><br/>convergent beam in each medium<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>divergent beam in each medium<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>divergent beam in one medium and convergent beam in the other medium</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>parallel beam in each medium<br/></span> </div>

answer:
<div class="solution">Wavefronts are parallel in both media. Therefore, light which is perpendicular to wavefront travels as a parallel beam in each medium. Hence, the correct option is (a).</div>


tags: ['Physics', 'Ray Optics', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-the-figure-shows-a-surface-x-y-separating-two-transparent-media-medium1-and-medium2-the-lines-ab-and-c-d-represent-wavefronts-of-a-light-wav-2

slug:
paragraph-the-figure-shows-a-surface-x-y-separating-two-transparent-media-medium1-and-medium2-the-lines-ab-and-c-d-represent-wavefronts-of-a-light-wav-2-27371

question:
<div class="question"><strong>Paragraph:</strong><br/>The figure shows a surface $X Y$ separating two transparent media, medium-1 and medium-2. The lines $a b$ and $c d$ represent wavefronts of a light wave travelling in medium-1 and incident on $X Y$. The lines ef and $g h$ represent wavefronts of the light wave in medium-2 after refraction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tm_QoNKNACdV0vkT1URUx9Z9uiV2_apI_Zxl1TkT2TA.original.fullsize.png"/><br/><strong>Question:</strong><br/>The phases of the light wave at $c, d, e$ and $f$ are $\phi_c, \phi_d, \phi_e$ and $\phi_f$, respectively. It is given that $\phi_c \neq \phi_f$.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\phi_c$ cannot be equal to $\phi_d$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\phi_d$ can be equal to $\phi_e$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\left(\phi_d-\phi_f\right)$ is equal to $\left(\phi_c-\phi_e\right)$<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"><br/>$\left(\phi_d-\phi_c\right)$ is not equal to $\left(\phi_f-\phi_e\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\left(\phi_d-\phi_f\right)$ is equal to $\left(\phi_c-\phi_e\right)$<br/></span> </div>

answer:
<div class="solution">All points on a wavefront are at the same phase.<br/>$$<br/>\begin{array}{rlrl}<br/>\therefore &amp; \phi_d &amp; =\phi_c \text { and } \phi_f=\phi_e \\<br/>&amp; \therefore &amp; \phi_d-\phi_f &amp; =\phi_c-\phi_e<br/>\end{array}<br/>$$<br/>Hence, the correct option is (c).</div>


tags: ['Physics', 'Ray Optics', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-the-figure-shows-a-surface-x-y-separating-two-transparent-media-medium1-and-medium2-the-lines-ab-and-c-d-represent-wavefronts-of-a-light-wav

slug:
paragraph-the-figure-shows-a-surface-x-y-separating-two-transparent-media-medium1-and-medium2-the-lines-ab-and-c-d-represent-wavefronts-of-a-light-wav-77246

question:
<div class="question"><strong>Paragraph:</strong><br/>The figure shows a surface $X Y$ separating two transparent media, medium-1 and medium-2. The lines $a b$ and $c d$ represent wavefronts of a light wave travelling in medium-1 and incident on $X Y$. The lines ef and $g h$ represent wavefronts of the light wave in medium-2 after refraction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tm_QoNKNACdV0vkT1URUx9Z9uiV2_apI_Zxl1TkT2TA.original.fullsize.png"/><br/><strong>Question:</strong><br/>Speed of light is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>the same in medium-1 and medium-2<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>larger in medium-1 than in medium-2<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">C</span> <span class="option-data"><br/>larger in medium-2 than in medium-1<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>different at $b$ and $d$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>larger in medium-1 than in medium-2<br/></span> </div>

answer:
<div class="solution">In medium-2 wavefront bends away from the normal after refraction. Therefore, ray of light which is perpendicular to wavefront bends towards the normal in medium-2 during refraction. So, medium-2 is denser or its speed in medium-1 is more. Hence, option (b) is correct.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/kmERJkMOW5BgYYxAZ08NF8h5YO7pGDXY_swArSgnZ38.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Structure of Atom', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-the-hydrogenlike-species-li-2-is-in-a-spherically-symmetric-state-s-1-with-one-radial-node-upon-absorbing-light-the-ion-undergoes-transition-1

slug:
paragraph-the-hydrogenlike-species-li-2-is-in-a-spherically-symmetric-state-s-1-with-one-radial-node-upon-absorbing-light-the-ion-undergoes-transition-1-24930

question:
<div class="question"><strong>Paragraph:</strong><br/>The hydrogen-like species $\mathrm{Li}^{2+}$ is in a spherically symmetric state $S_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state $S_2$. The state $S_2$ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.<strong>Question:</strong><br/>The state $S_1$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$1 s$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$2 \mathrm{~s}$<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">C</span> <span class="option-data"><br/>$2 p$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$3 \mathrm{~s}$</span> </li> </ul>

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

answer:
<div class="solution">Given : Hydrogen like species, $\mathrm{Li}^{2+}$<br/>Spherically symmetric state, $S_1 \Rightarrow s$-orbital<br/>$S_1$ has radial node $1 \Rightarrow 2 s \quad$ (No. of radial node $=1=n-l-1$, so $n=2$ ) Species undergoes state $S_2$<br/>$S_2$ has energy equal to the ground state energy of $\mathrm{H}$-atom $=-13.6 \mathrm{eV}$<br/>So, $\quad-13.6=-13.6\left(\frac{3^2}{n^2}\right)$<br/>$n=3$<br/>Again radial node $=1=n-1-1$<br/>or $1=3-l-1 \quad$ so $\quad l=1$<br/>It suggests $S_2$ is $3 p$</div>


tags: ['Chemistry', 'Structure of Atom', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-the-hydrogenlike-species-li-2-is-in-a-spherically-symmetric-state-s-1-with-one-radial-node-upon-absorbing-light-the-ion-undergoes-transition-2

slug:
paragraph-the-hydrogenlike-species-li-2-is-in-a-spherically-symmetric-state-s-1-with-one-radial-node-upon-absorbing-light-the-ion-undergoes-transition-2-78778

question:
<div class="question"><strong>Paragraph:</strong><br/>The hydrogen-like species $\mathrm{Li}^{2+}$ is in a spherically symmetric state $S_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state $S_2$. The state $S_2$ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.<strong>Question:</strong><br/>The orbtial angular momentum quantum number of the state $S_2$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>0<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>1<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">C</span> <span class="option-data"><br/>2<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>3</span> </li> </ul>

answer:
<div class="solution">For $p$-orbital, orbital angular momentum quantum number $=1$ Atomic structure Conceptual data analysis IV</div>


tags: ['Chemistry', 'Structure of Atom', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-the-hydrogenlike-species-li-2-is-in-a-spherically-symmetric-state-s-1-with-one-radial-node-upon-absorbing-light-the-ion-undergoes-transition

slug:
paragraph-the-hydrogenlike-species-li-2-is-in-a-spherically-symmetric-state-s-1-with-one-radial-node-upon-absorbing-light-the-ion-undergoes-transition-53790

question:
<div class="question"><strong>Paragraph:</strong><br/>The hydrogen-like species $\mathrm{Li}^{2+}$ is in a spherically symmetric state $S_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state $S_2$. The state $S_2$ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.<strong>Question:</strong><br/>Energy of the state $S_1$ in units of the hydrogen atom ground state energy is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$0.75$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$1.50$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$2.25$<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"><br/>$4.50$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$2.25$<br/></span> </div>

answer:
<div class="solution">Energy of state, $S_1=-13.6\left(\frac{3^2}{2^2}\right) \mathrm{eV} /$ atom $=\frac{9}{4}$ of energy of $\mathrm{H}$-atom in ground state $=2.25$ of energy of $\mathrm{H}$-atom in ground state</div>


tags: ['Physics', 'Atomic Physics', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-the-key-feature-of-bohrs-theory-of-spectrum-of-hydrogen-atom-is-the-quantization-of-angular-momentum-when-an-electron-is-revolving-around-a--1

slug:
paragraph-the-key-feature-of-bohrs-theory-of-spectrum-of-hydrogen-atom-is-the-quantization-of-angular-momentum-when-an-electron-is-revolving-around-a-1-54595

question:
<div class="question"><strong>Paragraph:</strong><br/>The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.<strong>Question:</strong><br/>In a CO molecule, the distance between $\mathrm{C}$ (mass $=12 \mathrm{amu}$ ) and $\mathrm{O}$ (mass = $16 \mathrm{amu}$ ), where $1 \mathrm{amu}=\frac{5}{3} \times 10^{-27} \mathrm{~kg}$, is close to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$2.4 \times 10^{-10} \mathrm{~m}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$1.9 \times 10^{-10} \mathrm{~m}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$1.3 \times 10^{-10} \mathrm{~m}$<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"><br/>$4.4 \times 10^{-11} \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$1.3 \times 10^{-10} \mathrm{~m}$<br/></span> </div>

answer:
<div class="solution">$I=\mu r^2$ ( where $\mu=$ reduced mass) $\mu=\frac{m_1 m_2}{m_1+m_2}=\frac{48}{7} \mathrm{amu}$ $=11.43 \times 10^{-27} \mathrm{~kg}$<br/>Substituting in $I=\mu r^2$ we get,<br/>$$<br/>\begin{aligned}<br/>r &amp; =\sqrt{\frac{I}{\mu}}=\sqrt{\frac{1.87 \times 10^{-46}}{11.43 \times 10^{-27}}} \\<br/>&amp; =1.28 \times 10^{-10} \mathrm{~m}<br/>\end{aligned}<br/>$$<br/>$\therefore$ The correct answer is (c).</div>


tags: ['Physics', 'Atomic Physics', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-the-key-feature-of-bohrs-theory-of-spectrum-of-hydrogen-atom-is-the-quantization-of-angular-momentum-when-an-electron-is-revolving-around-a--2

slug:
paragraph-the-key-feature-of-bohrs-theory-of-spectrum-of-hydrogen-atom-is-the-quantization-of-angular-momentum-when-an-electron-is-revolving-around-a-2-94332

question:
<div class="question"><strong>Paragraph:</strong><br/>The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.<strong>Question:</strong><br/>It is found that the excitation frequency from ground to the first excited state of rotation for the $\mathrm{CO}$ molecule is close to $\frac{4}{\pi} \times 10^{11} \mathrm{~Hz}$. Then the moment of inertia of CO molecule about its centre of mass is close to (Take $h=2 \pi \times 10^{-34} J-s$ )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$2.76 \times 10^{-46} \mathrm{~kg}-\mathrm{m}^2$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$1.87 \times 10^{-46} \mathrm{~kg}-\mathrm{m}^2$<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">C</span> <span class="option-data"><br/>$4.67 \times 10^{-47} \mathrm{~kg}-\mathrm{m}^2$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$1.17 \times 10^{-47} \mathrm{~kg}-\mathrm{m}^2$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$1.87 \times 10^{-46} \mathrm{~kg}-\mathrm{m}^2$<br/></span> </div>

answer:
<div class="solution">$$<br/>\begin{gathered}<br/>h v=K_2-K_1=\frac{3 h^2}{8 \pi^2 I} \\<br/>\therefore I=\frac{3 h}{8 \pi^2 f}=\frac{3 \times 2 \pi \times 10^{-34} \times \pi}{8 \times \pi^2 \times 4 \times 10^{11}}<br/>\end{gathered}<br/>$$<br/>$$<br/>=1.87 \times 10^{-46} \mathrm{~kg}-\mathrm{m}^2<br/>$$<br/>$\therefore$ The correct answer is (b).</div>


tags: ['Physics', 'Atomic Physics', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-the-key-feature-of-bohrs-theory-of-spectrum-of-hydrogen-atom-is-the-quantization-of-angular-momentum-when-an-electron-is-revolving-around-a-

slug:
paragraph-the-key-feature-of-bohrs-theory-of-spectrum-of-hydrogen-atom-is-the-quantization-of-angular-momentum-when-an-electron-is-revolving-around-a-14575

question:
<div class="question"><strong>Paragraph:</strong><br/>The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.<strong>Question:</strong><br/>A diatomic molecule has moment of inertia I. By Bohr's quantization condition its rotational energy in the $n$th level ( $n=0$ is not allowed) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{1}{n^2}\left(\frac{h^2}{8 \pi^2 I}\right)$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{1}{n}\left(\frac{h^2}{8 \pi^2 I}\right)$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$n\left(\frac{h^2}{8 \pi^2 I}\right)$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$n^2\left(\frac{h^2}{8 \pi^2 I}\right)$</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"><br/>$n^2\left(\frac{h^2}{8 \pi^2 I}\right)$</span> </div>

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>L=I \omega &amp; =\frac{n h}{2 \pi} \therefore \omega=\frac{n h}{2 \pi I} \\<br/>K &amp; =\frac{1}{2} I \omega^2=\frac{1}{2} I\left(\frac{n h}{2 \pi I}\right)^2 \\<br/>&amp; =\frac{n^2 h^2}{8 \pi^2 I}<br/>\end{aligned}<br/>$$<br/>$\therefore$ The correct answer is (d).</div>


source_db: MarksBatch2_P2.db
title:
paragraph-the-noble-gases-have-closedshell-electronic-configuration-and-are-monoatomic-gases-under-normal-conditions-the-low-boiling-points-of-the-lig-1

slug:
paragraph-the-noble-gases-have-closedshell-electronic-configuration-and-are-monoatomic-gases-under-normal-conditions-the-low-boiling-points-of-the-lig-1-76653

question:
<div class="question"><strong>Paragraph:</strong><br/>The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.<br/>The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers $+2,+4$ and $+6 . \mathrm{XeF}_4$ reacts violently with water to give $\mathrm{XeO}_3$. The compounds of xenon exhibit rich stereochemistry and their geometries can be deduced considering the total number of electron pairs in the valence shell.<strong>Question:</strong><br/>Argon is used in are welding because of its</div>

tags:
['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>low reactivity with metal<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">B</span> <span class="option-data"><br/>ability to lower the melting point of metal<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>flammability<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>high calorific value</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>low reactivity with metal<br/></span> </div>

answer:
<div class="solution">Argon is used in arc welding to cause the inert atmosphere around without interaction with metal.</div>


source_db: MarksBatch2_P2.db
title:
paragraph-the-noble-gases-have-closedshell-electronic-configuration-and-are-monoatomic-gases-under-normal-conditions-the-low-boiling-points-of-the-lig-2

slug:
paragraph-the-noble-gases-have-closedshell-electronic-configuration-and-are-monoatomic-gases-under-normal-conditions-the-low-boiling-points-of-the-lig-2-24083

question:
<div class="question"><strong>Paragraph:</strong><br/>The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.<br/>The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers $+2,+4$ and $+6 . \mathrm{XeF}_4$ reacts violently with water to give $\mathrm{XeO}_3$. The compounds of xenon exhibit rich stereochemistry and their geometries can be deduced considering the total number of electron pairs in the valence shell.<strong>Question:</strong><br/>The structure of $\mathrm{XeO}_3$ is</div>

tags:
['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>linear<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>planar<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>pyramidal<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"><br/>$T$-shaped</span> </li> </ul>

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

answer:
<div class="solution">$\mathrm{XeO}_3$ total $e^{-}$pairs $=4(3 p b+1 l p)$ $s p^3$-hybridisation $\Rightarrow$ pyramidal shape.</div>


source_db: MarksBatch2_P2.db
title:
paragraph-the-noble-gases-have-closedshell-electronic-configuration-and-are-monoatomic-gases-under-normal-conditions-the-low-boiling-points-of-the-lig

slug:
paragraph-the-noble-gases-have-closedshell-electronic-configuration-and-are-monoatomic-gases-under-normal-conditions-the-low-boiling-points-of-the-lig-29621

question:
<div class="question"><strong>Paragraph:</strong><br/>The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.<br/>The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers $+2,+4$ and $+6 . \mathrm{XeF}_4$ reacts violently with water to give $\mathrm{XeO}_3$. The compounds of xenon exhibit rich stereochemistry and their geometries can be deduced considering the total number of electron pairs in the valence shell.<strong>Question:</strong><br/>$\mathrm{XeF}_4$ and $\mathrm{XeF}_6$ are expected to be</div>

tags:
['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>oxidising<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">B</span> <span class="option-data"><br/>reducing<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>unreactive<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>strongly basic</span> </li> </ul>

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

answer:
<div class="solution">$\mathrm{XeF}_4$ oxidises potassium iodide<br/>$$<br/>\mathrm{XeF}_4+4 \mathrm{I}^{-} \longrightarrow 2 \mathrm{I}_2+4 \mathrm{~F}^{-1}+\mathrm{Xe}<br/>$$<br/>$\mathrm{XeF}_6$ oxidises hydrogen like other xenon fluorides.</div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-the-nuclear-charge-ze-is-nonuniformly-distributed-within-a-nucleus-of-radius-r-the-charge-density-r-charge-per-unit-volume-is-dependent-only-1

slug:
paragraph-the-nuclear-charge-ze-is-nonuniformly-distributed-within-a-nucleus-of-radius-r-the-charge-density-r-charge-per-unit-volume-is-dependent-only-1-20772

question:
<div class="question"><strong>Paragraph:</strong><br/>The nuclear charge $(\mathrm{Ze})$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho(r)$ [charge per unit volume] is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/jlFKxAkJt_03DKXWqhIFlKSRLGpw3OZjlz0a8gNGa4M.original.fullsize.png"/><br/><strong>Question:</strong><br/>The electric field within the nucleus is generally observed to be linearly dependent on $r$. This implies</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$a=0$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$a=\frac{R}{2}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$a=R$<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"><br/>$a=\frac{2 R}{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$a=R$<br/></span> </div>

answer:
<div class="solution">In case of solid sphere of charge of uniform volume density.<br/>$$<br/>E=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{q}{R^3} \cdot r \text { or } E \propto r<br/>$$<br/>Thus, for $E$ to be linearly dependent on $r$, volume charge density should be constant.<br/>or $\quad a=R$<br/>$\therefore$ correct option is (c).<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/VsVVtDqMKnBK3h17v1qy70Lf_sV00VrHsuOzxggW71w.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-the-nuclear-charge-ze-is-nonuniformly-distributed-within-a-nucleus-of-radius-r-the-charge-density-r-charge-per-unit-volume-is-dependent-only-2

slug:
paragraph-the-nuclear-charge-ze-is-nonuniformly-distributed-within-a-nucleus-of-radius-r-the-charge-density-r-charge-per-unit-volume-is-dependent-only-2-13276

question:
<div class="question"><strong>Paragraph:</strong><br/>The nuclear charge $(\mathrm{Ze})$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho(r)$ [charge per unit volume] is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/jlFKxAkJt_03DKXWqhIFlKSRLGpw3OZjlz0a8gNGa4M.original.fullsize.png"/><br/><strong>Question:</strong><br/>The electric field at $r=R$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>independent of $a$<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">B</span> <span class="option-data"><br/>directly proportional to $a$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>directly proportional to $a^2$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>inversely proportional to $a$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>independent of $a$<br/></span> </div>

answer:
<div class="solution">At $r=R$, from Gauss's law<br/>or<br/>$$<br/>\begin{aligned}<br/>E\left(4 \pi R^2\right) &amp; =\frac{q_{\text {net }}}{\varepsilon_0}=\frac{Z e}{\varepsilon_0} \\<br/>E &amp; =\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e}{R^2}<br/>\end{aligned}<br/>$$<br/>$E$ is independent of ' $a$ '<br/>$\therefore$ correct option is (a).</div>


tags: ['Physics', 'Electrostatics', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
paragraph-the-nuclear-charge-ze-is-nonuniformly-distributed-within-a-nucleus-of-radius-r-the-charge-density-r-charge-per-unit-volume-is-dependent-only-3

slug:
paragraph-the-nuclear-charge-ze-is-nonuniformly-distributed-within-a-nucleus-of-radius-r-the-charge-density-r-charge-per-unit-volume-is-dependent-only-3-17566

question:
<div class="question"><strong>Paragraph:</strong><br/>The nuclear charge $(\mathrm{Ze})$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho(r)$ [charge per unit volume] is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/jlFKxAkJt_03DKXWqhIFlKSRLGpw3OZjlz0a8gNGa4M.original.fullsize.png"/><br/><strong>Question:</strong><br/>The electric field at $r=R$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>independent of $a$<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">B</span> <span class="option-data"><br/>directly proportional to $a$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>directly proportional to $a^2$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>inversely proportional to $a$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>independent of $a$<br/></span> </div>

answer:
<div class="solution">At $r=R$, from Gauss's law<br/>or<br/>$$<br/>\begin{aligned}<br/>E\left(4 \pi R^2\right) &amp; =\frac{q_{\text {net }}}{\varepsilon_0}=\frac{Z e}{\varepsilon_0} \\<br/>E &amp; =\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e}{R^2}<br/>\end{aligned}<br/>$$<br/>$E$ is independent of ' $a$ '<br/>$\therefore$ correct option is (a).</div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-the-nuclear-charge-ze-is-nonuniformly-distributed-within-a-nucleus-of-radius-r-the-charge-density-r-charge-per-unit-volume-is-dependent-only

slug:
paragraph-the-nuclear-charge-ze-is-nonuniformly-distributed-within-a-nucleus-of-radius-r-the-charge-density-r-charge-per-unit-volume-is-dependent-only-69092

question:
<div class="question"><strong>Paragraph:</strong><br/>The nuclear charge $(\mathrm{Ze})$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho(r)$ [charge per unit volume] is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/jlFKxAkJt_03DKXWqhIFlKSRLGpw3OZjlz0a8gNGa4M.original.fullsize.png"/><br/><strong>Question:</strong><br/>For $a=0$, the value of $d$ (maximum value of $\rho$ as shown in the figure) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{3 Z e}{4 \pi R^3}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{3 Z e}{\pi R^3}$<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">C</span> <span class="option-data"><br/>$\frac{4 Z e}{3 \pi R^3}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{Z e}{3 \pi R^3}$</span> </li> </ul>

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

answer:
<div class="solution">For $a=0$<br/>$$<br/>\begin{aligned}<br/>&amp; \rho(r)=\left(-\frac{d}{R} \cdot r+d\right) \\<br/>&amp; \text { Now } \int_0^R\left(4 \pi r^2\right)\left(d-\frac{d}{R} r\right) d r=\text { net charge }=Z e<br/>\end{aligned}<br/>$$<br/>Solving this equation, we get $d=\frac{3 Z e}{\pi R^3}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/LyvPQp1nkAouhegtu45_JVyeZAs0gj3wpNxj90T5ADo.original.fullsize.png"/><br/></div>


tags: ['Mathematics', 'Probability', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
paragraph-there-are-n-urns-each-containing-n-1-balls-such-that-the-ith-urn-contains-i-white-balls-and-n-1-i-red-balls-let-u-i-be-the-event-of-selectin-1

slug:
paragraph-there-are-n-urns-each-containing-n-1-balls-such-that-the-ith-urn-contains-i-white-balls-and-n-1-i-red-balls-let-u-i-be-the-event-of-selectin-1-47960

question:
<div class="question"><strong>Paragraph:</strong><br/>There are $n$ urns each containing $(n+1)$ balls such that the ith urn contains $i$ white balls and $(n+1-i)$ red balls. Let $u_i$ be the event of selecting ith urn, $i=1,2,3, \ldots, n$ and $W$ denotes the event of getting a white balls.<strong>Question:</strong><br/>If $P\left(u_i\right)=c$, where $c$ is a constant, then $P\left(u_i / W\right)$ is equal to</div>

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

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

answer:
<div class="solution">$P\left(\frac{u_i}{W}\right)=\frac{\frac{n}{n+1}}{\frac{\Sigma i}{n+1}}=\frac{2}{n+1}$</div>


tags: ['Mathematics', 'Probability', 'JEE Advanced', 'JEE Advanced 2006']
answer: <div class="solution">$P(W / E)=\frac{2+4+6+\ldots}{\frac{n(n+1)}{2}}=\frac{n+2}{2(n+1)}$</div>
source_db: MarksBatch2_P2.db
title:
paragraph-there-are-n-urns-each-containing-n-1-balls-such-that-the-ith-urn-contains-i-white-balls-and-n-1-i-red-balls-let-u-i-be-the-event-of-selectin-2

slug:
paragraph-there-are-n-urns-each-containing-n-1-balls-such-that-the-ith-urn-contains-i-white-balls-and-n-1-i-red-balls-let-u-i-be-the-event-of-selectin-2-52096

question:
<div class="question"><strong>Paragraph:</strong><br/>There are $n$ urns each containing $(n+1)$ balls such that the ith urn contains $i$ white balls and $(n+1-i)$ red balls. Let $u_i$ be the event of selecting ith urn, $i=1,2,3, \ldots, n$ and $W$ denotes the event of getting a white balls.<strong>Question:</strong><br/>If $n$ is even and $E$ denotes the event of choosing even numbered urn $\left(P\left(u_i\right)=\frac{1}{n}\right)$, then the value of $P(W / E)$ is</div>

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

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


tags: ['Mathematics', 'Probability', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
paragraph-there-are-n-urns-each-containing-n-1-balls-such-that-the-ith-urn-contains-i-white-balls-and-n-1-i-red-balls-let-u-i-be-the-event-of-selectin-3

slug:
paragraph-there-are-n-urns-each-containing-n-1-balls-such-that-the-ith-urn-contains-i-white-balls-and-n-1-i-red-balls-let-u-i-be-the-event-of-selectin-3-47711

question:
<div class="question"><strong>Paragraph:</strong><br/>There are $n$ urns each containing $(n+1)$ balls such that the ith urn contains $i$ white balls and $(n+1-i)$ red balls. Let $u_i$ be the event of selecting ith urn, $i=1,2,3, \ldots, n$ and $W$ denotes the event of getting a white balls.<strong>Question:</strong><br/>If $P\left(u_i\right) \propto i$, where $i=1,2,3, \ldots, n$, then $\lim _{n \rightarrow \infty} P(W)$ is equal to</div>

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

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/P2FXcCfLyF2E7Scmlez396yBvjhkeK-dJUDHezmuJrc.original.fullsize.png"/><br/></div>


tags: ['Mathematics', 'Probability', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
paragraph-there-are-n-urns-each-containing-n-1-balls-such-that-the-ith-urn-contains-i-white-balls-and-n-1-i-red-balls-let-u-i-be-the-event-of-selectin

slug:
paragraph-there-are-n-urns-each-containing-n-1-balls-such-that-the-ith-urn-contains-i-white-balls-and-n-1-i-red-balls-let-u-i-be-the-event-of-selectin-92672

question:
<div class="question"><strong>Paragraph:</strong><br/>There are $n$ urns each containing $(n+1)$ balls such that the ith urn contains $i$ white balls and $(n+1-i)$ red balls. Let $u_i$ be the event of selecting ith urn, $i=1,2,3, \ldots, n$ and $W$ denotes the event of getting a white balls.<strong>Question:</strong><br/>If $P\left(u_i\right) \propto i$, where $i=1,2,3, \ldots, n$, then $\lim _{n \rightarrow \infty} P(W)$ is equal to</div>

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

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/P2FXcCfLyF2E7Scmlez396yBvjhkeK-dJUDHezmuJrc.original.fullsize.png"/><br/></div>


source_db: MarksBatch2_P2.db
title:
paragraph-there-are-some-deposits-of-nitrates-and-phosphates-in-earths-crust-nitrates-are-more-soluble-in-water-nitrates-are-difficult-to-reduce-under-1

slug:
paragraph-there-are-some-deposits-of-nitrates-and-phosphates-in-earths-crust-nitrates-are-more-soluble-in-water-nitrates-are-difficult-to-reduce-under-1-83986

question:
<div class="question"><strong>Paragraph:</strong><br/>There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions. Hybridisation easily explains the ease of sigma donation capability of $\mathrm{NH}_3$ and $\mathrm{PH}_3$. Phosphine is a flammable gas and is prepared from white phosphorus.<strong>Question:</strong><br/>Among the following, the correct statement is</div>

tags:
['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>between $\mathrm{NH}_3$ and $\mathrm{PH}_3, \mathrm{NH}_3$ is a better electron donor because the lone pair of electrons occupies spherical 's' orbital and is less directional<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>between $\mathrm{NH}_3$ and $\mathrm{PH}_3, \mathrm{PH}_3$ is a better electron donor because the lone pair of electrons occupies $\mathrm{sp}^3$ orbital and is more directional<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>between $\mathrm{NH}_3$ and $\mathrm{PH}_3, \mathrm{NH}_3$ is a better electron donor because the lone pair of electrons occupies $\mathrm{sp}^3$ orbital and is more directional<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"><br/>between $\mathrm{NH}_3$ and $\mathrm{PH}_3, \mathrm{PH}_3$ is a better electron donor because the lone pair of electrons occupies spherical ' $s$ ' orbital and is less directional</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>between $\mathrm{NH}_3$ and $\mathrm{PH}_3, \mathrm{NH}_3$ is a better electron donor because the lone pair of electrons occupies $\mathrm{sp}^3$ orbital and is more directional<br/></span> </div>

answer:
<div class="solution">$\mathrm{NH}_3$ is better electron donor because the lone pair of electrons occupies $\mathrm{sp}^3$-orbital and is more directional.</div>


source_db: MarksBatch2_P2.db
title:
paragraph-there-are-some-deposits-of-nitrates-and-phosphates-in-earths-crust-nitrates-are-more-soluble-in-water-nitrates-are-difficult-to-reduce-under-2

slug:
paragraph-there-are-some-deposits-of-nitrates-and-phosphates-in-earths-crust-nitrates-are-more-soluble-in-water-nitrates-are-difficult-to-reduce-under-2-56171

question:
<div class="question"><strong>Paragraph:</strong><br/>There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions. Hybridisation easily explains the ease of sigma donation capability of $\mathrm{NH}_3$ and $\mathrm{PH}_3$. Phosphine is a flammable gas and is prepared from white phosphorus.<strong>Question:</strong><br/>White phosphorus on reaction with $\mathrm{NaOH}$ gives $\mathrm{PH}_3$ as one of the products. This is a</div>

tags:
['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>dimerisation reaction<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>disproportionation reaction<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">C</span> <span class="option-data"><br/>condensation reaction<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>precipitation reaction</span> </li> </ul>

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

answer:
<div class="solution">White phosphorus on reaction with $\mathrm{NaOH}$ gives $\mathrm{PH}_3$ as one of the product in disproportionation reaction<br/>$$<br/>\mathrm{P}_4+3 \mathrm{NaOH}+3 \mathrm{H}_2 \mathrm{O} \longrightarrow 3 \mathrm{NaH}_2 \mathrm{PO}_2+\mathrm{PH}_3<br/>$$</div>


source_db: MarksBatch2_P2.db
title:
paragraph-there-are-some-deposits-of-nitrates-and-phosphates-in-earths-crust-nitrates-are-more-soluble-in-water-nitrates-are-difficult-to-reduce-under

slug:
paragraph-there-are-some-deposits-of-nitrates-and-phosphates-in-earths-crust-nitrates-are-more-soluble-in-water-nitrates-are-difficult-to-reduce-under-16619

question:
<div class="question"><strong>Paragraph:</strong><br/>There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions. Hybridisation easily explains the ease of sigma donation capability of $\mathrm{NH}_3$ and $\mathrm{PH}_3$. Phosphine is a flammable gas and is prepared from white phosphorus.<strong>Question:</strong><br/>Among the following, the correct statement is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>phosphates have no biological significance in humans<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>between nitrates and phosphates, phosphates are less abundant in earth's crust<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>between nitrates and phosphates, nitrates are less abundant in earth's crust<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"><br/>oxidation of nitrates is possible in soil</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>between nitrates and phosphates, nitrates are less abundant in earth's crust<br/></span> </div>

answer:
<div class="solution">Due to greater solubility and nature to be prone to microbial action, nitrates are less abundant in earth's crust.</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
paragraph-tollens-reagent-is-used-for-the-detection-of-aldehyde-when-a-solution-of-agno-3-is-added-to-glucose-with-nh-4-oh-then-gluconic-acid-is-forme-1

slug:
paragraph-tollens-reagent-is-used-for-the-detection-of-aldehyde-when-a-solution-of-agno-3-is-added-to-glucose-with-nh-4-oh-then-gluconic-acid-is-forme-1-55157

question:
<div class="question"><strong>Paragraph:</strong><br/>Tollen's reagent is used for the detection of aldehyde when a solution of $\mathrm{AgNO}_3$ is added to glucose with $\mathrm{NH}_4 \mathrm{OH}$ then gluconic acid is formed<br/>$\begin{array}{rr}\mathrm{Ag}^{+}+e^{-} \rightarrow \mathrm{Ag} &amp; E_{\text {red }}^{\circ}=0.8 \mathrm{~V} \\ \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow \text { Gluconic acid }\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_7\right)+2 \mathrm{H}^{+}+2 e^{-} ; &amp; -E_{\mathrm{red}}^{\circ}=-0.05 \mathrm{~V} \\ \mathrm{Ag}\left(\mathrm{NH}_3\right)_2^{+}+e^{-} \rightarrow \mathrm{Ag}(s)+2 \mathrm{NH}_3 ; &amp; E_{\mathrm{red}}^{\circ}=0.337 \mathrm{~V}\end{array}$<br/>[Use $2.303 \times \frac{R T}{F}=0.0592$ and $\frac{F}{R T}=38.92$ at $298 \mathrm{~K}$ ]<strong>Question:</strong><br/>When ammonia is added to the solution, $\mathrm{pH}$ is raised to 11 . Which half-cell reaction is affected by $\mathrm{pH}$ and by how much?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$E_{\text {oxd }}$ will increase by a factor of $0.65$ from $E_{\text {oxd }}^{\circ}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$E_{\text {oxd }}$ will decrease by a factor of $0.65$ from $E_{\text {oxd }}^{\circ}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$E_{\text {red }}$ will increase by a factor of $0.65$ from $E_{\text {red }}^{\circ}$<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"><br/>$E_{\text {red }}$ will decrease by a factor of $0.65$ from $E_{\text {red }}^{\circ}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$E_{\text {red }}$ will increase by a factor of $0.65$ from $E_{\text {red }}^{\circ}$<br/></span> </div>

answer:
<div class="solution">On increasing concentration of $\mathrm{NH}_3$, the concentration of $\mathrm{H}^{+}$ion decreases, therefore<br/>$$<br/>\begin{aligned}<br/>E_{\mathrm{red}} &amp; =E_{\mathrm{red}}^{\circ}-\frac{0.0592}{n} \log _{10}\left[\mathrm{H}^{+}\right]^2 \\<br/>&amp; =0-\frac{0.0592}{2} \times 2 \log _{10} 10^{-11} \quad\left(\because \mathrm{pH}=11 ; \therefore\left[\mathrm{H}^{+}\right]=10^{-11} \mathrm{M}\right) \\<br/>&amp; =-0.0592 \times 11=0.6512 \mathrm{~V}=0.65 \mathrm{~V}<br/>\end{aligned}<br/>$$<br/>$E_{\text {red }}$ increased by a factor of $0.65$ from $E_{\text {red }}^{\circ}$.</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Advanced', 'JEE Advanced 2006']
answer: <div class="solution">Ammonia has no effect on the standard reduction potential.</div>
source_db: MarksBatch2_P2.db
title:
paragraph-tollens-reagent-is-used-for-the-detection-of-aldehyde-when-a-solution-of-agno-3-is-added-to-glucose-with-nh-4-oh-then-gluconic-acid-is-forme-2

slug:
paragraph-tollens-reagent-is-used-for-the-detection-of-aldehyde-when-a-solution-of-agno-3-is-added-to-glucose-with-nh-4-oh-then-gluconic-acid-is-forme-2-20513

question:
<div class="question"><strong>Paragraph:</strong><br/>Tollen's reagent is used for the detection of aldehyde when a solution of $\mathrm{AgNO}_3$ is added to glucose with $\mathrm{NH}_4 \mathrm{OH}$ then gluconic acid is formed<br/>$\begin{array}{rr}\mathrm{Ag}^{+}+e^{-} \rightarrow \mathrm{Ag} &amp; E_{\text {red }}^{\circ}=0.8 \mathrm{~V} \\ \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow \text { Gluconic acid }\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_7\right)+2 \mathrm{H}^{+}+2 e^{-} ; &amp; -E_{\mathrm{red}}^{\circ}=-0.05 \mathrm{~V} \\ \mathrm{Ag}\left(\mathrm{NH}_3\right)_2^{+}+e^{-} \rightarrow \mathrm{Ag}(s)+2 \mathrm{NH}_3 ; &amp; E_{\mathrm{red}}^{\circ}=0.337 \mathrm{~V}\end{array}$<br/>[Use $2.303 \times \frac{R T}{F}=0.0592$ and $\frac{F}{R T}=38.92$ at $298 \mathrm{~K}$ ]<strong>Question:</strong><br/>Ammonia is always added in this reaction. Which of the following must be incorrect?</div>

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


tags: ['Chemistry', 'Electrochemistry', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
paragraph-tollens-reagent-is-used-for-the-detection-of-aldehyde-when-a-solution-of-agno-3-is-added-to-glucose-with-nh-4-oh-then-gluconic-acid-is-forme

slug:
paragraph-tollens-reagent-is-used-for-the-detection-of-aldehyde-when-a-solution-of-agno-3-is-added-to-glucose-with-nh-4-oh-then-gluconic-acid-is-forme-29027

question:
<div class="question"><strong>Paragraph:</strong><br/>Tollen's reagent is used for the detection of aldehyde when a solution of $\mathrm{AgNO}_3$ is added to glucose with $\mathrm{NH}_4 \mathrm{OH}$ then gluconic acid is formed<br/>$\begin{array}{rr}\mathrm{Ag}^{+}+e^{-} \rightarrow \mathrm{Ag} &amp; E_{\text {red }}^{\circ}=0.8 \mathrm{~V} \\ \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow \text { Gluconic acid }\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_7\right)+2 \mathrm{H}^{+}+2 e^{-} ; &amp; -E_{\mathrm{red}}^{\circ}=-0.05 \mathrm{~V} \\ \mathrm{Ag}\left(\mathrm{NH}_3\right)_2^{+}+e^{-} \rightarrow \mathrm{Ag}(s)+2 \mathrm{NH}_3 ; &amp; E_{\mathrm{red}}^{\circ}=0.337 \mathrm{~V}\end{array}$<br/>[Use $2.303 \times \frac{R T}{F}=0.0592$ and $\frac{F}{R T}=38.92$ at $298 \mathrm{~K}$ ]<strong>Question:</strong><br/>$2 \mathrm{Ag}^{+}+\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow 2 \mathrm{Ag}(\mathrm{s})+\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_4+2 \mathrm{H}^{+}$. Find $\ln \mathrm{K}$ of this reaction.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$66.13$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$58.38$<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">C</span> <span class="option-data"><br/>$28.30$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$46.29$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$58.38$<br/></span> </div>

answer:
<div class="solution">Cell reaction,<br/>(i) $\mathrm{Ag}^{+}+e^{-} \longrightarrow \mathrm{Ag}(\mathrm{s}), E_{\mathrm{red}}^{\circ}=0.8 \mathrm{~V}$<br/>(ii) $\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_7+2 \mathrm{H}^{+}+2 e^{-}, E_{\text {oxid }}=-0.05 \mathrm{~V}$<br/>Hence, for reaction<br/>$$<br/>\begin{aligned}<br/>2 \mathrm{Ag}^{+}+\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} &amp; \longrightarrow 2 \mathrm{Ag}(s)+\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O} 7+2 \mathrm{H}^{+} \\<br/>E_{\text {cell }}^{\circ} &amp; =(0.8-0.05)=0.75 \mathrm{~V} \\<br/>E_{\text {cell }}^{\circ} &amp; =E_{\text {anode }}^{\circ}-E_{\text {cathode }}^{\circ}=[-0.05-(-0.8)]_{\mathrm{V}}<br/>\end{aligned}<br/>$$<br/>On the basis of oxidised electrode potential $=0.75 \mathrm{~V}$<br/>By Nernst equation, $E_{\text {cell }}=E_{\text {cell }}^{\circ}-\frac{2.303 R T}{n F} \log _{10} K$<br/>At equilibrium, $E_{\text {cell }}=0$<br/><br/>$$<br/>\begin{aligned}<br/>E_{\text {cell }}^{\circ} &amp; =\frac{2.303 R T}{n F} \log _{10} K \\<br/>0.75 &amp; =\frac{0.0592}{2} \log _{10} K \\<br/>\log _{10} K &amp; =\frac{2 \times 0.75}{0.0592}=25.33<br/>\end{aligned}<br/>$$<br/>or In $K=2.303 \times \log _{10} K=2.303 \times 25.33=58.35$</div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-two-aliphatic-aldehydes-p-and-q-react-in-the-presence-of-aqueous-k-2-co-3-to-give-compound-r-which-upon-treatment-with-hcn-provides-compound-1

slug:
paragraph-two-aliphatic-aldehydes-p-and-q-react-in-the-presence-of-aqueous-k-2-co-3-to-give-compound-r-which-upon-treatment-with-hcn-provides-compound-1-59304

question:
<div class="question"><strong>Paragraph:</strong><br/>Two aliphatic aldehydes $\mathrm{P}$ and $\mathrm{Q}$ react in the presence of aqueous $\mathrm{K}_2 \mathrm{CO}_3$ to give compound R, which upon treatment with HCN provides compound $\mathrm{S}$. On acidification and heating, S gives the product shown below :<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/fNKC7BRqyIG0XUhPQ9I2Jk7TQZkubA1XHiW9jOv0YY0.original.fullsize.png"/><br/><strong>Question:</strong><br/>$$<br/>\text { The compound } R \text { is }<br/>$$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/u_YwwvUlHeiPhW65xViBpGcBxqt8HU514eXHCbA3geQ.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">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/IDJssAH1ncINmZ5akVkIM_FUNloUGOu8t4BpmySVkyA.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/OGVZ0Fw5frdcrCcs2tsy0DkdyE4HH1ZMpVo4t5yffvY.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Oi9S2vlqWFuLp344kRTeSO0M0ZhRfPe7Noo9mqLWyDE.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/u_YwwvUlHeiPhW65xViBpGcBxqt8HU514eXHCbA3geQ.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ub0i1Roguh0VykvMYjTBnPZBFg5b20aVJPzytT7IND8.original.fullsize.png"/><br/><br/>Some inferences from above data<br/>- $a q \mathrm{~K}_2 \mathrm{CO}_3$ can facilitate aldol condensation to aliphatic aldehydes.<br/>- HCN can lead to cyanohydrin formation<br/>- $\mathrm{H}^{+}, \Delta$ can lead to hydrolysis of cyanide to acid and following esterification. So $S$ is cyanohydrin.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/PSYRzrrQMjFhPEo-HPgMnRsEh0hKBpYpzHThIfd51OA.original.fullsize.png"/><br/><br/>Carbonyl compounds (Aldol condensation) Conceptual reaction and mechanistic understanding IV</div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-two-aliphatic-aldehydes-p-and-q-react-in-the-presence-of-aqueous-k-2-co-3-to-give-compound-r-which-upon-treatment-with-hcn-provides-compound-2

slug:
paragraph-two-aliphatic-aldehydes-p-and-q-react-in-the-presence-of-aqueous-k-2-co-3-to-give-compound-r-which-upon-treatment-with-hcn-provides-compound-2-86714

question:
<div class="question"><strong>Paragraph:</strong><br/>Two aliphatic aldehydes $\mathrm{P}$ and $\mathrm{Q}$ react in the presence of aqueous $\mathrm{K}_2 \mathrm{CO}_3$ to give compound R, which upon treatment with HCN provides compound $\mathrm{S}$. On acidification and heating, S gives the product shown below :<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/fNKC7BRqyIG0XUhPQ9I2Jk7TQZkubA1XHiW9jOv0YY0.original.fullsize.png"/><br/><strong>Question:</strong><br/>The compounds $P$ and $Q$ respectively are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/XY3JBMOyrm-KVvXIZxh5pV6xAvBhHJWZiMIlukGMOKU.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/C2l-Yu0JxplE9MQVK9s1Xi5LEJUy4GkVnyKS90ZuwTA.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">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/NhiFPpUESgSYDDhaq0k91PHm239pKR3rWBeZPstpShM.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ERVwJ12xZZSGOLlgQrDC59mU5Ps2L_8iJbdy6bnzhII.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/C2l-Yu0JxplE9MQVK9s1Xi5LEJUy4GkVnyKS90ZuwTA.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ub0i1Roguh0VykvMYjTBnPZBFg5b20aVJPzytT7IND8.original.fullsize.png"/><br/><br/>Some inferences from above data<br/>- $a q \mathrm{~K}_2 \mathrm{CO}_3$ can facilitate aldol condensation to aliphatic aldehydes.<br/>- HCN can lead to cyanohydrin formation<br/>- $\mathrm{H}^{+}, \Delta$ can lead to hydrolysis of cyanide to acid and following esterification. So $S$ is cyanohydrin.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/PSYRzrrQMjFhPEo-HPgMnRsEh0hKBpYpzHThIfd51OA.original.fullsize.png"/><br/><br/>Carbonyl compounds (Aldol condensation) Conceptual reaction and mechanistic understanding IV</div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
paragraph-two-aliphatic-aldehydes-p-and-q-react-in-the-presence-of-aqueous-k-2-co-3-to-give-compound-r-which-upon-treatment-with-hcn-provides-compound-3

slug:
paragraph-two-aliphatic-aldehydes-p-and-q-react-in-the-presence-of-aqueous-k-2-co-3-to-give-compound-r-which-upon-treatment-with-hcn-provides-compound-3-44304

question:
<div class="question"><strong>Paragraph:</strong><br/>Two aliphatic aldehydes $\mathrm{P}$ and $\mathrm{Q}$ react in the presence of aqueous $\mathrm{K}_2 \mathrm{CO}_3$ to give compound R, which upon treatment with HCN provides compound $\mathrm{S}$. On acidification and heating, S gives the product shown below :<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/fNKC7BRqyIG0XUhPQ9I2Jk7TQZkubA1XHiW9jOv0YY0.original.fullsize.png"/><br/><strong>Question:</strong><br/>The compounds $P$ and $Q$ respectively are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/XY3JBMOyrm-KVvXIZxh5pV6xAvBhHJWZiMIlukGMOKU.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/C2l-Yu0JxplE9MQVK9s1Xi5LEJUy4GkVnyKS90ZuwTA.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">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/NhiFPpUESgSYDDhaq0k91PHm239pKR3rWBeZPstpShM.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ERVwJ12xZZSGOLlgQrDC59mU5Ps2L_8iJbdy6bnzhII.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/C2l-Yu0JxplE9MQVK9s1Xi5LEJUy4GkVnyKS90ZuwTA.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ub0i1Roguh0VykvMYjTBnPZBFg5b20aVJPzytT7IND8.original.fullsize.png"/><br/><br/>Some inferences from above data<br/>- $a q \mathrm{~K}_2 \mathrm{CO}_3$ can facilitate aldol condensation to aliphatic aldehydes.<br/>- HCN can lead to cyanohydrin formation<br/>- $\mathrm{H}^{+}, \Delta$ can lead to hydrolysis of cyanide to acid and following esterification. So $S$ is cyanohydrin.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/PSYRzrrQMjFhPEo-HPgMnRsEh0hKBpYpzHThIfd51OA.original.fullsize.png"/><br/><br/>Carbonyl compounds (Aldol condensation) Conceptual reaction and mechanistic understanding IV</div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-two-aliphatic-aldehydes-p-and-q-react-in-the-presence-of-aqueous-k-2-co-3-to-give-compound-r-which-upon-treatment-with-hcn-provides-compound

slug:
paragraph-two-aliphatic-aldehydes-p-and-q-react-in-the-presence-of-aqueous-k-2-co-3-to-give-compound-r-which-upon-treatment-with-hcn-provides-compound-20074

question:
<div class="question"><strong>Paragraph:</strong><br/>Two aliphatic aldehydes $\mathrm{P}$ and $\mathrm{Q}$ react in the presence of aqueous $\mathrm{K}_2 \mathrm{CO}_3$ to give compound R, which upon treatment with HCN provides compound $\mathrm{S}$. On acidification and heating, S gives the product shown below :<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/fNKC7BRqyIG0XUhPQ9I2Jk7TQZkubA1XHiW9jOv0YY0.original.fullsize.png"/><br/><strong>Question:</strong><br/>$$<br/>\text { The compound } S \text { is }<br/>$$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/W2i03VR1gK7Qr4T_WOKeq3I96FIBBuUvoKm7xKdGK-Y.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/G9_8jzFZqmWKpCzFKUOeW5Xq91B9jKbPMbg518R61nA.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/NT9w7eE3UMktIq93Z5hzvJIxUawkL3QUMAQqX1LGw1c.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tSY6q_dKIG2CrUTQPNiPGtsm3Y8HTl8xyUc0fPfWNek.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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tSY6q_dKIG2CrUTQPNiPGtsm3Y8HTl8xyUc0fPfWNek.original.fullsize.png"/><br/></span> </div>


tags: ['Physics', 'Waves and Sound', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
paragraph-two-plane-harmonic-sound-waves-are-expressed-by-the-equations-y-1-x-t-a-cos-05-x-100-t-y-2-x-t-a-cos-046-x-92-t-a-llp-a-r-am-e-t-ers-a-re-in

slug:
paragraph-two-plane-harmonic-sound-waves-are-expressed-by-the-equations-y-1-x-t-a-cos-05-x-100-t-y-2-x-t-a-cos-046-x-92-t-a-llp-a-r-am-e-t-ers-a-re-in-28172

question:
<div class="question"><strong>Paragraph:</strong><br/>Two plane harmonic sound waves are expressed by the equations.<br/>$$<br/>\begin{aligned}<br/>&amp; y_1(x, t)=A \cos (0.5 \pi x-100 \pi t) \\<br/>&amp; y_2(x, t)=A \cos (0.46 \pi x-92 \pi t)<br/>\end{aligned}<br/>$$<br/>(All parameters are in MKS)<strong>Question:</strong><br/>At $x=0$ how many times the amplitude of $y_1+y_2$ is zero in one second at $x=0$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>192<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>48<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>100<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>96</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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"><br/>96</span> </div>

answer:
<div class="solution">At $x=0, y=y_1+y_2=2 A \cos 96 \pi t \cos 4 \pi t$<br/>Frequency of $\cos (96 \pi t)$ function is $48 \mathrm{~Hz}$ and that of $\cos (4 \pi t)$ function is $2 \mathrm{~Hz}$. In one second cos function becomes zero at $2 f$ times, where $f$ is the frequency. Therefore, first function will become zero at 96 times and the second at 4 times. But second overlaps with first. Hence, net $y$ will become zero 96 times in 1 second.</div>


tags: ['Physics', 'Waves and Sound', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
paragraph-two-plane-harmonic-sound-waves-are-expressed-by-the-equations-y-1-x-t-a-cos-05-x-100-t-y-2-x-t-a-cos-046-x-92-t-all-parameters-are-in-mks-qu-1

slug:
paragraph-two-plane-harmonic-sound-waves-are-expressed-by-the-equations-y-1-x-t-a-cos-05-x-100-t-y-2-x-t-a-cos-046-x-92-t-all-parameters-are-in-mks-qu-1-45282

question:
<div class="question"><strong>Paragraph:</strong><br/>Two plane harmonic sound waves are expressed by the equations.<br/>$$<br/>\begin{aligned}<br/>&amp; y_1(x, t)=A \cos (0.5 \pi x-100 \pi t) \\<br/>&amp; y_2(x, t)=A \cos (0.46 \pi x-92 \pi t)<br/>\end{aligned}<br/>$$<br/>(All parameters are in MKS)<strong>Question:</strong><br/>What is the speed of the sound?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$200 \mathrm{~m} / \mathrm{s}$<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">B</span> <span class="option-data"><br/>$180 \mathrm{~m} / \mathrm{s}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$192 \mathrm{~m} / \mathrm{s}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$96 \mathrm{~m} / \mathrm{s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$200 \mathrm{~m} / \mathrm{s}$<br/></span> </div>

answer:
<div class="solution">Speed of wave $v=\frac{\omega}{R}$ or $\quad v=\frac{100 \pi}{0.5 \pi}$ or $\frac{92 \pi}{0.46 \pi}=200 \mathrm{~m} / \mathrm{s}$</div>


tags: ['Physics', 'Waves and Sound', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
paragraph-two-plane-harmonic-sound-waves-are-expressed-by-the-equations-y-1-x-t-a-cos-05-x-100-t-y-2-x-t-a-cos-046-x-92-t-all-parameters-are-in-mks-qu

slug:
paragraph-two-plane-harmonic-sound-waves-are-expressed-by-the-equations-y-1-x-t-a-cos-05-x-100-t-y-2-x-t-a-cos-046-x-92-t-all-parameters-are-in-mks-qu-65540

question:
<div class="question"><strong>Paragraph:</strong><br/>Two plane harmonic sound waves are expressed by the equations.<br/>$$<br/>\begin{aligned}<br/>&amp; y_1(x, t)=A \cos (0.5 \pi x-100 \pi t) \\<br/>&amp; y_2(x, t)=A \cos (0.46 \pi x-92 \pi t)<br/>\end{aligned}<br/>$$<br/>(All parameters are in MKS)<strong>Question:</strong><br/>How many times does an observer hear maximum intensity in one second?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>4<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">B</span> <span class="option-data"><br/>10<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>6<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>8</span> </li> </ul>

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

answer:
<div class="solution">In one second number of maximas is called the beat frequency. Hence,<br/>$$<br/>f_b=f_1-f_2=\frac{100 \pi}{2 \pi}-\frac{92 \pi}{2 \pi}=4 \mathrm{~Hz}<br/>$$</div>


tags: ['Physics', 'Waves and Sound', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-two-trains-a-and-b-are-moving-with-speeds-20-m-s-and-30-m-s-respectively-in-the-same-direction-on-the-same-straight-track-with-b-ahead-of-a--1

slug:
paragraph-two-trains-a-and-b-are-moving-with-speeds-20-m-s-and-30-m-s-respectively-in-the-same-direction-on-the-same-straight-track-with-b-ahead-of-a-1-10007

question:
<div class="question"><strong>Paragraph:</strong><br/>Two trains $A$ and $B$ are moving with speeds $20 \mathrm{~m} / \mathrm{s}$ and $30 \mathrm{~m} / \mathrm{s}$, respectively in the same direction on the same straight track, with $B$ ahead of $A$. The engines are at the front ends. The engine of train $A$ blows a long whistle.<br/>Assume that the sound of the whistle is composed of components varying in frequency from $f_1=800 \mathrm{~Hz}$ to $f_2=1120 \mathrm{~Hz}$, as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus $320 \mathrm{~Hz}$. The speed of sound in still air is $340 \mathrm{~m} / \mathrm{s}$.<strong>Question:</strong><br/>The speed of sound of the whistle is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$340 \mathrm{~m} / \mathrm{s}$ for passengers in $A$ and $310 \mathrm{~m} / \mathrm{s}$ for passengers in $B$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$360 \mathrm{~m} / \mathrm{s}$ for passengers in $A$ and $310 \mathrm{~m} / \mathrm{s}$ for passengers in $B$<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">C</span> <span class="option-data"><br/>$310 \mathrm{~m} / \mathrm{s}$ for passengers in $A$ and $360 \mathrm{~m} / \mathrm{s}$ for passengers in $B$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$340 \mathrm{~m} / \mathrm{s}$ for passengers in both the trains</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$360 \mathrm{~m} / \mathrm{s}$ for passengers in $A$ and $310 \mathrm{~m} / \mathrm{s}$ for passengers in $B$<br/></span> </div>

answer:
<div class="solution">$v_{S A}=340+20=360 \mathrm{~m} / \mathrm{s}$ $v_{S B}=340-30=310 \mathrm{~m} / \mathrm{s}$<br/>Therefore, correct option is (b).</div>


tags: ['Physics', 'Waves and Sound', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-two-trains-a-and-b-are-moving-with-speeds-20-m-s-and-30-m-s-respectively-in-the-same-direction-on-the-same-straight-track-with-b-ahead-of-a--2

slug:
paragraph-two-trains-a-and-b-are-moving-with-speeds-20-m-s-and-30-m-s-respectively-in-the-same-direction-on-the-same-straight-track-with-b-ahead-of-a-2-92256

question:
<div class="question"><strong>Paragraph:</strong><br/>Two trains $A$ and $B$ are moving with speeds $20 \mathrm{~m} / \mathrm{s}$ and $30 \mathrm{~m} / \mathrm{s}$, respectively in the same direction on the same straight track, with $B$ ahead of $A$. The engines are at the front ends. The engine of train $A$ blows a long whistle.<br/>Assume that the sound of the whistle is composed of components varying in frequency from $f_1=800 \mathrm{~Hz}$ to $f_2=1120 \mathrm{~Hz}$, as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus $320 \mathrm{~Hz}$. The speed of sound in still air is $340 \mathrm{~m} / \mathrm{s}$.<strong>Question:</strong><br/>The spread of frequency as observed by the passengers in train $B$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$310 \mathrm{~Hz}$<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">B</span> <span class="option-data"><br/>$330 \mathrm{~Hz}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$350 \mathrm{~Hz}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$290 \mathrm{~Hz}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$310 \mathrm{~Hz}$<br/></span> </div>

answer:
<div class="solution">For the passengers in train $B$, observer is receding with velocity $30 \mathrm{~m} / \mathrm{s}$ and source is approaching with velocity $20 \mathrm{~m} / \mathrm{s}$.<br/>$$<br/>\begin{array}{ll}<br/>\therefore &amp; f_1^{\prime}=800\left(\frac{340-30}{340-20}\right)=775 \mathrm{~Hz} \\<br/>\text { and } &amp; f_2^{\prime}=1120\left(\frac{340-30}{340-20}\right)=1085 \mathrm{~Hz}<br/>\end{array}<br/>$$<br/>$\therefore$ Spread of frequency $=f_2^{\prime}-f_1^{\prime}=310 \mathrm{~Hz}$<br/>$\therefore$ The correct option is (a).</div>


tags: ['Physics', 'Waves and Sound', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-two-trains-a-and-b-are-moving-with-speeds-20-m-s-and-30-m-s-respectively-in-the-same-direction-on-the-same-straight-track-with-b-ahead-of-a-

slug:
paragraph-two-trains-a-and-b-are-moving-with-speeds-20-m-s-and-30-m-s-respectively-in-the-same-direction-on-the-same-straight-track-with-b-ahead-of-a-32716

question:
<div class="question"><strong>Paragraph:</strong><br/>Two trains $A$ and $B$ are moving with speeds $20 \mathrm{~m} / \mathrm{s}$ and $30 \mathrm{~m} / \mathrm{s}$, respectively in the same direction on the same straight track, with $B$ ahead of $A$. The engines are at the front ends. The engine of train $A$ blows a long whistle.<br/>Assume that the sound of the whistle is composed of components varying in frequency from $f_1=800 \mathrm{~Hz}$ to $f_2=1120 \mathrm{~Hz}$, as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus $320 \mathrm{~Hz}$. The speed of sound in still air is $340 \mathrm{~m} / \mathrm{s}$.<strong>Question:</strong><br/>The distribution of the sound intensity of the whistle as observed by the passengers in train $A$ is best represented by</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/wuRCJ2p_bfYdDJSOFw6Xk5oB-j7w1f8xArEYG8U5Uu4.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">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ktxPSlK8a2B-ksEERi-lD0bu5uxiJe879x73_NGcvEM.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/DnDjD3b9B_OXJDBIUUi6oUxY0Zg3nn-sBM89IXlnNVk.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/E-mFj8r40_dvAtzRiOOOAim0H1RWUHeOZYo95ZfPIjE.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/wuRCJ2p_bfYdDJSOFw6Xk5oB-j7w1f8xArEYG8U5Uu4.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">For the passengers in train $A$, there is no relative motion between source and observe, as both are moving with velocity $20 \mathrm{~m} / \mathrm{s}$. Therefore, there is no change in observed frequencies and correspondingly there is no change in their intensities. Therefore, the correct option is (a).</div>


tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
paragraph-when-a-metal-rod-m-is-dipped-into-an-aqueous-colourless-concentrated-solution-of-compound-n-the-solution-turns-light-blue-addition-of-aqueou-1

slug:
paragraph-when-a-metal-rod-m-is-dipped-into-an-aqueous-colourless-concentrated-solution-of-compound-n-the-solution-turns-light-blue-addition-of-aqueou-1-34879

question:
<div class="question"><strong>Paragraph:</strong><br/>When a metal rod $M$ is dipped into an aqueous colourless concentrated solution of compound $\mathrm{N}$, the solution turns light blue. Addition of aqueous $\mathrm{NaCl}$ to the blue solution gives a white precipitate $\mathrm{O}$. Addition of aqueous $\mathrm{NH}_3$ dissolves $\mathrm{O}$ and gives an intense blue solution.<strong>Question:</strong><br/>The final solution contains</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\left[\mathrm{Pb}\left(\mathrm{NH}_3\right)_4\right]^{2+}$ and $\left[\mathrm{CoCl}_4\right]^{2-}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\left[\mathrm{Al}\left(\mathrm{NH}_3\right)_4\right]^{3+}$ and $\left[\mathrm{Cu}\left(\mathrm{NH}_3\right)_4\right]^{2+}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}$and $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4\right]^{2+}$<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"><br/>$\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}$and $\left[\mathrm{Ni}\left(\mathrm{NH}_3\right)_6\right]^{2+}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}$and $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4\right]^{2+}$<br/></span> </div>

answer:
<div class="solution">Since in the beginning, concentrated $\mathrm{AgNO}_3$ solution was taken, some $\mathrm{AgNO}_3$ remain in solution which gives white precipitate of $\mathrm{AgCl}$ on addition of $\mathrm{NaCl}$. The precipitate finally dissolve in ammonia and $\mathrm{Cu}^{2+}$ present in solution also forms complex with ammonia as<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0KiXv4U06vNW5FbrV5m7CUN62IIheDXOxWz1mqF3Bng.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'd and f Block Elements', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
paragraph-when-a-metal-rod-m-is-dipped-into-an-aqueous-colourless-concentrated-solution-of-compound-n-the-solution-turns-light-blue-addition-of-aqueou-2

slug:
paragraph-when-a-metal-rod-m-is-dipped-into-an-aqueous-colourless-concentrated-solution-of-compound-n-the-solution-turns-light-blue-addition-of-aqueou-2-30486

question:
<div class="question"><strong>Paragraph:</strong><br/>When a metal rod $M$ is dipped into an aqueous colourless concentrated solution of compound $\mathrm{N}$, the solution turns light blue. Addition of aqueous $\mathrm{NaCl}$ to the blue solution gives a white precipitate $\mathrm{O}$. Addition of aqueous $\mathrm{NH}_3$ dissolves $\mathrm{O}$ and gives an intense blue solution.<strong>Question:</strong><br/>The metal $\operatorname{rod} M$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{Fe}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{Cu}$<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">C</span> <span class="option-data"><br/>$\mathrm{Ni}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{Co}$</span> </li> </ul>

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

answer:
<div class="solution">Appearance of blue colour on addition of the metal rod $M$ to the solution of $N$ is an indication that metal may be $\mathrm{Cu}$. Later formation of white precipitate on addition of $\mathrm{NaCl}$ and dissolution of this precipitate in aqueous ammonia confirm that while preipitate is of $\mathrm{AgCl}$. This implies that the solution $N$ is of $\mathrm{AgNO}_3$. This confirm that the metal $M$ is only $\mathrm{Cu}$.</div>


tags: ['Chemistry', 'Coordination Compounds', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
paragraph-when-a-metal-rod-m-is-dipped-into-an-aqueous-colourless-concentrated-solution-of-compound-n-the-solution-turns-light-blue-addition-of-aqueou-4

slug:
paragraph-when-a-metal-rod-m-is-dipped-into-an-aqueous-colourless-concentrated-solution-of-compound-n-the-solution-turns-light-blue-addition-of-aqueou-4-63949

question:
<div class="question"><strong>Paragraph:</strong><br/>When a metal rod $M$ is dipped into an aqueous colourless concentrated solution of compound $\mathrm{N}$, the solution turns light blue. Addition of aqueous $\mathrm{NaCl}$ to the blue solution gives a white precipitate $\mathrm{O}$. Addition of aqueous $\mathrm{NH}_3$ dissolves $\mathrm{O}$ and gives an intense blue solution.<strong>Question:</strong><br/>The final solution contains</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\left[\mathrm{Pb}\left(\mathrm{NH}_3\right)_4\right]^{2+}$ and $\left[\mathrm{CoCl}_4\right]^{2-}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\left[\mathrm{Al}\left(\mathrm{NH}_3\right)_4\right]^{3+}$ and $\left[\mathrm{Cu}\left(\mathrm{NH}_3\right)_4\right]^{2+}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}$and $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4\right]^{2+}$<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"><br/>$\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}$and $\left[\mathrm{Ni}\left(\mathrm{NH}_3\right)_6\right]^{2+}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}$and $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4\right]^{2+}$<br/></span> </div>

answer:
<div class="solution">Since in the beginning, concentrated $\mathrm{AgNO}_3$ solution was taken, some $\mathrm{AgNO}_3$ remain in solution which gives white precipitate of $\mathrm{AgCl}$ on addition of $\mathrm{NaCl}$. The precipitate finally dissolve in ammonia and $\mathrm{Cu}^{2+}$ present in solution also forms complex with ammonia as<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0KiXv4U06vNW5FbrV5m7CUN62IIheDXOxWz1mqF3Bng.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'd and f Block Elements', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
answer: <div class="solution">The compound $N$ is $\mathrm{AgNO}_3$, explained above.</div>
source_db: MarksBatch2_P2.db
title:
paragraph-when-a-metal-rod-m-is-dipped-into-an-aqueous-colourless-concentrated-solution-of-compound-n-the-solution-turns-light-blue-addition-of-aqueou

slug:
paragraph-when-a-metal-rod-m-is-dipped-into-an-aqueous-colourless-concentrated-solution-of-compound-n-the-solution-turns-light-blue-addition-of-aqueou-34765

question:
<div class="question"><strong>Paragraph:</strong><br/>When a metal rod $M$ is dipped into an aqueous colourless concentrated solution of compound $\mathrm{N}$, the solution turns light blue. Addition of aqueous $\mathrm{NaCl}$ to the blue solution gives a white precipitate $\mathrm{O}$. Addition of aqueous $\mathrm{NH}_3$ dissolves $\mathrm{O}$ and gives an intense blue solution.<strong>Question:</strong><br/>The compound $N$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{AgNO}_3$<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">B</span> <span class="option-data"><br/>$\mathrm{Zn}\left(\mathrm{NO}_3\right)_2$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{Al}\left(\mathrm{NO}_3\right)_3$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{Pb}\left(\mathrm{NO}_3\right)_2$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{AgNO}_3$<br/></span> </div>


tags: ['Physics', 'Atomic Physics', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
answer: <div class="solution">From Eq. (i)</div>
source_db: MarksBatch2_P2.db
title:
paragraph-when-a-particle-is-restricted-to-move-along-x-axis-between-x-0-and-x-a-where-a-is-of-nanometer-dimension-its-energy-can-take-only-certain-sp-1

slug:
paragraph-when-a-particle-is-restricted-to-move-along-x-axis-between-x-0-and-x-a-where-a-is-of-nanometer-dimension-its-energy-can-take-only-certain-sp-1-88449

question:
<div class="question"><strong>Paragraph:</strong><br/>When a particle is restricted to move along $x$-axis between $x=0$ and $x=a$, where $a$ is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends $x=0$ and $x=a$. The wavelength of this standing wave is related to the liner momentum $p$ of the particle according to the de Broglie relation. The energy of the particle of mass $m$ is related to its linear momentum as $E=\frac{p^2}{2 m}$. Thus, the energy of the particle can be denoted by a quantum number $n$ taking values $1,2,3, \ldots(n=1$, called the ground state) corresponding to the number of loops in the standing wave.<br/>Use the model described above to answer the following three questions for a particle moving in the line $x=0$ to $x=a$ [Take $h=6.6 \times 10^{-34} \mathrm{Js}$ and $e=1.6 \times 10^{-19} \mathrm{C}$ ]<strong>Question:</strong><br/>The speed of the particle that can take discrete values is proportional to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$n^{-3 / 2}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$n^{-1}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$n^{1 / 2}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$n$</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"><br/>$n$</span> </div>


tags: ['Physics', 'Atomic Physics', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
paragraph-when-a-particle-is-restricted-to-move-along-x-axis-between-x-0-and-x-a-where-a-is-of-nanometer-dimension-its-energy-can-take-only-certain-sp-2

slug:
paragraph-when-a-particle-is-restricted-to-move-along-x-axis-between-x-0-and-x-a-where-a-is-of-nanometer-dimension-its-energy-can-take-only-certain-sp-2-46006

question:
<div class="question"><strong>Paragraph:</strong><br/>When a particle is restricted to move along $x$-axis between $x=0$ and $x=a$, where $a$ is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends $x=0$ and $x=a$. The wavelength of this standing wave is related to the liner momentum $p$ of the particle according to the de Broglie relation. The energy of the particle of mass $m$ is related to its linear momentum as $E=\frac{p^2}{2 m}$. Thus, the energy of the particle can be denoted by a quantum number $n$ taking values $1,2,3, \ldots(n=1$, called the ground state) corresponding to the number of loops in the standing wave.<br/>Use the model described above to answer the following three questions for a particle moving in the line $x=0$ to $x=a$ [Take $h=6.6 \times 10^{-34} \mathrm{Js}$ and $e=1.6 \times 10^{-19} \mathrm{C}$ ]<strong>Question:</strong><br/>The allowed energy for the particle for a particular value of $n$ is proportional to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$a^{-2}$<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">B</span> <span class="option-data"><br/>$a^{-3 / 2}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$a^{-1}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$a^2$</span> </li> </ul>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/-S8_dG1o737Zw4q1aXyRbIfCMhQCFP25n8zQXUG9Y3s.original.fullsize.png"/><br/><br/>$$<br/>\begin{array}{rlrl} <br/>&amp; a &amp; =\frac{n \lambda}{2} \\<br/>\therefore &amp; \lambda &amp; =\frac{2 a}{n}=\frac{h}{p}=\frac{h}{\sqrt{2 E m}} \\<br/>\text { or } &amp; \sqrt{E} \propto \frac{1}{a} \Rightarrow E \propto \frac{1}{a^2}<br/>\end{array}<br/>$$</div>


tags: ['Physics', 'Atomic Physics', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
paragraph-when-a-particle-is-restricted-to-move-along-x-axis-between-x-0-and-x-a-where-a-is-of-nanometer-dimension-its-energy-can-take-only-certain-sp

slug:
paragraph-when-a-particle-is-restricted-to-move-along-x-axis-between-x-0-and-x-a-where-a-is-of-nanometer-dimension-its-energy-can-take-only-certain-sp-37614

question:
<div class="question"><strong>Paragraph:</strong><br/>When a particle is restricted to move along $x$-axis between $x=0$ and $x=a$, where $a$ is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends $x=0$ and $x=a$. The wavelength of this standing wave is related to the liner momentum $p$ of the particle according to the de Broglie relation. The energy of the particle of mass $m$ is related to its linear momentum as $E=\frac{p^2}{2 m}$. Thus, the energy of the particle can be denoted by a quantum number $n$ taking values $1,2,3, \ldots(n=1$, called the ground state) corresponding to the number of loops in the standing wave.<br/>Use the model described above to answer the following three questions for a particle moving in the line $x=0$ to $x=a$ [Take $h=6.6 \times 10^{-34} \mathrm{Js}$ and $e=1.6 \times 10^{-19} \mathrm{C}$ ]<strong>Question:</strong><br/>If the mass of the particle is $m=1.0 \times 10^{-30} \mathrm{~kg}$ and $a=6.6 \mathrm{~nm}$, the energy of the particle in its ground state is closest to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$0.8 \mathrm{meV}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$8 \mathrm{meV}$<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">C</span> <span class="option-data"><br/>$80 \mathrm{meV}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$800 \mathrm{meV}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$8 \mathrm{meV}$<br/></span> </div>

answer:
<div class="solution">From Eq. (i)<br/>$$<br/>E=\frac{n^2 h^2}{8 a^2 m}<br/>$$<br/>In ground state $n=1$<br/>$$<br/>\therefore \quad E_1=\frac{h^2}{8 m a^2}<br/>$$<br/>Substituting the values, we get<br/>$$<br/>E_1=8 \mathrm{meV}<br/>$$</div>


tags: ['Physics', 'Oscillations', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
paragraph-when-a-particle-of-mass-m-moves-on-the-x-axis-in-a-potential-of-the-form-v-x-k-x-2-it-performs-simple-harmonic-motion-the-corresponding-time-1

slug:
paragraph-when-a-particle-of-mass-m-moves-on-the-x-axis-in-a-potential-of-the-form-v-x-k-x-2-it-performs-simple-harmonic-motion-the-corresponding-time-1-75147

question:
<div class="question"><strong>Paragraph:</strong><br/>When a particle of mass $m$ moves on the $x$-axis in a potential of the form $V(x)=k x^2$, it performs simple harmonic motion.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/JO88T86U1WBTz3r9tZnSSGCHdiXBMHNTHb4YYwVukEs.original.fullsize.png"/><br/><br/>The corresponding time period is proportional to $\sqrt{\frac{m}{k}}$, as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of $x=0$ in a way different from $k x^2$ and its total energy is such that the particle does not escape to infinity. Consider a particle of mass $\mathrm{m}$ moving on the $x$-axis. Its potential energy is $V(x)=\alpha x^4(\alpha&gt;0)$ for $|x|$ near the origin and becomes a constant equal to $V_0$ for $|x| \geq X_0$ (see figure).<strong>Question:</strong><br/>For periodic motion of small amplitude $A$, the time period $T$ of this particle is proportional to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$A \sqrt{\frac{m}{\alpha}}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{1}{A} \sqrt{\frac{m}{\alpha}}$<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">C</span> <span class="option-data"><br/>$A \sqrt{\frac{\alpha}{m}}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{1}{A} \sqrt{\frac{\alpha}{m}}$</span> </li> </ul>

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

answer:
<div class="solution">$[\alpha]=\left[\frac{\mathrm{PE}}{x^4}\right]=\left[\frac{\mathrm{ML}^2 \mathrm{~T}^{-2}}{\mathrm{~L}^4}\right]=\left[\mathrm{ML}^{-2} \mathrm{~T}^{-2}\right]$<br/>$$<br/>\begin{array}{ll}<br/>\therefore &amp; {\left[\frac{m}{\alpha}\right]=\left[\mathrm{L}^2 \mathrm{~T}^2\right]} \\<br/>\therefore &amp; {\left[\frac{1}{A} \sqrt{\frac{m}{\alpha}}\right]=[\mathrm{T}]}<br/>\end{array}<br/>$$<br/>As dimensions of amplitude $A$ is [L].<br/>Hence, the correct option is (b).</div>


tags: ['Physics', 'Oscillations', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
paragraph-when-a-particle-of-mass-m-moves-on-the-x-axis-in-a-potential-of-the-form-v-x-k-x-2-it-performs-simple-harmonic-motion-the-corresponding-time-2

slug:
paragraph-when-a-particle-of-mass-m-moves-on-the-x-axis-in-a-potential-of-the-form-v-x-k-x-2-it-performs-simple-harmonic-motion-the-corresponding-time-2-95759

question:
<div class="question"><strong>Paragraph:</strong><br/>When a particle of mass $m$ moves on the $x$-axis in a potential of the form $V(x)=k x^2$, it performs simple harmonic motion.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/JO88T86U1WBTz3r9tZnSSGCHdiXBMHNTHb4YYwVukEs.original.fullsize.png"/><br/><br/>The corresponding time period is proportional to $\sqrt{\frac{m}{k}}$, as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of $x=0$ in a way different from $k x^2$ and its total energy is such that the particle does not escape to infinity. Consider a particle of mass $\mathrm{m}$ moving on the $x$-axis. Its potential energy is $V(x)=\alpha x^4(\alpha&gt;0)$ for $|x|$ near the origin and becomes a constant equal to $V_0$ for $|x| \geq X_0$ (see figure).<strong>Question:</strong><br/>The acceleration of this particle for $|x|&gt;X_0$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>proportional to $V_0$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>proportional to $\frac{V_0}{m X_0}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>proportional to $\sqrt{\frac{V_0}{m X_0}}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>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>

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

answer:
<div class="solution">For $|x|&gt;X_0$, potential energy is constant. Hence, kinetic energy, speed or velocity will also remain constant.<br/>$\therefore$ Acceleration will be zero.<br/>Hence, the correct option is (d).</div>


tags: ['Physics', 'Oscillations', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
paragraph-when-a-particle-of-mass-m-moves-on-the-x-axis-in-a-potential-of-the-form-v-x-k-x-2-it-performs-simple-harmonic-motion-the-corresponding-time

slug:
paragraph-when-a-particle-of-mass-m-moves-on-the-x-axis-in-a-potential-of-the-form-v-x-k-x-2-it-performs-simple-harmonic-motion-the-corresponding-time-83784

question:
<div class="question"><strong>Paragraph:</strong><br/>When a particle of mass $m$ moves on the $x$-axis in a potential of the form $V(x)=k x^2$, it performs simple harmonic motion.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/JO88T86U1WBTz3r9tZnSSGCHdiXBMHNTHb4YYwVukEs.original.fullsize.png"/><br/><br/>The corresponding time period is proportional to $\sqrt{\frac{m}{k}}$, as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of $x=0$ in a way different from $k x^2$ and its total energy is such that the particle does not escape to infinity. Consider a particle of mass $\mathrm{m}$ moving on the $x$-axis. Its potential energy is $V(x)=\alpha x^4(\alpha&gt;0)$ for $|x|$ near the origin and becomes a constant equal to $V_0$ for $|x| \geq X_0$ (see figure).<strong>Question:</strong><br/>If the total energy of the particle is $E$, it will perform periodic motion only if</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$E &lt; 0$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$E&gt;0$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$V_0&gt;E&gt;0$<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"><br/>$E&gt;V_0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$V_0&gt;E&gt;0$<br/></span> </div>

answer:
<div class="solution">If $E&gt;V_0$, particle will escape. But simultaneously for oscillations, $E&gt;0$. Hence, the correct answer is $V_0&gt;E&gt;0$ or the correct option is (c).</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-when-liquid-medicine-of-density-is-to-be-put-in-the-eye-it-is-done-with-the-help-of-a-dropper-as-the-bulb-on-the-top-of-the-dropper-is-press-1

slug:
paragraph-when-liquid-medicine-of-density-is-to-be-put-in-the-eye-it-is-done-with-the-help-of-a-dropper-as-the-bulb-on-the-top-of-the-dropper-is-press-1-70142

question:
<div class="question"><strong>Paragraph:</strong><br/>When liquid medicine of density $\rho$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop.<br/>We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension $T$ when the radius of the drop is $R$. When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.<strong>Question:</strong><br/>If $r=5 \times 10^{-4} \mathrm{~m}, \rho=10^3 \mathrm{~kg} \mathrm{~m}^{-3}$, $g=10 \mathrm{~ms}^{-2}, T=0.11 \mathrm{Nm}^{-1}$, the radius of the drop when it detaches from the dropper is approximately</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$1.4 \times 10^{-3} \mathrm{~m}$<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">B</span> <span class="option-data"><br/>$3.3 \times 10^{-3} \mathrm{~m}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$2.0 \times 10^{-3} \mathrm{~m}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$4.1 \times 10^{-3} \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$1.4 \times 10^{-3} \mathrm{~m}$<br/></span> </div>

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>&amp; \frac{2 \pi r^2 T}{R}=m g=\frac{4}{3} \pi R^3 \cdot \rho \cdot g \\<br/>&amp; \begin{aligned}<br/>\therefore \quad R^4 &amp; =\frac{3 r^2 T}{2 \rho g}=\frac{3 \times\left(5 \times 10^{-4}\right)^2(0.11)}{2 \times 10^3 \times 10} \\<br/>&amp; =4.125 \times 10^{-12} \mathrm{~m}^4<br/>\end{aligned} \\<br/>&amp; \therefore R=1.425 \times 10^{-3} \mathrm{~m} \approx 1.4 \times 10^{-3} \mathrm{~m} \\<br/>&amp; \therefore \text { The correct option is (a). }<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-when-liquid-medicine-of-density-is-to-be-put-in-the-eye-it-is-done-with-the-help-of-a-dropper-as-the-bulb-on-the-top-of-the-dropper-is-press-2

slug:
paragraph-when-liquid-medicine-of-density-is-to-be-put-in-the-eye-it-is-done-with-the-help-of-a-dropper-as-the-bulb-on-the-top-of-the-dropper-is-press-2-87778

question:
<div class="question"><strong>Paragraph:</strong><br/>When liquid medicine of density $\rho$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop.<br/>We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension $T$ when the radius of the drop is $R$. When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.<strong>Question:</strong><br/>If the radius of the opening of the dropper is $r$, the vertical force due to the surface tension on the drop of radius $R$ (assuming $r&lt; &lt; R$ ) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$2 \pi r T$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$2 \pi R T$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{2 \pi r^2 T}{R}$<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"><br/>$\frac{2 \pi R^2 T}{r}$</span> </li> </ul>

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

answer:
<div class="solution">Vertical force due to surface tension,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/o4deu4ddbC-5yG25YqfzhyYmEFYug3P_Lf7lKpjW0tY.original.fullsize.png"/><br/><br/>$$<br/>\begin{aligned}<br/>F_v &amp; =F \sin \theta=(T \cdot 2 \pi r)(r / R) \\<br/>&amp; =\frac{2 \pi r^2 T}{R}<br/>\end{aligned}<br/>$$<br/>$\therefore$ The correct option is (c).</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
paragraph-when-liquid-medicine-of-density-is-to-be-put-in-the-eye-it-is-done-with-the-help-of-a-dropper-as-the-bulb-on-the-top-of-the-dropper-is-press

slug:
paragraph-when-liquid-medicine-of-density-is-to-be-put-in-the-eye-it-is-done-with-the-help-of-a-dropper-as-the-bulb-on-the-top-of-the-dropper-is-press-66757

question:
<div class="question"><strong>Paragraph:</strong><br/>When liquid medicine of density $\rho$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop.<br/>We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension $T$ when the radius of the drop is $R$. When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.<strong>Question:</strong><br/>After the drop detaches, its surface energy is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$1.4 \times 10^{-6} \mathrm{~J}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$2.7 \times 10^{-6} \mathrm{~J}$<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">C</span> <span class="option-data"><br/>$5.4 \times 10^{-6} \mathrm{~J}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$8.1 \times 10^{-9} \mathrm{~J}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$2.7 \times 10^{-6} \mathrm{~J}$<br/></span> </div>

answer:
<div class="solution">Surface energy,<br/>$$<br/>\begin{aligned}<br/>E &amp; =\left(4 \pi R^2\right) T \\<br/>&amp; =(4 \pi)\left(1.4 \times 10^{-3}\right)^2(0.11) \\<br/>&amp; =2.7 \times 10^{-6} \mathrm{~J}<br/>\end{aligned}<br/>$$<br/>$\therefore$ The correct option is (b).</div>


source_db: MarksBatch2_P2.db
title:
passing-h-2-s-gas-into-a-mixture-of-mn-2-ni-2-cu-2-and-hg-2-ions-in-an-acidified-aqueous-solution-precipitates

slug:
passing-h-2-s-gas-into-a-mixture-of-mn-2-ni-2-cu-2-and-hg-2-ions-in-an-acidified-aqueous-solution-precipitates-14095

question:
<div class="question">Passing $\mathrm{H}_2 \mathrm{~S}$ gas into a mixture of $\mathrm{Mn}^{2+}, \mathrm{Ni}^{2+}, \mathrm{Cu}^{2+}$ and $\mathrm{Hg}^{2+}$ ions in an acidified aqueous solution precipitates</div>

tags:
['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{CuS}$ and $\mathrm{HgS}$<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">B</span> <span class="option-data"><br/>$\mathrm{MnS}$ and $\mathrm{CuS}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{MnS}$ and $\mathrm{NiS}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{NiS}$ and $\mathrm{HgS}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{CuS}$ and $\mathrm{HgS}$<br/></span> </div>

answer:
<div class="solution">In acidic medium, $\mathrm{H}_2 \mathrm{~S}$ is very feebly ionized giving very small concentration of sulphide ion for precipitation. Therefore, the most insoluble salts $\mathrm{CuS}$ and $\mathrm{HgS}$ are precipitated only.</div>


tags: ['Physics', 'Dual Nature of Matter', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
photoelectric-effect-experiments-are-performed-using-three-different-metal-plates-p-q-and-r-having-work-functions-p-20-ev-q-25-ev-and-r-30-ev-respecti-1

slug:
photoelectric-effect-experiments-are-performed-using-three-different-metal-plates-p-q-and-r-having-work-functions-p-20-ev-q-25-ev-and-r-30-ev-respecti-1-89128

question:
<div class="question">Photoelectric effect experiments are performed using three different metal plates $p, \quad q$ and $r$ having work functions $\varphi_p=2.0 \mathrm{eV}, \varphi_q=2.5 \mathrm{eV}$ and $\varphi_r=3.0 \mathrm{eV}$, respectively. A light beam containing wavelengths of $550 \mathrm{~nm}$, $450 \mathrm{~nm}$ and $350 \mathrm{~nm}$ with equal intensities illuminates each of the plates. The correct $I-V$ graph for the experiment is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/8gqO7thopOJzGlQ9pDUL_lC--xm2lipVk9RdDK48P18.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/6Yha14QE5ecgcKW1rCihKK-A4yRVTTcuOpB6VBHIqrk.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/WtXlrOd4Fl_5Schqee2hXSKf9Vl1EhIXPzBJ05W6Lwo.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>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"><br/>None of these</span> </div>

answer:
<div class="solution">$$<br/>\begin{gathered}<br/>\text { 1. } K_p=E_p-\phi_p=\frac{1240}{550}-20=0.2545 \mathrm{eV} \\<br/>K_q=E_q-\phi_q=\frac{1240}{450}-25=0.255 \mathrm{eV} \\<br/>K_r=E_r-\phi_r=\frac{1240}{350}-3.0=0.543 \mathrm{eV}<br/>\end{gathered}<br/>$$<br/>In the above equation $K$ represents maximum kinetic energy of photoelectrons and $E$, the energy of incident right. From the above values we can see that stopping potential, $\left|V_r\right|&gt;\left|V_q\right|&gt;\left|V_p\right|$<br/>Further, their intensities are equal, but energy of individual photon of $r$ is maximum. Hence, number of photons incident (per unit area per unit time) of $r$ can be assumed to be least. Hence, saturation current of $r$ should be minimum.<br/>Keeping these points in mind no option seems to be correct. The correct graph is shown below,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ZssLLzGjx-oP96ATdC4k8dbeZqjya_pqS6yPBSp_fqk.original.fullsize.png"/><br/><br/>$$<br/>\therefore \text { No choice is correct. }<br/>$$</div>


tags: ['Physics', 'Dual Nature of Matter', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
photoelectric-effect-experiments-are-performed-using-three-different-metal-plates-p-q-and-r-having-work-functions-p-20-ev-q-25-ev-and-r-30-ev-respecti

slug:
photoelectric-effect-experiments-are-performed-using-three-different-metal-plates-p-q-and-r-having-work-functions-p-20-ev-q-25-ev-and-r-30-ev-respecti-45783

question:
<div class="question">Photoelectric effect experiments are performed using three different metal plates $p, \quad q$ and $r$ having work functions $\varphi_p=2.0 \mathrm{eV}, \varphi_q=2.5 \mathrm{eV}$ and $\varphi_r=3.0 \mathrm{eV}$, respectively. A light beam containing wavelengths of $550 \mathrm{~nm}$, $450 \mathrm{~nm}$ and $350 \mathrm{~nm}$ with equal intensities illuminates each of the plates. The correct $I-V$ graph for the experiment is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/8gqO7thopOJzGlQ9pDUL_lC--xm2lipVk9RdDK48P18.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/6Yha14QE5ecgcKW1rCihKK-A4yRVTTcuOpB6VBHIqrk.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/WtXlrOd4Fl_5Schqee2hXSKf9Vl1EhIXPzBJ05W6Lwo.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>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"><br/>None of these</span> </div>

answer:
<div class="solution">$$<br/>\begin{gathered}<br/>\text { 1. } K_p=E_p-\phi_p=\frac{1240}{550}-20=0.2545 \mathrm{eV} \\<br/>K_q=E_q-\phi_q=\frac{1240}{450}-25=0.255 \mathrm{eV} \\<br/>K_r=E_r-\phi_r=\frac{1240}{350}-3.0=0.543 \mathrm{eV}<br/>\end{gathered}<br/>$$<br/>In the above equation $K$ represents maximum kinetic energy of photoelectrons and $E$, the energy of incident right. From the above values we can see that stopping potential, $\left|V_r\right|&gt;\left|V_q\right|&gt;\left|V_p\right|$<br/>Further, their intensities are equal, but energy of individual photon of $r$ is maximum. Hence, number of photons incident (per unit area per unit time) of $r$ can be assumed to be least. Hence, saturation current of $r$ should be minimum.<br/>Keeping these points in mind no option seems to be correct. The correct graph is shown below,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ZssLLzGjx-oP96ATdC4k8dbeZqjya_pqS6yPBSp_fqk.original.fullsize.png"/><br/><br/>$$<br/>\therefore \text { No choice is correct. }<br/>$$</div>


tags: ['Chemistry', 'Chemical Kinetics', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
plots-showing-the-variation-of-the-rate-constant-k-with-temperature-t-are-given-below-the-plot-that-follows-arrhenius-equation-is-2

slug:
plots-showing-the-variation-of-the-rate-constant-k-with-temperature-t-are-given-below-the-plot-that-follows-arrhenius-equation-is-2-37218

question:
<div class="question">Plots showing the variation of the rate constant $(k)$ with temperature $(T)$ are given below. The plot that follows Arrhenius equation is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/bBedyTUwOt1eLOFZiwi1MPSuJxPJn50Hejpee9qJpSc.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">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/kp3C4NCB2daXgW6i0LDh4DAfOXG9YpKMW-HawADi_8Q.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/OGeL6AlXQQCvgmEfuRumFkRjPbU0KTWJ-kz6MnCOhrM.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/SGXhcjtDKqxWCyhO3ysXxgUSjzamNVjExpoNID2Ov-I.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/bBedyTUwOt1eLOFZiwi1MPSuJxPJn50Hejpee9qJpSc.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">$k=A e^{-E_a / R T}, \quad$ As temperature increases $k$ increases exponentially. Chemical kinetics Conceptual mathematical analysis of data I</div>


tags: ['Chemistry', 'Chemical Kinetics', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
plots-showing-the-variation-of-the-rate-constant-k-with-temperature-t-are-given-below-the-plot-that-follows-arrhenius-equation-is

slug:
plots-showing-the-variation-of-the-rate-constant-k-with-temperature-t-are-given-below-the-plot-that-follows-arrhenius-equation-is-78899

question:
<div class="question">Plots showing the variation of the rate constant $(k)$ with temperature $(T)$ are given below. The plot that follows Arrhenius equation is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/bBedyTUwOt1eLOFZiwi1MPSuJxPJn50Hejpee9qJpSc.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">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/kp3C4NCB2daXgW6i0LDh4DAfOXG9YpKMW-HawADi_8Q.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/OGeL6AlXQQCvgmEfuRumFkRjPbU0KTWJ-kz6MnCOhrM.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/SGXhcjtDKqxWCyhO3ysXxgUSjzamNVjExpoNID2Ov-I.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/bBedyTUwOt1eLOFZiwi1MPSuJxPJn50Hejpee9qJpSc.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">$k=A e^{-E_a / R T}, \quad$ As temperature increases $k$ increases exponentially. Chemical kinetics Conceptual mathematical analysis of data I</div>


tags: ['Physics', 'Electrostatics', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
positive-and-negative-point-charges-of-equal-magnitude-are-kept-at-0-0-2-a-and-0-0-2-a-respectively-the-work-done-by-the-electric-field-when-another-p-1

slug:
positive-and-negative-point-charges-of-equal-magnitude-are-kept-at-0-0-2-a-and-0-0-2-a-respectively-the-work-done-by-the-electric-field-when-another-p-1-23656

question:
<div class="question">Positive and negative point charges of equal magnitude are kept at $\left(0,0, \frac{a}{2}\right)$ and $\left(0,0, \frac{-a}{2}\right)$, respectively. The work done by the electric field when another positive point charge is moved from $(-a, 0,0)$ to $(0, a, 0)$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>positive<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>negative<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>zero<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"><br/>depends on the path connecting the initial and final positions</span> </li> </ul>

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

answer:
<div class="solution">$A \equiv(-a, 0,0) B \equiv(0, a, 0)$<br/>Point charge is moved from $A$ to $B$<br/>$$<br/>\begin{aligned}<br/>V_A &amp; =V_B=0 \\<br/>W &amp; =0<br/>\end{aligned}<br/>$$<br/>$$<br/>\therefore \quad W=0<br/>$$<br/>or the correct option is (c).<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/DiaY3X6xlxWW2TjNqO0u9R-XGUrorZAnreRtLsMUkok.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
positive-and-negative-point-charges-of-equal-magnitude-are-kept-at-0-0-2-a-and-0-0-2-a-respectively-the-work-done-by-the-electric-field-when-another-p

slug:
positive-and-negative-point-charges-of-equal-magnitude-are-kept-at-0-0-2-a-and-0-0-2-a-respectively-the-work-done-by-the-electric-field-when-another-p-34837

question:
<div class="question">Positive and negative point charges of equal magnitude are kept at $\left(0,0, \frac{a}{2}\right)$ and $\left(0,0, \frac{-a}{2}\right)$, respectively. The work done by the electric field when another positive point charge is moved from $(-a, 0,0)$ to $(0, a, 0)$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>positive<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>negative<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>zero<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"><br/>depends on the path connecting the initial and final positions</span> </li> </ul>

answer:
<div class="solution">$A \equiv(-a, 0,0) B \equiv(0, a, 0)$<br/>Point charge is moved from $A$ to $B$<br/>$$<br/>\begin{aligned}<br/>V_A &amp; =V_B=0 \\<br/>W &amp; =0<br/>\end{aligned}<br/>$$<br/>$$<br/>\therefore \quad W=0<br/>$$<br/>or the correct option is (c).<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/DiaY3X6xlxWW2TjNqO0u9R-XGUrorZAnreRtLsMUkok.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Redox Reactions', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch2_P2.db
title:
reaction-of-br-2-with-na-2-co-3-in-aqueous-solution-gives-sodium-bromide-and-sodium-bromate-with-evolution-of-co-2-gas-the-number-of-sodium-bromide-mo

slug:
reaction-of-br-2-with-na-2-co-3-in-aqueous-solution-gives-sodium-bromide-and-sodium-bromate-with-evolution-of-co-2-gas-the-number-of-sodium-bromide-mo-76051

question:
<div class="question">Reaction of $\mathrm{Br}_2$ with $\mathrm{Na}_2 \mathrm{CO}_3$ in aqueous solution gives sodium bromide and sodium bromate with evolution of $\mathrm{CO}_2$ gas. The number of sodium bromide molecules involved in the balanced chemical equation is</div>

answer:
<div class="solution">$\mathrm{Br}_2$ is disproportionated in basic medium as<br/>$$<br/>3 \mathrm{Br}_2+3 \mathrm{Na}_2 \mathrm{CO}_3 \longrightarrow 5 \mathrm{NaBr}+\mathrm{NaBrO}_3+3 \mathrm{CO}_2<br/>$$</div>


title: reduction-of-the-metal-centre-in-aqueous-permanganate-ion-involves
slug: reduction-of-the-metal-centre-in-aqueous-permanganate-ion-involves-39271
question: <div class="question">Reduction of the metal centre in aqueous permanganate ion involves</div>
tags: ['Chemistry', 'd and f Block Elements', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>three electrons in neutral medium<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">B</span> <span class="option-data"><br/>five electrons in neutral medium<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>three electrons in alkaline medium<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="correct"> <span class="option-label">D</span> <span class="option-data"><br/>five electrons in acidic medium</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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"><br/>three electrons in neutral medium<br/>, <br/>three electrons in alkaline medium<br/>, <br/>five electrons in acidic medium</span> </div>

answer:
<div class="solution">In neutral medium: $\quad \mathrm{MnO}_4^{-} \rightarrow \mathrm{MnO}_2\left(\mathrm{Mn}^{7+}+3 e^{-} \rightarrow \mathrm{Mn}^{4+}\right)$<br/>In alkaline medium : $\quad \mathrm{MnO}_4^{-} \rightarrow \mathrm{MnO}_2\left(\mathrm{Mn}^{7+}+3 \varepsilon^{-} \rightarrow \mathrm{Mn}^{4+}\right)$<br/>In acidic medium : $\quad \mathrm{Mn}_4^{-} \rightarrow \mathrm{Mn}^{2+}\left(\mathrm{Mn}^{7+}+5 e^{-} \rightarrow \mathrm{Mn}^{2+}\right)$</div>


title: retrogressive-metamorphosis-occurs-in
slug: retrogressive-metamorphosis-occurs-in-29755
question: <div class="question">Retrogressive metamorphosis occurs in</div>
tags: ['Biology', 'Animal Kingdom', 'AIIMS', 'AIIMS 2016']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Hemichordata</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Cephalochordata</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Urochordata</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Vertebrata.</span> </li> </ul>

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

answer:
<div class="solution">In retrogressive metamorphosis, degeneration is shown by larva to form less developed adult. It is a type of metamorphosis seen in Herdmania (Urochordate). It involves transformation of an active, free swimming larva with advanced characters into sedentary and simple adult.</div>


title: selaginella-can-be-regarded-as-an-evolutionary-advanced-pteridophyte-because-of
slug: selaginella-can-be-regarded-as-an-evolutionary-advanced-pteridophyte-because-of-92300
tags: ['Biology', 'Plant Kingdom', 'NEET']
source_db: MarksBatch2_P2.db
question:
<div class="question"><em>Selaginella</em> can be regarded as an evolutionary advanced Pteridophyte<em> </em>because of</div>

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

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

answer:
<div class="solution">Heterospory is the occurrence of two types of spore, smaller microspore, and larger macrospore. Heterospory has led to the evolution of seed habit in plants. Heterospory first evolved in Pteridophyta in which megaspore was retained on parent sporophyte which is considered as a precursor to seed habit.</div>


title: select-the-animal-that-exhibits-retrogressive-metamorphosis
slug: select-the-animal-that-exhibits-retrogressive-metamorphosis-22625
question: <div class="question">Select the animal that exhibits retrogressive metamorphosis.</div>
tags: ['Biology', 'Animal Kingdom', 'AIIMS', 'AIIMS 2015']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Bufo</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Amphioxus</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Limulus</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Herdmania</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Herdmania</span> </div>

answer:
<div class="solution">Retrogressive metamorphosis occurs in Urochordates (e.g., Herdmania, Ascidia, Doliolum etc.), in which better developed (advanced) larva changes to less developed (primitive) adult.</div>


title: sexual-reproduction-in-spirogyra-is-an-advanced-feature-because-it-shows
slug: sexual-reproduction-in-spirogyra-is-an-advanced-feature-because-it-shows-99966
tags: ['Biology', 'Sexual Reproduction in Flowering Plants', 'NEET', 'NEET 2003']
source_db: MarksBatch2_P2.db
question:
<div class="question">Sexual reproduction in Spirogyra is an advanced feature because it shows:</div>

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

answer:
<div class="solution">In Spirogyra, the sexual reproduction involves the fusion of two morphologically identical isogametes and physiologically dissimilar anisogametes. This is a case of primitive anisogamy.</div>


tags: ['Chemistry', 'Solid State', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: MarksBatch2_P2.db
title:
silver-atomic-weight-108-g-mol-1-has-a-density-of-105-g-cm-3-the-number-of-silver-atoms-on-a-surface-of-area-1-0-12-m-2-can-be-expressed-in-scientific

slug:
silver-atomic-weight-108-g-mol-1-has-a-density-of-105-g-cm-3-the-number-of-silver-atoms-on-a-surface-of-area-1-0-12-m-2-can-be-expressed-in-scientific-85989

question:
<div class="question">Silver (atomic weight $=108 \mathrm{~g} \mathrm{~mol}^{-1}$ ) has a density of $10.5 \mathrm{~g} \mathrm{~cm}^{-3}$. The number of silver atoms on a surface of area $10^{-12} \mathrm{~m}^2$ can be expressed in scientific notation as $y \times 10^x$. The value of $x$ is</div>

answer:
<div class="solution">Volume of one mole of silver atoms $=\frac{108}{10.5} \mathrm{~cm}^3 /$ mole Volume of one silver atom $=\frac{108}{10.5} \times \frac{1}{6.022 \times 10^{23}} \mathrm{~cm}^3$<br/>So,<br/>$$<br/>\begin{aligned}<br/>\frac{4}{3} \pi R^3 &amp; =\frac{108}{10.5} \times \frac{1}{6.022 \times 10^{23}}=1.708 \times 10^{-23} \\<br/>R^3 &amp; =0.407 \times 10^{-23} \mathrm{~cm}^3 \\<br/>&amp; =0.407 \times 10^{-29} \mathrm{~m}^3<br/>\end{aligned}<br/>$$<br/>Area of each silver atom<br/>$$<br/>\pi R^2=\pi \times\left(0.407 \times 10^{-29} \mathrm{~m}^3\right)^{2 / 3}<br/>$$<br/>So number of silver atoms in given area<br/>$$<br/>=\frac{10^{-12}}{\left(0.407 \times 10^{-29} \mathrm{~m}^3\right)^{2 / 3}}=\frac{10^8}{(\pi \times 2)}=1.6 \times 10^7=y \times 10^x \quad \text { so, } \quad x=7<br/>$$<br/>Solid state<br/>Mathematical understanding<br/>III</div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2022 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
six-charges-are-placed-around-a-regular-hexagon-of-side-length-a-as-shown-in-the-figure-five-of-them-have-charge-q-and-the-remaining-one-has-charge-x-

slug:
six-charges-are-placed-around-a-regular-hexagon-of-side-length-a-as-shown-in-the-figure-five-of-them-have-charge-q-and-the-remaining-one-has-charge-x-62468

question:
<div class="question"><p>Six charges are placed around a regular hexagon of side length <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> as shown in the figure. Five of them have charge <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math>, and the remaining one has charge <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>. The perpendicular from each charge to the nearest hexagon side passes through the center <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math> of the hexagon and is bisected by the side.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/94e37fce-1df2-4d0d-be7f-1e094ce9e879-image.png" style="width: 200px; height: 226px;"/></p><p>Which of the following statement(s) is(are) correct in SI units?</p></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><p>When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>q</mi></math>, the magnitude of the electric field at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math> is zero.</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="correct"> <span class="option-label">B</span> <span class="option-data">When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mi>q</mi></math>, the magnitude of the electric field at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>q</mi><mrow><mn>6</mn><mi>π</mi><msub><mo>∈</mo><mn>0</mn></msub><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></math>.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn><mi>q</mi></math>, the potential at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>7</mn><mi>q</mi></mrow><mrow><mn>4</mn><msqrt><mn>3</mn></msqrt><mi>π</mi><msub><mo>∈</mo><mn>0</mn></msub><mi>a</mi></mrow></mfrac></math>.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>3</mn><mi>q</mi></math>, the potential at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mi>q</mi></mrow><mrow><mn>4</mn><msqrt><mn>3</mn></msqrt><mi>π</mi><msub><mi>ϵ</mi><mn>0</mn></msub><mi>a</mi></mrow></mfrac></math>.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><p>When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>q</mi></math>, the magnitude of the electric field at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math> is zero.</p>, When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mi>q</mi></math>, the magnitude of the electric field at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>q</mi><mrow><mn>6</mn><mi>π</mi><msub><mo>∈</mo><mn>0</mn></msub><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></math>., When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn><mi>q</mi></math>, the potential at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>7</mn><mi>q</mi></mrow><mrow><mn>4</mn><msqrt><mn>3</mn></msqrt><mi>π</mi><msub><mo>∈</mo><mn>0</mn></msub><mi>a</mi></mrow></mfrac></math>.</span> </div>

answer:
<div class="solution"><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/62650f55-ab4a-4bd6-84ba-b377a89c04bb-image.png" style="width: 179px; height: 186px;"/>âââââââ</p><p>The given arrangements of the charges also form a regular hexagon with side length equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn></msqrt><mi>a</mi></math></p><p>When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>q</mi></math>, the situation is symmetric</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo></math> Electric field at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math> would be zero.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfenced><mi>A</mi></mfenced></math> is correct.</p><p>When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mi>q</mi></math>, we can think of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>+</mo><mfenced><mrow><mo>-</mo></mrow></mfenced><mfenced><mrow><mn>2</mn><mi>q</mi></mrow></mfenced></math>. Therefore, the magnitude of the electric field will be equivalent to that if only charge of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mi>q</mi></math> is kept at the the bottom point. Hence,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>O</mi></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>4</mn><mi>π</mi><msub><mi>Ïµ</mi><mn>0</mn></msub></mrow></mfrac><mfrac><mfenced><mrow><mn>2</mn><mi>q</mi></mrow></mfenced><msup><mfenced><mrow><msqrt><mn>3</mn></msqrt><mi>a</mi></mrow></mfenced><mn>2</mn></msup></mfrac></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mrow><mn>4</mn><mi>π</mi><msub><mi>Ïµ</mi><mn>0</mn></msub></mrow></mfrac><mfrac><mrow><mn>2</mn><mi>q</mi></mrow><mrow><mn>3</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mfrac><mi>q</mi><mrow><mn>6</mn><mi>π</mi><msub><mi>Ïµ</mi><mn>0</mn></msub><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfenced><mi>B</mi></mfenced></math> is correct</p><p>For <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn><mi>q</mi></math>, potential at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math> is</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>O</mi></msub><mo>=</mo><mn>5</mn><mo>×</mo><mfrac><mn>1</mn><mrow><mn>4</mn><mi>π</mi><msub><mi>Ïµ</mi><mn>0</mn></msub></mrow></mfrac><mfrac><mi>q</mi><mrow><msqrt><mn>3</mn></msqrt><mi>a</mi></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>4</mn><mi>π</mi><msub><mi>Ïµ</mi><mn>0</mn></msub></mrow></mfrac><mfrac><mrow><mn>2</mn><mi>q</mi></mrow><mrow><msqrt><mn>3</mn></msqrt><mi>a</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>7</mn><mi>q</mi></mrow><mrow><mn>4</mn><msqrt><mn>3</mn></msqrt><mi>π</mi><msub><mi>Ïµ</mi><mn>0</mn></msub><mi>a</mi></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfenced><mi>C</mi></mfenced></math> is correct</p><p>For <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>3</mn><mi>q</mi><mo>,</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>O</mi></msub><mo>=</mo><mn>5</mn><mo>×</mo><mfrac><mn>1</mn><mrow><mn>4</mn><mi>π</mi><msub><mi>Ïµ</mi><mn>0</mn></msub></mrow></mfrac><mfrac><mi>q</mi><mrow><msqrt><mn>3</mn></msqrt><mi>a</mi></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>4</mn><mi>π</mi><msub><mi>Ïµ</mi><mn>0</mn></msub></mrow></mfrac><mfrac><mrow><mo>-</mo><mn>3</mn><mi>q</mi></mrow><mrow><msqrt><mn>3</mn></msqrt><mi>a</mi></mrow></mfrac><mo>=</mo><mfrac><mi>q</mi><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt><mi>π</mi><msub><mi>Ïµ</mi><mn>0</mn></msub><mi>a</mi></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>D</mi></mfenced></math>is not correct.</p></div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
six-point-charges-are-kept-at-the-vertices-of-a-regular-hexagon-of-side-l-and-centre-o-as-shown-in-the-figure-given-that-k-4-0-1-l-2-q-which-of-the-fo

slug:
six-point-charges-are-kept-at-the-vertices-of-a-regular-hexagon-of-side-l-and-centre-o-as-shown-in-the-figure-given-that-k-4-0-1-l-2-q-which-of-the-fo-77467

question:
<div class="question">Six point charges are kept at the vertices of a regular hexagon of side $\mathrm{L}$ and centre $O$, as shown in the figure.
<br/> <br/>Given that $K=\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{L^{2}}$, which of the following statement(s) is (are) correct?
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/TNA-fS4zD7LB7P7tWEr2kEXM9E2IyiOZmGWksHzD46E.original.fullsize.png"/><br/></div>

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

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">The electric field at $O$ is $6 \mathrm{~K}$ along $O D$, The potential at $O$ is zero, The potential at all points on the line $P R$ is same</span> </div>

answer:
<div class="solution">Here
<br/> <br/>$\begin{aligned}
<br/> <br/>&amp; \frac{\left|\overrightarrow{E_{A}}\right|}{2}=\left|\overrightarrow{E_{B}}\right|=\left|\overrightarrow{E_{C}}\right|=\frac{\left|\overrightarrow{E_{D}}\right|}{2}=\left|\overrightarrow{E_{E}}\right|=\left|\overrightarrow{E_{F}}\right|=K \\
<br/> <br/>\therefore &amp; E_{O}=E_{A}+E_{D}+\left(E_{F}+E_{C}\right) \cos 60^{\circ}+\left(E_{B}+E_{C}\right) \cos 60^{\circ} \\
<br/> <br/>=&amp; 2 \mathrm{~K}+2 \mathrm{~K}+(\mathrm{K}+\mathrm{K}) \times \frac{1}{2}+(\mathrm{K}+\mathrm{K}) \times \frac{1}{2}=6 \mathrm{~K}
<br/> <br/>\end{aligned}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/po-pHHTRh1HGuC_SLte7BHab4PCfekrn560sGFdEobg.original.fullsize.png"/><br/> <br/> <br/>Electric potential at $O$
<br/> <br/>$V_{O}=\frac{1}{4 \pi \varepsilon_{0} L}[2 q+q+q-q-q-2 q]=0$
<br/> <br/>Potential at all points on the line PR is same not on line ST. $P R$ is perpendicular bisector (the equatorial line) for the electric dipoles $A B, F E$ and $B C$. Therefore the electric potential will be zero at any point on $P R$.</div>


tags: ['Physics', 'Electrostatics', 'JEE Main']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch2_P2.db
title:
six-point-charges-each-of-the-same-magnitude-q-are-arranged-in-different-manners-as-shown-in-columnii-in-each-case-a-point-m-and-a-line-pq-passing-thr-1

slug:
six-point-charges-each-of-the-same-magnitude-q-are-arranged-in-different-manners-as-shown-in-columnii-in-each-case-a-point-m-and-a-line-pq-passing-thr-1-99885

question:
<div class="question">Six point charges, each of the same magnitude $q$, are arranged in different manners as shown in Column-II. In each case, a point $M$ and a line $P Q$ passing through $M$ are shown. Let $E$ be the electric field and $V$ be the electric potential at $M$ (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line $P Q$. Let $B$ the magnetic field at $M$ and $\mu$ be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/7gVh6lG9bFXFpAYpwPukZPsSYUFuKLh7nm7jj5evels.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>(A) q,t, (B) q,s, (C) p,q,t, (D) r,s,t<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>(A) q,r,s, (B) r,s, (C) p,r, (D) r,s,t<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>(A) p,r,s, (B) r,s, (C) p,q,t, (D) r,s<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"><br/>(A) p,r, (B) q,s, (C) p,r,t, (D) r,s</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) p,r,s, (B) r,s, (C) p,q,t, (D) r,s<br/></span> </div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch2_P2.db
title:
six-point-charges-each-of-the-same-magnitude-q-are-arranged-in-different-manners-as-shown-in-columnii-in-each-case-a-point-m-and-a-line-pq-passing-thr

slug:
six-point-charges-each-of-the-same-magnitude-q-are-arranged-in-different-manners-as-shown-in-columnii-in-each-case-a-point-m-and-a-line-pq-passing-thr-19155

question:
<div class="question">Six point charges, each of the same magnitude $q$, are arranged in different manners as shown in Column-II. In each case, a point $M$ and a line $P Q$ passing through $M$ are shown. Let $E$ be the electric field and $V$ be the electric potential at $M$ (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line $P Q$. Let $B$ the magnetic field at $M$ and $\mu$ be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/7gVh6lG9bFXFpAYpwPukZPsSYUFuKLh7nm7jj5evels.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>(A) q,t, (B) q,s, (C) p,q,t, (D) r,s,t<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>(A) q,r,s, (B) r,s, (C) p,r, (D) r,s,t<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>(A) p,r,s, (B) r,s, (C) p,q,t, (D) r,s<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"><br/>(A) p,r, (B) q,s, (C) p,r,t, (D) r,s</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) p,r,s, (B) r,s, (C) p,q,t, (D) r,s<br/></span> </div>


tags: ['Chemistry', 'Ionic Equilibrium', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
solubility-product-constant-k-sp-of-salts-of-types-mx-m-x-2-and-m-3-x-at-temperature-t-are-40-1-0-8-32-1-0-14-and-27-1-0-15-respectively-solubilities-

slug:
solubility-product-constant-k-sp-of-salts-of-types-mx-m-x-2-and-m-3-x-at-temperature-t-are-40-1-0-8-32-1-0-14-and-27-1-0-15-respectively-solubilities-70456

question:
<div class="question">Solubility product constant $\left(K_{\mathrm{sp}}\right)$ of salts of types $M X, M X_2$ and $M_3 X$ at temperature ' $T$ ' are $4.0 \times 10^{-8}, 3.2 \times 10^{-14}$ and $2.7 \times 10^{-15}$, respectively. Solubilities $\left(\mathrm{mol} \mathrm{dm}^{-3}\right)$ of the salts at temperature ' $T$ ' are in the order</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$M X&gt;M X_2&gt;M_3 X$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$M_3 X&gt;M X_2&gt;M X$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$M X_2&gt;M_3 X &lt; M X$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$M X&gt;M_3 X&gt;M X_2$</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"><br/>$M X&gt;M_3 X&gt;M X_2$</span> </div>

answer:
<div class="solution">$\begin{array}{lcl}\text { Salt } &amp; \text { Solubility product } &amp; \text { Solubility } \\ M X &amp; S_1^2=4.0 \times 10^{-8} &amp; S_1=2 \times 10^{-4} \\ M X_2 &amp; 4 S_2^3=3.2 \times 10^{-14} &amp; S_2=2 \times 10^{-5} \\ M_3 X &amp; 27 S_3^4=2.7 \times 10^{-15} &amp; S_3=1 \times 10^{-4}\end{array}$<br/>Thus, solubility order $=M X&gt;M_3 X&gt;M X_2$.</div>


tags: ['Physics', 'Nuclear Physics', 'JEE Main']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch2_P2.db
title:
some-lawsprocesses-are-given-in-column-i-match-these-with-the-physical-phenomena-given-in-column-ii-and-indicate-your-answer-by-darkening-appropriate--1

slug:
some-lawsprocesses-are-given-in-column-i-match-these-with-the-physical-phenomena-given-in-column-ii-and-indicate-your-answer-by-darkening-appropriate-1-51782

question:
<div class="question">Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the ORS.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/si4dXTR4UIpetgefzMIUHF2z89aSCJZv3XAQxkFy254.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>A-p, r; B-p, q, s; C-p; D-q<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">B</span> <span class="option-data"><br/>A-p; B-p, s; C-p; D-q<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>A-p, r; B-p, q; C-p, r; D-q, s<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>A-r, s; B-q; C-p; D-p, q, s</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>A-p, r; B-p, q, s; C-p; D-q<br/></span> </div>


tags: ['Physics', 'Nuclear Physics', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch2_P2.db
title:
some-lawsprocesses-are-given-in-column-i-match-these-with-the-physical-phenomena-given-in-column-ii-and-indicate-your-answer-by-darkening-appropriate-

slug:
some-lawsprocesses-are-given-in-column-i-match-these-with-the-physical-phenomena-given-in-column-ii-and-indicate-your-answer-by-darkening-appropriate-36742

question:
<div class="question">Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the ORS.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/si4dXTR4UIpetgefzMIUHF2z89aSCJZv3XAQxkFy254.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>A-p, r; B-p, q, s; C-p; D-q<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">B</span> <span class="option-data"><br/>A-p; B-p, s; C-p; D-q<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>A-p, r; B-p, q; C-p, r; D-q, s<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>A-r, s; B-q; C-p; D-p, q, s</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>A-p, r; B-p, q, s; C-p; D-q<br/></span> </div>


tags: ['Physics', 'Units and Dimensions', 'JEE Main']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch2_P2.db
title:
some-physical-quantities-are-given-in-column-i-and-some-possible-si-units-in-which-these-quantities-may-be-expressed-are-given-in-column-ii-match-the--1

slug:
some-physical-quantities-are-given-in-column-i-and-some-possible-si-units-in-which-these-quantities-may-be-expressed-are-given-in-column-ii-match-the-1-72352

question:
<div class="question">Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the ORS.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/71rwiOBIl8y69LXU1c8nAsedgtxa0TzE-uNAQgeFDS4.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>A-p, r; B-r, s; C-q; D-p, q<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>A-p, q; B-r, s; C-r, s; D-r, s<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">C</span> <span class="option-data"><br/>A-q; B-r, s; C-s; D-p, q, r<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>A-r, s; B-q; C-p; D-p, q, s</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>A-p, q; B-r, s; C-r, s; D-r, s<br/></span> </div>


tags: ['Physics', 'Units and Dimensions', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch2_P2.db
title:
some-physical-quantities-are-given-in-column-i-and-some-possible-si-units-in-which-these-quantities-may-be-expressed-are-given-in-column-ii-match-the-

slug:
some-physical-quantities-are-given-in-column-i-and-some-possible-si-units-in-which-these-quantities-may-be-expressed-are-given-in-column-ii-match-the-59685

question:
<div class="question">Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the ORS.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/71rwiOBIl8y69LXU1c8nAsedgtxa0TzE-uNAQgeFDS4.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>A-p, r; B-r, s; C-q; D-p, q<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>A-p, q; B-r, s; C-r, s; D-r, s<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">C</span> <span class="option-data"><br/>A-q; B-r, s; C-s; D-p, q, r<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>A-r, s; B-q; C-p; D-p, q, s</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>A-p, q; B-r, s; C-r, s; D-r, s<br/></span> </div>


tags: ['Physics', 'Gravitation', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-1-an-astronaut-in-an-orbiting-space-station-above-the-earth-experiences-weightlessness-and-statement-2-an-object-moving-around-the-earth-und

slug:
statement-1-an-astronaut-in-an-orbiting-space-station-above-the-earth-experiences-weightlessness-and-statement-2-an-object-moving-around-the-earth-und-32304

question:
<div class="question">Statement 1 An astronaut in an orbiting space station above the earth experiences weightlessness.<br/>and Statement 2 An object moving around the earth under the influence of earth's gravitational force is in state of 'free fall'.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.<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">B</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is false.<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Statement 1 is false, Statement 2 is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.<br/></span> </div>

answer:
<div class="solution">Force acting on astronaut is utilised in providing necessary centripetal force; thus he feels weightlessness or he is in a state of free fall.<br/>$$<br/>\therefore \text { correct option is (a) }<br/>$$</div>


tags: ['Chemistry', 'Amines', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
statement-1-aniline-on-reaction-with-nano-2-hcl-at-0-c-followed-by-coupling-with-naphthol-gives-a-dark-coloured-precipitate-statement-2-the-colour-of-

slug:
statement-1-aniline-on-reaction-with-nano-2-hcl-at-0-c-followed-by-coupling-with-naphthol-gives-a-dark-coloured-precipitate-statement-2-the-colour-of-94294

question:
<div class="question">Statement 1 Aniline on reaction with $\mathrm{NaNO}_2 / \mathrm{HCl}$ at $0^{\circ} \mathrm{C}$ followed by coupling with $\beta$-naphthol gives a dark coloured precipitate.<br/>Statement 2 The colour of the compound formed in the reaction of aniline with $\mathrm{NaNO}_2 / \mathrm{HCl}$ at $0^{\circ} \mathrm{C}$ followed by coupling with $\beta$-naphthol is due to the extended conjugation.</div>

answer:
<div class="solution">Statement II is correct. Statement I appears correct in the light of Statement II. What is the colour of a dye that dye is not in included in JEE syllabus but what is the cause and understanding behind a colour could be essentially expected.<br/>Concept Usually a certain proportion of the flight is absorbed and the rest reflected, the substance has the colour of the reflected light.<br/>If only a single band is absorbed, the substance has the complementary colour.<br/>- The wavelength of photon absorbed depends on the energy difference between the excited and ground states. The smaller the difference, the longer being the wavelength.<br/>- The larger the number of electrons involved in resonance, the smaller is the energy difference between the ground and excited state. Hence, the more extended the conjugation in a molecule and the greater the contribution of charged structures, the longer is the wavelength of the photon required to excite the molecule.<br/>- Especially, the presence of $+I /+M$ and $-I /-M$ groups in the conjugated system will both extend the conjugation and increase the contributions of charged structures to the resonance hybrid. Therefore, in these circumstances, the wavelength should become progressively longer.<br/>- Depending on this discussion it is apparent that the concerned resultant azodye will absorb higher wavelength.<br/>$\begin{array}{ccc}\text { Wavelength } &amp; \text { Colour absorbed } &amp; \text { Complimentary colour } \\ 490-500 &amp; \text { Blue-green } &amp; \text { Red } \\ 580-595 &amp; \text { Yellow } &amp; \text { Blue } \\ 605-750 &amp; \text { Red } &amp; \text { Blue-green }\end{array}$</div>


tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-1-bromobenzene-upon-reaction-with-br-2-fe-gives-1-4dibromobenzene-as-the-major-product-statement-2-in-bromobenzene-the-inductive-effect-of-t

slug:
statement-1-bromobenzene-upon-reaction-with-br-2-fe-gives-1-4dibromobenzene-as-the-major-product-statement-2-in-bromobenzene-the-inductive-effect-of-t-46795

question:
<div class="question">Statement 1 Bromobenzene, upon reaction with $\mathrm{Br}_2 / \mathrm{Fe}$ gives 1, 4-dibromobenzene as the major product.<br/>Statement 2 In bromobenzene, the inductive effect of the bromo group is more dominant than the mesomeric effect in directing the incoming electrophile.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is false.<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"><br/>Statement 1 is false, Statement 2 is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Statement 1 is true, Statement 2 is false.<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/CLv1bF2Y6HPwJjITGAL6VFi66RjkGikxwnxz_mnR77I.original.fullsize.png"/><br/><br/>Bromine orientation is controlled by its mesomeric effect, its stabilisation of arenium ion by $+M$ activity<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/RzYv88pXdWx7lm2Tk1Irvwlld6qP3svdfXGGkPm2sb8.original.fullsize.png"/><br/><br/>In bromobenzene, the inductive effect of the bromo group is more dominant than the mesomeric effect in the activity of ring.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/1KHmA0z9cvYBIf5MEgGWzh9IkY7uXIDrp0YeDmlsD78.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
statement-1-fe-h-2-o-5-no-so-4-is-paramagnetic-statement-2-the-fe-in-fe-h-2-o-5-no-so-4-has-three-unpaired-electrons

slug:
statement-1-fe-h-2-o-5-no-so-4-is-paramagnetic-statement-2-the-fe-in-fe-h-2-o-5-no-so-4-has-three-unpaired-electrons-86511

question:
<div class="question">Statement $\mathbf{1}\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{NO}\right] \mathrm{SO}_4$ is paramagnetic.<br/>Statement 2 The $\mathrm{Fe}$ in $\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{NO}\right] \mathrm{SO}_4$ has three unpaired electrons.</div>

answer:
<div class="solution">The oxidation number of $\mathrm{Fe}$ in the complex, $\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{NO}\right] \mathrm{SO}_4$ is $+1$ [ $\mathrm{NO}$ has $+1$ charge ]<br/>$$<br/>\mathrm{Fe}^{+}=[\mathrm{Ar}] 3 d^6 4 s^1<br/>$$<br/>$\mathrm{NO}^{+}$causes pairing of 4 s electron inside .<br/>Thus, the configuration is $3 d^7$ and number of unpaired electrons $=3$</div>


tags: ['Physics', 'Motion In Two Dimensions', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
statement-1-for-an-observer-looking-out-through-the-window-of-a-fast-moving-train-the-nearby-objects-appear-to-move-in-the-opposite-direction-to-the-t-1

slug:
statement-1-for-an-observer-looking-out-through-the-window-of-a-fast-moving-train-the-nearby-objects-appear-to-move-in-the-opposite-direction-to-the-t-1-41676

question:
<div class="question">Statement 1 For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.<br/>and Statement 2 If the observer and the object are moving at velocities $\overrightarrow{\mathbf{v}}_{\mathbf{1}}$ and $\overrightarrow{\mathbf{v}_2}$ respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is $\overrightarrow{\mathbf{v}_2}-\overrightarrow{\mathbf{v}_1}$.</div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/KuQNeOX_19L4lWh8bt_HqtuWD8dcyrw23wpZ4PAV4lA.original.fullsize.png"/><br/><br/>Statement-2, is formula of relative velocity. But it does not explain statement-1 correctly. The correct explanation of statement-1 is due to visual perception of motion. The object appears to be moving faster, when its angular velocity is greater w.r.t observer.<br/>$\therefore$ correct answer is (b).</div>


tags: ['Physics', 'Motion In Two Dimensions', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
statement-1-for-an-observer-looking-out-through-the-window-of-a-fast-moving-train-the-nearby-objects-appear-to-move-in-the-opposite-direction-to-the-t

slug:
statement-1-for-an-observer-looking-out-through-the-window-of-a-fast-moving-train-the-nearby-objects-appear-to-move-in-the-opposite-direction-to-the-t-82420

question:
<div class="question">Statement 1 For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.<br/>and Statement 2 If the observer and the object are moving at velocities $\overrightarrow{\mathbf{v}}_{\mathbf{1}}$ and $\overrightarrow{\mathbf{v}_2}$ respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is $\overrightarrow{\mathbf{v}_2}-\overrightarrow{\mathbf{v}_1}$.</div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/KuQNeOX_19L4lWh8bt_HqtuWD8dcyrw23wpZ4PAV4lA.original.fullsize.png"/><br/><br/>Statement-2, is formula of relative velocity. But it does not explain statement-1 correctly. The correct explanation of statement-1 is due to visual perception of motion. The object appears to be moving faster, when its angular velocity is greater w.r.t observer.<br/>$\therefore$ correct answer is (b).</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-1-for-every-chemical-reaction-at-equilibrium-standard-gibbs-energy-of-reaction-is-zero-statement-2-at-constant-temperature-and-pressure-chem

slug:
statement-1-for-every-chemical-reaction-at-equilibrium-standard-gibbs-energy-of-reaction-is-zero-statement-2-at-constant-temperature-and-pressure-chem-12427

question:
<div class="question">Statement 1 For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero.<br/>Statement 2 At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs energy.</div>

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

answer:
<div class="solution">At equilibrium, its free energy change, is zero and for a spontaneous process, $\Delta G &lt; 0$ but at equilibrium standard free energy is not zero.<br/>Analysis of the Paragraph<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tHsQvv8Onx_VMm13JsbgLaMcMgI1uOlms0UbX1PPBmw.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
answer: <div class="solution">No solution is required.</div>
source_db: MarksBatch2_P2.db
title:
statement-1-for-practical-purposes-the-earth-is-used-as-a-reference-at-zero-potential-in-electrical-circuits-and-statement-2-the-electrical-potential-

slug:
statement-1-for-practical-purposes-the-earth-is-used-as-a-reference-at-zero-potential-in-electrical-circuits-and-statement-2-the-electrical-potential-96327

question:
<div class="question">Statement 1 For practical purposes, the earth is used as a reference at zero potential in electrical circuits.<br/>and Statement 2 The electrical potential of a sphere of radius $R$ with charge $Q$ uniformly distributed on the surface is given by $\frac{Q}{4 \pi \varepsilon_0 R}$.</div>


tags: ['Physics', 'Current Electricity', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-1-in-a-meter-bridge-experiment-null-point-for-an-unknown-resistance-is-measured-now-the-unknown-resistance-is-put-inside-an-enclosure-mainta

slug:
statement-1-in-a-meter-bridge-experiment-null-point-for-an-unknown-resistance-is-measured-now-the-unknown-resistance-is-put-inside-an-enclosure-mainta-47628

question:
<div class="question">Statement $1 \mathrm{In}$ a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.<br/>and Statement 2 Resistance of a metal increase with increase in temperature.</div>

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

answer:
<div class="solution">With increase in temperature, the value of unknown resistance will increase.<br/>In balanced Wheatstone bridge condition, $\frac{R}{X}=\frac{l_1}{l_2}$<br/>Here, $R=$ value of standard resistance,<br/>$X=$ value of unknown resistance .<br/>To take null point at same point or $\frac{l_1}{l_2}$ to remain unchanged, $\frac{R}{X}$ should also remain unchanged. Therefore, if $X$ is increasing $R$ should also increase.<br/>$\therefore$ correct option is (d).</div>


tags: ['Physics', 'Laws of Motion', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
statement-1-it-is-easier-to-pull-a-heavy-object-than-to-push-it-on-a-level-ground-and-statement-2-the-magnitude-of-frictional-force-depends-on-the-nat

slug:
statement-1-it-is-easier-to-pull-a-heavy-object-than-to-push-it-on-a-level-ground-and-statement-2-the-magnitude-of-frictional-force-depends-on-the-nat-22761

question:
<div class="question">Statement 1 It is easier to pull a heavy object than to push it on a level ground. <br/>and Statement 2 The magnitude of frictional force depends on the nature of the two surfaces in contact.</div>

answer:
<div class="solution">Both statements are correct. But statement-2, does not explain correctly, statement- 1 . Correct explanation is : "There is increase in nomal reaction when the object is pushed and there is decrease in normal reaction when the object is pulled (but strictly not horizontally).</div>


tags: ['Chemistry', 'Chemical Kinetics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-1-pb-4-compounds-are-stronger-oxidising-agents-than-sn-4-compounds-statement-2-the-higher-oxidation-states-for-the-group-14-elements-are-mor

slug:
statement-1-pb-4-compounds-are-stronger-oxidising-agents-than-sn-4-compounds-statement-2-the-higher-oxidation-states-for-the-group-14-elements-are-mor-92917

question:
<div class="question">Statement $1 \mathrm{~Pb}^{4+}$ compounds are stronger oxidising agents than $\mathrm{Sn}^{4+}$ compounds.<br/>Statement 2 The higher oxidation states for the group 14 elements are more stable for the heavier members of the group due to 'inert pair effect'.</div>

answer:
<div class="solution">In early p-block, on moving top to bottom, the stability of lower oxidation state increases due to inert pair effect. $\mathrm{Pb}^{4+}$ is less stable than $\mathrm{Sn}^{4+}$, making it a better oxidising agent The lower oxidation state for the group 14 elements are more stable for the heavier members.</div>


tags: ['Chemistry', 'Coordination Compounds', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
statement-1-the-geometrical-isomer-of-the-complex-m-nh-3-4-cl-2-are-optically-inactive-statement-2-both-geometrical-isomers-of-the-complex-m-nh-3-4-cl-1

slug:
statement-1-the-geometrical-isomer-of-the-complex-m-nh-3-4-cl-2-are-optically-inactive-statement-2-both-geometrical-isomers-of-the-complex-m-nh-3-4-cl-1-95145

question:
<div class="question">Statement 1 The geometrical isomer of the complex $\left.\left[\mathrm{M}_{\left(\mathrm{NH}_3\right.}\right)_4 \mathrm{Cl}_2\right]$ are optically inactive.<br/>Statement 2 Both geometrical isomers of the complex $\left[\mathrm{M}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right]$ possess axis of symmetry.</div>

answer:
<div class="solution">$$<br/>\text { The cis and trans both form of complex }\left[M\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right] \text { are optically inactive }<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/FtWdOPVTJlm8WqdfaL1ldx92aziJzGrJOU5ivVlGO0Q.original.fullsize.png"/><br/><br/>There are plane of symmetry in addition to that there is alternate axis of symmetry $\left(C_n\right)$ which also causes their optical inactivity.<br/>A molecule possesses $n$ fold alternating axis of symmetry, if when rotated through an angle of $360^{\circ} / \mathrm{n}$ about the axis and then followed by reflection in a plane perpendicular to the axis, the molecule is indistinguishable from the original molecule.</div>


tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
statement-1-the-geometrical-isomer-of-the-complex-m-nh-3-4-cl-2-are-optically-inactive-statement-2-both-geometrical-isomers-of-the-complex-m-nh-3-4-cl

slug:
statement-1-the-geometrical-isomer-of-the-complex-m-nh-3-4-cl-2-are-optically-inactive-statement-2-both-geometrical-isomers-of-the-complex-m-nh-3-4-cl-15143

question:
<div class="question">Statement 1 The geometrical isomer of the complex $\left.\left[\mathrm{M}_{\left(\mathrm{NH}_3\right.}\right)_4 \mathrm{Cl}_2\right]$ are optically inactive.<br/>Statement 2 Both geometrical isomers of the complex $\left[\mathrm{M}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right]$ possess axis of symmetry.</div>

answer:
<div class="solution">$$<br/>\text { The cis and trans both form of complex }\left[M\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right] \text { are optically inactive }<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/FtWdOPVTJlm8WqdfaL1ldx92aziJzGrJOU5ivVlGO0Q.original.fullsize.png"/><br/><br/>There are plane of symmetry in addition to that there is alternate axis of symmetry $\left(C_n\right)$ which also causes their optical inactivity.<br/>A molecule possesses $n$ fold alternating axis of symmetry, if when rotated through an angle of $360^{\circ} / \mathrm{n}$ about the axis and then followed by reflection in a plane perpendicular to the axis, the molecule is indistinguishable from the original molecule.</div>


tags: ['Chemistry', 'Structure of Atom', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
statement-1-the-plot-of-atomic-number-y-axis-versus-number-of-neutrons-x-axis-for-stable-nuclei-shows-a-curvature-towards-x-axis-from-the-line-of-4-5--1

slug:
statement-1-the-plot-of-atomic-number-y-axis-versus-number-of-neutrons-x-axis-for-stable-nuclei-shows-a-curvature-towards-x-axis-from-the-line-of-4-5-1-13416

question:
<div class="question">Statement 1 The plot of atomic number ( $Y$-axis) versus number of neutrons ( $x$-axis) for stable nuclei shows a curvature towards $X$-axis from the line of $45^{\circ}$ slope as the atomic number is increased.<br/>Statement 2 Proton-proton electrostatic repulsions begin to overcome attractive forces involving protons and neutrons in heavier nuclides.</div>

answer:
<div class="solution">The stability relationship can be represented by a line with a slope of $45^{\circ}$, i.e. the maximum stability is attained, when $N=Z$.<br/>Right or the curve a radioactive nuclide would be neutron rich and would decay be $\beta$-emission to produce a daughter nucleus with a lower $\frac{n}{p}$ ratio.<br/>For heavier nuclides, $p-p$ repulsions start to offset the attractive forces and an excess of neutrons over protons, is required for stability<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Py3NCU1zmM9XeBrO2-gMDPphNiQtSfAi1bDOb_oNNgk.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Structure of Atom', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-1-the-plot-of-atomic-number-y-axis-versus-number-of-neutrons-x-axis-for-stable-nuclei-shows-a-curvature-towards-x-axis-from-the-line-of-4-5-

slug:
statement-1-the-plot-of-atomic-number-y-axis-versus-number-of-neutrons-x-axis-for-stable-nuclei-shows-a-curvature-towards-x-axis-from-the-line-of-4-5-94953

question:
<div class="question">Statement 1 The plot of atomic number ( $Y$-axis) versus number of neutrons ( $x$-axis) for stable nuclei shows a curvature towards $X$-axis from the line of $45^{\circ}$ slope as the atomic number is increased.<br/>Statement 2 Proton-proton electrostatic repulsions begin to overcome attractive forces involving protons and neutrons in heavier nuclides.</div>

answer:
<div class="solution">The stability relationship can be represented by a line with a slope of $45^{\circ}$, i.e. the maximum stability is attained, when $N=Z$.<br/>Right or the curve a radioactive nuclide would be neutron rich and would decay be $\beta$-emission to produce a daughter nucleus with a lower $\frac{n}{p}$ ratio.<br/>For heavier nuclides, $p-p$ repulsions start to offset the attractive forces and an excess of neutrons over protons, is required for stability<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Py3NCU1zmM9XeBrO2-gMDPphNiQtSfAi1bDOb_oNNgk.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
statement-1-the-sensitivity-of-a-moving-coil-galvanometer-is-increased-by-placing-a-suitable-magnetic-material-as-a-core-inside-the-coil-and-statement

slug:
statement-1-the-sensitivity-of-a-moving-coil-galvanometer-is-increased-by-placing-a-suitable-magnetic-material-as-a-core-inside-the-coil-and-statement-32294

question:
<div class="question">Statement 1 The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.<br/>and Statement 2 Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized.</div>

answer:
<div class="solution">$c \phi=B I N A$<br/>$$<br/>\therefore \phi=\left(\frac{B N A}{c}\right) I<br/>$$<br/>Using iron core, value of magnetic field increases. So, deflection increases for same current. Hence, sensitivity increases. Soft iron can be easily magnetized or demagnetized.<br/>$\therefore$ correct option is (c).</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-1-the-stream-of-water-flowing-at-high-speed-from-a-garden-hose-pipe-tends-to-spread-like-a-fountain-when-held-vertically-up-but-tends-to-nar

slug:
statement-1-the-stream-of-water-flowing-at-high-speed-from-a-garden-hose-pipe-tends-to-spread-like-a-fountain-when-held-vertically-up-but-tends-to-nar-50242

question:
<div class="question">Statement 1 The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.<br/>and Statement 2 In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.</div>

answer:
<div class="solution">From continuity equation,<br/>$$<br/>A v=\text { constant or } A \propto \frac{1}{v}<br/>$$<br/>At lower heights, speed will be more. Therefore, area of cross-section will be less. $\therefore$ correct option is (a).</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
statement-1-there-is-a-natural-asymmetry-between-converting-work-to-heat-and-converting-heat-to-work-statement-2-no-process-is-possible-in-which-the-s

slug:
statement-1-there-is-a-natural-asymmetry-between-converting-work-to-heat-and-converting-heat-to-work-statement-2-no-process-is-possible-in-which-the-s-29434

question:
<div class="question">Statement 1 There is a natural asymmetry between converting work to heat and converting heat to work.<br/>Statement 2 No process is possible in which the sole result in the absorption of heat from a reservoir and its complete conversion into work.</div>

answer:
<div class="solution">There is natural asymmetry between converting work to heat and converting heat to work because of the lapse of energy in this process which has been generalised in the form of second law of thermodynamics (Statement II).</div>


tags: ['Physics', 'Rotational Motion', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-1-two-cylinders-one-hollow-metal-and-the-other-solid-wood-with-the-same-mass-and-identical-dimensions-are-simultaneously-allowed-to-roll-wit

slug:
statement-1-two-cylinders-one-hollow-metal-and-the-other-solid-wood-with-the-same-mass-and-identical-dimensions-are-simultaneously-allowed-to-roll-wit-15696

question:
<div class="question">Statement 1 Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.<br/>and Statement 2 By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.</div>

answer:
<div class="solution">In case of pure rolling on inclined plane,<br/>$$<br/>\begin{aligned}<br/>&amp; a=\frac{g \sin \theta}{1+I / m R^2} \\<br/>&amp; I_{\text {solid }} &lt; I_{\text {hollow }} \\<br/>\therefore \quad &amp; a_{\text {solid }}&gt;a_{\text {hollow }}<br/>\end{aligned}<br/>$$<br/>$\therefore$ solid cylinder will reach the bottom first.<br/>Further, in case of pure rolling on stationary ground, work done by friction is zero. Therefore, mechanical energy of both the cylinders will remain constant.<br/>$$<br/>\begin{aligned}<br/>&amp; \therefore(\mathrm{KE})_{\text {Hollow }}=(\mathrm{KE})_{\text {solid }}=\text { decrease in } \mathrm{PE}=m g h \\<br/>&amp; \therefore \text { correct option is }(\mathrm{d})<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Work Power Energy', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-i-a-block-of-mass-m-starts-moving-on-a-rough-horizontal-surface-with-a-velocity-v-it-stops-due-to-friction-between-the-block-and-the-surface

slug:
statement-i-a-block-of-mass-m-starts-moving-on-a-rough-horizontal-surface-with-a-velocity-v-it-stops-due-to-friction-between-the-block-and-the-surface-66941

question:
<div class="question">Statement I A block of mass $m$ starts moving on a rough horizontal surface with a velocity $v$. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of $30^{\circ}$ with the horizontal and the same block is made to go up on the surface with the same initial velocity $v$. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.<br/>Statement II The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is NOT a correct explanation for Statement I<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<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"><br/>Statement I is false, Statement II is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Statement I is true, Statement II is false<br/></span> </div>

answer:
<div class="solution">In statement I Decrease in mechanical energy in case I will be<br/>$$<br/>\Delta U_1=\frac{1}{2} m v^2<br/>$$<br/>But decrease in mechanical energy in case II will be<br/>$$<br/>\begin{aligned}<br/>&amp; \Delta U_2=\frac{1}{2} m v^2-m g h \\<br/>&amp; \Delta U_2 &lt; \Delta U_1<br/>\end{aligned}<br/>$$<br/>$$<br/>\therefore \quad \Delta U_2 &lt; \Delta U_1<br/>$$<br/>or Statement $\mathrm{I}$ is correct.<br/>In Statement II Coefficient of friction will not change or this Statement is wrong.<br/>$\therefore$ Option (c) is correct.</div>


tags: ['Physics', 'Laws of Motion', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
statement-i-a-cloth-covers-a-table-some-dishes-are-kept-on-it-the-cloth-can-be-pulled-out-without-dislodging-the-dishes-from-the-table-statement-ii-fo

slug:
statement-i-a-cloth-covers-a-table-some-dishes-are-kept-on-it-the-cloth-can-be-pulled-out-without-dislodging-the-dishes-from-the-table-statement-ii-fo-77607

question:
<div class="question">Statement I A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.<br/>Statement II For every action there is an equal and opposite reaction.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement.<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is NOT a correct explanation for Statement I<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">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Statement I is false, Statement II is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Statement I is true, Statement II is true; Statement II is NOT a correct explanation for Statement I<br/></span> </div>

answer:
<div class="solution">The cloth can be pulled out without dislodging the dishes from the table due to law of inertia, which is Newton's first law. While the Statement II is true, but it is Newton's third law.<br/>$\therefore$ Correct option is (b).</div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
statement-i-a-vertical-iron-rod-has-a-coil-of-wire-wound-over-it-at-the-bottom-end-an-alternating-current-flows-in-the-coil-the-rod-goes-through-a-con-1

slug:
statement-i-a-vertical-iron-rod-has-a-coil-of-wire-wound-over-it-at-the-bottom-end-an-alternating-current-flows-in-the-coil-the-rod-goes-through-a-con-1-40217

question:
<div class="question">Statement I A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as shown in the figure. The ring can float at a certain height above the coil.<br/>Statement II In the above situation, a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the the upward direction.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/VfxDHPfimERkhriPVyfbv6yyRPMB3cqA6B7YfjZ87qc.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement<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">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is NOT a correct explanation for Statement I<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Statement I is false, Statement II is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement<br/></span> </div>

answer:
<div class="solution">The induced current in the ring will interact with horizontal component of magnetic field and both will repel each other.<br/>This repulsion will balance the weight of ring.<br/>$$<br/>\text { Hence, option (a) is correct. }<br/>$$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
statement-i-a-vertical-iron-rod-has-a-coil-of-wire-wound-over-it-at-the-bottom-end-an-alternating-current-flows-in-the-coil-the-rod-goes-through-a-con

slug:
statement-i-a-vertical-iron-rod-has-a-coil-of-wire-wound-over-it-at-the-bottom-end-an-alternating-current-flows-in-the-coil-the-rod-goes-through-a-con-38131

question:
<div class="question">Statement I A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as shown in the figure. The ring can float at a certain height above the coil.<br/>Statement II In the above situation, a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the the upward direction.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/VfxDHPfimERkhriPVyfbv6yyRPMB3cqA6B7YfjZ87qc.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement<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">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is NOT a correct explanation for Statement I<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Statement I is false, Statement II is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement<br/></span> </div>

answer:
<div class="solution">The induced current in the ring will interact with horizontal component of magnetic field and both will repel each other.<br/>This repulsion will balance the weight of ring.<br/>$$<br/>\text { Hence, option (a) is correct. }<br/>$$</div>


tags: ['Chemistry', 's Block Elements', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
answer: <div class="solution">Alkali metals in ammonia gives blue colour due to ammoniated $e^{-}$</div>
source_db: MarksBatch2_P2.db
title:
statement-i-alkali-metals-dissolve-in-liquid-ammonia-to-give-blue-solutions-statement-ii-alkali-metals-in-liquid-ammonia-give-solvated-species-of-the-

slug:
statement-i-alkali-metals-dissolve-in-liquid-ammonia-to-give-blue-solutions-statement-ii-alkali-metals-in-liquid-ammonia-give-solvated-species-of-the-67150

question:
<div class="question">Statement I Alkali metals dissolve in liquid ammonia to give blue solutions. Statement II Alkali metals in liquid ammonia give solvated species of the type $\left(M\left(\mathrm{NH}_3\right)_n\right]^{+}(M=$ alkali metals $)$.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true, Statement II is a correct explanation for Statement I<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true, Statement II is not a correct explanation for Statement I<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">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Statement $\mathrm{I}$ is false, Statement $\mathrm{II}$ is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Statement I is true, Statement II is true, Statement II is not a correct explanation for Statement I<br/></span> </div>


tags: ['Chemistry', 'Structure of Atom', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
statement-i-band-gap-in-germanium-is-small-statement-ii-the-energy-spread-of-each-germanium-atomic-energy-level-is-infinitesimally-small

slug:
statement-i-band-gap-in-germanium-is-small-statement-ii-the-energy-spread-of-each-germanium-atomic-energy-level-is-infinitesimally-small-11424

question:
<div class="question">Statement I Band gap in germanium is small.<br/>Statement II The energy spread of each germanium atomic energy level is infinitesimally small.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true, Statement II is a correct explanation for Statement I<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true, Statement II is not a correct explanation for Statement I<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>Statement-I is true, Statement II is false<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"><br/>Statement-I is talse, Statement II is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Statement-I is true, Statement II is false<br/></span> </div>

answer:
<div class="solution">Germanium, semi-conductor substance, has small band gap in comparison to insulator (non-metal).<br/>On moving top to bottom in the group 14 band gap decreases.</div>


tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-i-boron-always-forms-covalent-bond-statement-ii-the-small-size-of-b-3-favours-formation-of-covalent-bond

slug:
statement-i-boron-always-forms-covalent-bond-statement-ii-the-small-size-of-b-3-favours-formation-of-covalent-bond-89710

question:
<div class="question">Statement I Boron always forms covalent bond<br/>Statement II The small size of $\mathrm{B}^{3+}$ favours formation of covalent bond.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true, Statement II is a correct explanation for Statement I<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">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true, Statement II is not a correct explanation for Statement II<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Statement I is false, Statement II is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Statement I is true, Statement II is true, Statement II is a correct explanation for Statement I<br/></span> </div>

answer:
<div class="solution">Boron always form covalent bond because boron requires very high energy to form $\mathrm{B}^{3+}$ and again $\mathrm{B}^{3+}$ due to its very small size having high polarising power thus cause greater polarisation and eventually significant covalent characteristics-Fajans rule.</div>


tags: ['Chemistry', 'Biomolecules', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
statement-i-glucose-gives-a-reddishbrown-precipitate-with-fehlings-solution-statement-ii-reaction-of-glucose-with-fehlings-solution-gives-cuo-and-gluc

slug:
statement-i-glucose-gives-a-reddishbrown-precipitate-with-fehlings-solution-statement-ii-reaction-of-glucose-with-fehlings-solution-gives-cuo-and-gluc-27236

question:
<div class="question">Statement I Glucose gives a reddish-brown precipitate with Fehling's solution. <br/>Statement II Reaction of glucose with Fehling's solution gives $\mathrm{CuO}$ and gluconic acid.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true, Statement II is a correct explanation for Statement I<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<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"><br/>Statement I is false, Statement II is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Statement I is true, Statement II is false<br/></span> </div>

answer:
<div class="solution">Glucose gives a reddish brown precipitate with Fehling's solution. Solution consists of $\mathrm{Cu}^{2+}$ which gets reduced to $\mathrm{Cu}^{+}\left(\mathrm{Cu}_2 \mathrm{O}\right)$.</div>


tags: ['Physics', 'Electromagnetic Waves', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-i-if-the-accelerating-potential-in-an-xray-tube-is-increased-the-wavelengths-of-the-characteristic-x-rays-do-not-change-statement-ii-when-an

slug:
statement-i-if-the-accelerating-potential-in-an-xray-tube-is-increased-the-wavelengths-of-the-characteristic-x-rays-do-not-change-statement-ii-when-an-99706

question:
<div class="question">Statement I If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic $X$-rays do not change.<br/>Statement II When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is NOT a correct explanation for Statement I<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">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Statement I is false, Statement II is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Statement I is true, Statement II is true; Statement II is NOT a correct explanation for Statement I<br/></span> </div>

answer:
<div class="solution">Cut-off wavelength depends on the accelerating voltage, not the characteristic $\mathrm{X}$-rays. Further approximately $2 \%$ kinetic energy of the electrons is utilised in producing X-rays. Rest $98 \%$ is lost in heat.<br/>$\therefore$ Option (b) is correct.</div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
statement-i-if-there-is-no-external-torque-on-a-body-about-its-centre-of-mass-then-the-velocity-of-the-centre-of-mass-remains-constant-statement-ii-th-1

slug:
statement-i-if-there-is-no-external-torque-on-a-body-about-its-centre-of-mass-then-the-velocity-of-the-centre-of-mass-remains-constant-statement-ii-th-1-45202

question:
<div class="question">Statement I If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass remains constant.<br/>Statement II The linear momentum of an isolated system remains constant.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is NOT a correct explanation for Statement I<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>Statement I is false, Statement II is true</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">If a force is applied at centre of mass of a rigid body, its torque about centre of mass will be zero, but acceleration will be non-zero. Hence, velocity will change.<br/>$\therefore$ Correct option is $(\mathrm{d})$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/yCSMAN6PC8Zm5HMTYvh9XI3XxhFUNW8AbOUSFFi7Klo.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
statement-i-if-there-is-no-external-torque-on-a-body-about-its-centre-of-mass-then-the-velocity-of-the-centre-of-mass-remains-constant-statement-ii-th

slug:
statement-i-if-there-is-no-external-torque-on-a-body-about-its-centre-of-mass-then-the-velocity-of-the-centre-of-mass-remains-constant-statement-ii-th-86432

question:
<div class="question">Statement I If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass remains constant.<br/>Statement II The linear momentum of an isolated system remains constant.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is NOT a correct explanation for Statement I<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>Statement I is false, Statement II is true</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">If a force is applied at centre of mass of a rigid body, its torque about centre of mass will be zero, but acceleration will be non-zero. Hence, velocity will change.<br/>$\therefore$ Correct option is $(\mathrm{d})$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/yCSMAN6PC8Zm5HMTYvh9XI3XxhFUNW8AbOUSFFi7Klo.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-i-in-an-elastic-collision-between-two-bodies-the-relative-speed-of-the-bodies-after-collision-is-equal-to-the-relative-speed-before-the-coll

slug:
statement-i-in-an-elastic-collision-between-two-bodies-the-relative-speed-of-the-bodies-after-collision-is-equal-to-the-relative-speed-before-the-coll-83084

question:
<div class="question">Statement I In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.<br/>Statement II In an elastic collision, the linear momentum of the system is conserved.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is NOT a correct explanation for Statement I<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">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Statement I is false, Statement II is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Statement I is true, Statement II is true; Statement II is NOT a correct explanation for Statement I<br/></span> </div>

answer:
<div class="solution">In case of elastic collision, coefficient of restitution $e=1$ or relative speed of separation.<br/>$\therefore$ Option (b) is correct.</div>


tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-i-in-water-orthoboric-acid-behaves-as-a-weak-monobasic-acid-statement-ii-in-water-orthoboric-acid-acts-as-proton-donor

slug:
statement-i-in-water-orthoboric-acid-behaves-as-a-weak-monobasic-acid-statement-ii-in-water-orthoboric-acid-acts-as-proton-donor-32516

question:
<div class="question">Statement I In water, orthoboric acid behaves as a weak monobasic acid.<br/>Statement II In water, orthoboric acid acts as proton donor.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true, Statement II is a correct explanation for Statement I<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true, Statement II is not a correct explanation for Statement I<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<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"><br/>Statement I is false, Statement II is true</span> </li> </ul>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/OQOeazUA4dd1iVMdu8Earsn8kQ_qy9Kvxjtan4JOfPw.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Surface Chemistry', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-i-micelles-are-formed-by-surfactant-molecules-above-the-critical-micellar-concentration-cmc-statement-ii-the-conductivity-of-a-solution-havi

slug:
statement-i-micelles-are-formed-by-surfactant-molecules-above-the-critical-micellar-concentration-cmc-statement-ii-the-conductivity-of-a-solution-havi-81694

question:
<div class="question">Statement I Micelles are formed by surfactant molecules above the critical micellar concentration (CMC).<br/>Statement II The conductivity of a solution having surfactant molecules deceases sharply at the CMC.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true, Statement II is a correct explanation for Statement I<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true, Statement II is not a correct explanation for Statement I<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">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Statement I is false, Statement II is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Statement I is true, Statement II is true, Statement II is not a correct explanation for Statement I<br/></span> </div>

answer:
<div class="solution">At a certain concentration surfactant molecules start to aggregate and form micelle, the concentration is called critical micellisation concentration (CMC).<br/>Aggregation of surfactant molecules (ions; $\mathrm{RCOO}^{-}$) micelle formation cause effective fall in number of free ions to conduct electricity, thus, conductivity decreases at CMC.</div>


tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
statement-i-molecules-that-are-not-superimposable-on-their-mirror-images-are-chiral-statement-ii-all-chiral-molecules-have-chiral-centres

slug:
statement-i-molecules-that-are-not-superimposable-on-their-mirror-images-are-chiral-statement-ii-all-chiral-molecules-have-chiral-centres-28170

question:
<div class="question">Statement I Molecules that are not superimposable on their mirror images are chiral.<br/>Statement II All chiral molecules have chiral centres.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<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"><br/>Statement I is false, Statement II is true</span> </li> </ul>

answer:
<div class="solution">Molecules having perpendicular dissymmetric plane are supposed to have chirality without having chiral centre. For e.g.,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tFZQfp6dezjS_ydCk6zaEP0IrdkNJY4UgtYbHYTq-QA.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/AsUh76Jmb6CwH1mbL_ZMG1i0cP_tL_B3nNt9rET_bhg.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'General Organic Chemistry', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
statement-i-phydroxybenzoic-acid-has-a-lower-boiling-point-than-ohydroxybenzoic-acid-statement-ii-ohydroxybenzoic-acid-has-intramolecular-hydrogen-bon-1

slug:
statement-i-phydroxybenzoic-acid-has-a-lower-boiling-point-than-ohydroxybenzoic-acid-statement-ii-ohydroxybenzoic-acid-has-intramolecular-hydrogen-bon-1-93107

question:
<div class="question">Statement I p-hydroxybenzoic acid has a lower boiling point than o-hydroxybenzoic acid.<br/>Statement II o-hydroxybenzoic acid has intramolecular hydrogen bonding.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true, Statement II is a correct explanation for Statement I<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true, Statement II is not a correct explanation for Statement I<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>Statement I is false, Statement II is true</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/MOtOUfxobjJjqb-CQckuxAPH5FCfWdzfvPVBLkeL73U.original.fullsize.png"/><br/></div>


