# questions

tags: ['Physics', 'Waves and Sound']
source_db: MarksBatch1_P1.db
title:
a-transverse-harmonic-wave-on-a-string-is-described-by-y-x-t-30-sin-36-t-0018-x-4-where-x-and-y-in-cm-and-t-is-in-sec-the-positive-direction-of-x-is-f

slug:
a-transverse-harmonic-wave-on-a-string-is-described-by-y-x-t-30-sin-36-t-0018-x-4-where-x-and-y-in-cm-and-t-is-in-sec-the-positive-direction-of-x-is-f-23394

question:
<div class="question">A transverse harmonic wave on a string is described by $y(x, t)=3.0 \sin \left(36 t+0.018 x+\frac{\pi}{4}\right)$ where $x$ and $y$ in $\mathrm{cm}$ and $t$ is in sec. The positive direction of $x$ is from left to right.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>the wave is travelling from right to left<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">B</span> <span class="option-data"><br/>the speed of the wave is $20 \mathrm{~m} / \mathrm{s}$<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="correct"> <span class="option-label">C</span> <span class="option-data"><br/>frequency of the wave is $5.7 \mathrm{~Hz}$<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">D</span> <span class="option-data"><br/>the least distance between two successive crests in the wave is $2.5 \mathrm{~cm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>the wave is travelling from right to left<br/>, <br/>the speed of the wave is $20 \mathrm{~m} / \mathrm{s}$<br/>, <br/>frequency of the wave is $5.7 \mathrm{~Hz}$<br/></span> </div>

answer:
<div class="solution">As given equation<br/>$$<br/>y(x, t)=3.0 \sin \left(36 t+0.018 x+\frac{\pi}{4}\right)<br/>$$<br/>As we know that the standard form of wave propagated from left to right in (+ve) direction.<br/>$$<br/>y=a \sin (\omega t+k x+\phi)<br/>$$<br/>(a) As the given equation involves positive sign with $x$, hence the given wave travelling from right to left. Hence, option (a) is correct.<br/>(b) Compare given equation to standard equation<br/>$$<br/>\begin{aligned}<br/>&amp;\omega=36 \Rightarrow 2 \pi v=36 \\<br/>&amp;v=\text { frequency }=\frac{36}{2 \pi}=\frac{18}{\pi}=5.7 \mathrm{~Hz} \\<br/>&amp;k=0.018 \\<br/>&amp;\Rightarrow \frac{2 \pi}{\lambda}=0.018 \\<br/>&amp;\lambda=\left(\frac{2 \pi}{0.018}\right)<br/>\end{aligned}<br/>$$<br/>We know that,<br/>$$<br/>\begin{aligned}<br/>&amp;v=v \lambda=\frac{18}{\pi} * \frac{2 \pi}{0.018} \\<br/>&amp;=2000 \mathrm{~cm} / \mathrm{sec}=20 \mathrm{~m} / \mathrm{sec}<br/>\end{aligned}<br/>$$<br/>(c) $v$ is the frequency which can be find by compairing given equation to standard equation<br/>So, $v=\frac{36}{2 \pi} \mathrm{Hz}=\frac{18}{\pi}=5.7 \mathrm{~Hz}$<br/>(d) Distance between two successive crests $(\lambda)$<br/>$$<br/>\begin{aligned}<br/>\lambda &amp;=\frac{2 \pi}{0.018} \mathrm{~cm} \\<br/>&amp;=\frac{2000 \pi}{18} \mathrm{~cm}=\frac{20 \pi}{18} \mathrm{~m}=3.48 \mathrm{~m} .<br/>\end{aligned}<br/>$$<br/>Hence, least distance between two successive crests $=\lambda=3.48 \mathrm{~m}$, this is not equal to $2.5 \mathrm{~cm}$.<br/>Hence, option (d) is not verified.</div>


tags: ['Biology', 'Anatomy of Flowering Plants']
options: None
correct_option: None
source_db: MarksBatch1_P1.db
title:
a-transverse-section-of-the-trunk-of-a-tree-shows-concentric-rings-which-are-known-as-growth-rings-how-are-these-rings-formed-what-is-the-significance

slug:
a-transverse-section-of-the-trunk-of-a-tree-shows-concentric-rings-which-are-known-as-growth-rings-how-are-these-rings-formed-what-is-the-significance-49660

question:
<div class="question">A transverse section of the trunk of a tree shows concentric rings which are known as growth rings. How are these rings formed? What is the significance of these rings?</div>

answer:
<div class="solution">The concentric growth rings are called annual rings. These rings are formed due to the secondary growth. Secondary growth occurs due to the activity of cambium which is a meristermatic tissue in dicot trees.<br/>The rate of activity of cambium is more in spring so wood formed has larger wider xylem cells, whereas wood formed in autumn has narrower and smaller xylem elements. This results in the formation of two rings called growth rings. By counting these rings, age of the tree can be determined. This branch of science is known as dendrochronology or growth ring analysis.</div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2021 (22 Sep Shift 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">15m</span> </div>
source_db: MarksBatch1_P1.db
title:
a-transverse-wave-given-by-y-2-sin-001-x-30-t-moves-on-a-stretched-string-from-one-end-to-another-end-in-05-second-if-x-and-y-are-in-cm-and-t-is-in-se

slug:
a-transverse-wave-given-by-y-2-sin-001-x-30-t-moves-on-a-stretched-string-from-one-end-to-another-end-in-05-second-if-x-and-y-are-in-cm-and-t-is-in-se-75358

question:
<div class="question">A transverse wave given by $\mathrm{y}=2 \sin (0.01 \mathrm{x}+30 \mathrm{t})$ moves on a stretched string from one end to another end in 0.5 second. If ' $x$ ' and ' $y$ ' are in $\mathrm{cm}$ and ' $\mathrm{t}$ ' is in second, then the length of the string is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">6m</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">9m</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">12m</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">15m</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Comparing with the standard equation<br/>$$<br/>\mathrm{y}=\mathrm{A} \sin (\mathrm{kx}+\omega \mathrm{t})<br/>$$<br/>we get $\mathrm{k}=0.01 \mathrm{rad} / \mathrm{cm}$ and $\omega=30 \mathrm{rad} / \mathrm{s}$<br/>speed of the wave, $v=\frac{\omega}{\mathrm{k}}=\frac{30}{0.01}=300 \mathrm{~cm} / \mathrm{s}=30 \mathrm{~m} / \mathrm{s}$<br/>$\therefore$ Distance $=\mathrm{vt}=30 \times 0.5=15 \mathrm{~m}$</div>


tags: ['Physics', 'Waves and Sound', 'AP EAMCET', 'AP EAMCET 2015']
source_db: MarksBatch1_P1.db
title:
a-transverse-wave-is-represented-by-the-equation-y-2-sin-30-t-40-x-and-the-measurements-of-distances-are-in-meters-then-the-velocity-of-propagation-is

slug:
a-transverse-wave-is-represented-by-the-equation-y-2-sin-30-t-40-x-and-the-measurements-of-distances-are-in-meters-then-the-velocity-of-propagation-is-51021

question:
<div class="question">A transverse wave is represented by the equation $y=2 \sin (30 t-40 x)$ and the measurements of distances are in meters, then the velocity of propagation is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$15\ ms{-1}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$0.75\ ms{-1}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3.75\ ms{-1}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$300\ ms{-1}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.75\ ms{-1}$</span> </div>

answer:
<div class="solution">We have $y=2 \sin (30 t-40 x)$<br/>The standard transverse wave is $y=A \sin (\omega t-k x)$<br/>So, $\omega=30$ and $k=40$<br/>On comparing, we get<br/>$v=\frac{\omega}{k}=\frac{30}{40}=0.75 \mathrm{~m} / \mathrm{s}$</div>


tags: ['Physics', 'Dual Nature of Matter', 'JIPMER', 'JIPMER 2013']
source_db: MarksBatch1_P1.db
title:
a-transverse-wave-is-represented-by-the-equation-y-y-0-sin-2-v-t-k-for-what-value-of-is-the-particle-velocity-equal-to-two-times-the-wave-velocity

slug:
a-transverse-wave-is-represented-by-the-equation-y-y-0-sin-2-v-t-k-for-what-value-of-is-the-particle-velocity-equal-to-two-times-the-wave-velocity-36480

question:
<div class="question">A transverse wave is represented by the equation<br/>$y=y_0 \sin \frac{2 \pi}{\lambda}(v t-k)$<br/>For what value of $\lambda$ is the particle velocity equal to two times the wave velocity</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\lambda=\pi y_0$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\lambda=\frac{\pi y_0}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\lambda=\frac{\pi y_0}{3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\lambda=2 \pi i y_0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\lambda=\pi y_0$</span> </div>

answer:
<div class="solution">Comparing the given equation of the standard equation of wave<br/>$\begin{aligned} w y_0 &amp; =2 v \\ 2 \pi n y_0 &amp; =2 n \lambda, \\ \lambda &amp; =\pi y_0\end{aligned}$</div>


tags: ['Physics', 'Waves and Sound', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-transverse-wave-propagating-along-the-x-axis-is-represented-by-y-x-t-8-0-sin-0-5-x-4-t-4-where-x-is-in-metres-and-t-is-in-seconds-the-speed-of-the-w

slug:
a-transverse-wave-propagating-along-the-x-axis-is-represented-by-y-x-t-8-0-sin-0-5-x-4-t-4-where-x-is-in-metres-and-t-is-in-seconds-the-speed-of-the-w-98657

question:
<div class="question">A transverse wave propagating along the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis is represented by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>(</mo><mi>x</mi><mo>,</mo><mo> </mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>8</mn><mo>.</mo><mn>0</mn><mo> </mo><mi>sin</mi><mo> </mo><mo>(</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>Ï</mi><mi>x</mi><mo>â</mo><mn>4</mn><mi>Ï</mi><mi>t</mi><mo>â</mo><mi>Ï</mi><mo>/</mo><mn>4</mn><mo>)</mo></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> is in metres and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is in seconds. The speed of the wave is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math><mn>8</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></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">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mi mathvariant="normal">π</mi><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.5</mn><mi mathvariant="normal">Ï</mi><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac bevelled="true"><mi mathvariant="normal">π</mi><mn>4</mn></mfrac><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>8</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </div>

answer:
<div class="solution"><math> <mrow> <mi>y</mi> <mfenced close=")" open="(" separators=","> <mrow> <mi>x</mi> </mrow> <mrow> <mi>t</mi> </mrow> </mfenced> <mo>=</mo> <mn>8</mn> <mo>Â·</mo> <mn>0</mn> <mspace width="0.5em"></mspace> <mtext>sin</mtext> <mfenced close=")" open="(" separators=","> <mrow> <mn>0</mn> <mo>Â·</mo> <mn>5</mn> <mi>Ï</mi> <mi>x</mi> <mo>-</mo> <mn>4</mn> <mi>Ï</mi> <mi>t</mi> <mo>-</mo> <mfrac> <mrow> <mi>Ï</mi> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> </mrow> </mfenced> </mrow> </math><br/><br/>Compare with a standard wave equation,<br/><br/><math> <mrow> <mi>y</mi> <mo>=</mo> <mi>a</mi> <mspace width="0.5em"></mspace> <mtext>sin</mtext> <mfenced close=")" open="(" separators=","> <mrow> <mfrac> <mrow> <mn>2</mn> <mi>Ï</mi> <mi>x</mi> </mrow> <mrow> <mi>Î»</mi> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <mn>2</mn> <mi>Ï</mi> <mi>t</mi> </mrow> <mrow> <mi></mi><mi></mi><mi></mi><mi></mi><mi>T</mi><mo>â¡</mo> </mrow> </mfrac> <mo>+</mo> <mi>Ï</mi> </mrow> </mfenced> </mrow> </math><br/><br/><math> <mrow> <mtext>we get </mtext> <mfrac> <mrow> <mn>2</mn> <mi>Ï</mi> </mrow> <mrow> <mi>Î»</mi> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> <mo>Â·</mo> <mn>5</mn> <mi>Ï</mi> <mspace width="0.5em"></mspace> <mspace width="0.5em"></mspace> <mtext>or,</mtext> <mspace width="0.5em"></mspace> <mspace width="0.5em"></mspace> <mi>Î»</mi> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>Ï</mi> </mrow> <mrow> <mn>0</mn> <mo>Â·</mo> <mn>5</mn> <mi>Ï</mi> </mrow> </mfrac> <mo>=</mo> <mn>4</mn> <mspace width="0.5em"></mspace> <mtext>m</mtext> </mrow> </math><br/><br/><math> <mrow> <mfrac> <mrow> <mn>2</mn> <mi>Ï</mi> </mrow> <mrow> <mi></mi><mi></mi><mi>T</mi><mo>â¡</mo> </mrow> </mfrac> <mo>=</mo> <mn>4</mn> <mi>Ï</mi> <mspace width="0.5em"></mspace> <mspace width="0.5em"></mspace> <mtext>or,</mtext> <mspace width="0.5em"></mspace> <mspace width="0.5em"></mspace> <mi></mi><mi></mi><mi>T</mi><mo>â¡</mo> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>Ï</mi> </mrow> <mrow> <mn>4</mn> <mi>Ï</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mi></mi><mi>s</mi><mo>â¡</mo> </mrow> </math><br/><br/><math> <mrow> <mi>Ï</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mtext mathvariant="italic">T</mtext> <mo>=</mo> <mtext>2 Hz</mtext> </mrow> </math><br/><br/>Wave velocity, <math> <mrow> <mi>Î½</mi> <mo>=</mo> <mi>Î»</mi> <mi>Ï</mi> <mo>=</mo> <mn>4</mn> <mo>Ã</mo> <mn>2</mn> <mo>=</mo> <mn>8</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup> </mrow></math></div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch1_P1.db
title:
a-transverse-wave-propagating-along-the-x-axis-is-represented-by-y-x-t-8-0-sin-0-5-x-4-t-4-where-x-is-in-metres-and-t-is-in-seconds-what-is-the-speed-

slug:
a-transverse-wave-propagating-along-the-x-axis-is-represented-by-y-x-t-8-0-sin-0-5-x-4-t-4-where-x-is-in-metres-and-t-is-in-seconds-what-is-the-speed-31522

question:
<div class="question">A transverse wave propagating along the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis is represented by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>(</mo><mi>x</mi><mo>,</mo><mo> </mo><mi>t</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mn>8</mn><mo>.</mo><mn>0</mn><mo> </mo><mi>sin</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>Ï</mi><mi>x</mi><mo> </mo><mo>â</mo><mo> </mo><mn>4</mn><mi>Ï</mi><mi>t</mi><mo> </mo><mo>â</mo><mo> </mo><mfrac bevelled="true"><mi>Ï</mi><mn>4</mn></mfrac><mo>)</mo></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> is in metres and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is in seconds. What is the speed (in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>) of the wave?</div>

answer:
<div class="solution"><math> <mrow> <mi>y</mi> <mfenced close=")" open="(" separators=","> <mrow> <mi>x</mi> </mrow> <mrow> <mi>t</mi> </mrow> </mfenced> <mo>=</mo> <mn>8</mn> <mo>·</mo> <mn>0</mn> <mspace width="0.5em"></mspace> <mtext>sin</mtext> <mfenced close=")" open="(" separators=","> <mrow> <mn>0</mn> <mo>·</mo> <mn>5</mn> <mi>π</mi> <mi>x</mi> <mo>-</mo> <mn>4</mn> <mi>π</mi> <mi>t</mi> <mo>-</mo> <mfrac> <mrow> <mi>π</mi> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> </mrow> </mfenced> </mrow> </math><br/><br/>Compare with a standard wave equation,<br/><br/><math> <mrow> <mi>y</mi> <mo>=</mo> <mi>a</mi> <mspace width="0.5em"></mspace> <mtext>sin</mtext> <mfenced close=")" open="(" separators=","> <mrow> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> <mi>x</mi> </mrow> <mrow> <mi>λ</mi> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> <mi>t</mi> </mrow> <mrow> <mi></mi><mi></mi><mi></mi><mi></mi><mi>T</mi><mo>⁡</mo> </mrow> </mfrac> <mo>+</mo> <mi>ϕ</mi> </mrow> </mfenced> </mrow> </math><br/><br/><math> <mrow> <mtext>we get </mtext> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mrow> <mi>λ</mi> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> <mo>·</mo> <mn>5</mn> <mi>π</mi> <mspace width="0.5em"></mspace> <mspace width="0.5em"></mspace> <mtext>or,</mtext> <mspace width="0.5em"></mspace> <mspace width="0.5em"></mspace> <mi>λ</mi> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mrow> <mn>0</mn> <mo>·</mo> <mn>5</mn> <mi>π</mi> </mrow> </mfrac> <mo>=</mo> <mn>4</mn> <mspace width="0.5em"></mspace> <mtext>m</mtext> </mrow> </math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mi>T</mi><mo>⁡</mo></mrow></mfrac><mo>=</mo><mn>4</mn><mi>π</mi><mspace width="0.5em"></mspace><mspace width="0.5em"></mspace><mtext>or,</mtext><mspace width="0.5em"></mspace><mspace width="0.5em"></mspace><mi>T</mi><mo>⁡</mo><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mn>4</mn><mi>π</mi></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo> </mo><mi mathvariant="normal">s</mi></math><br/><br/><math> <mrow> <mi>υ</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mtext mathvariant="italic">T</mtext> <mo>=</mo> <mtext>2 Hz</mtext> </mrow> </math><br/><br/>Wave velocity, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ν</mi><mo>=</mo><mi>λ</mi><mi>υ</mi><mo>=</mo><mn>4</mn><mo>×</mo><mn>2</mn><mo>=</mo><msup><mtext>8 m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></div>


tags: ['Physics', 'Waves and Sound', 'NEET', 'NEET 2006']
source_db: MarksBatch1_P1.db
title:
a-transverse-wave-propagating-along-x-axis-is-represented-by-y-x-t-80-sin-05-x-4-t-4-where-x-is-in-metres-and-t-is-in-seconds-the-speed-of-the-wave-is

slug:
a-transverse-wave-propagating-along-x-axis-is-represented-by-y-x-t-80-sin-05-x-4-t-4-where-x-is-in-metres-and-t-is-in-seconds-the-speed-of-the-wave-is-43325

question:
<div class="question">A transverse wave propagating along $x$-axis is represented by $y(x, t)=8.0$ $\sin (0.5 \pi x-4 \pi t-\pi / 4)$ where $x$ is in metres and $t$ is in seconds. The speed of the wave is:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$8 \mathrm{~m} / \mathrm{s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$4 \pi \mathrm{m} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.5 \pi \mathrm{m} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{2} \mathrm{~m} / \mathrm{s}$</span> </li> </ul>

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

answer:
<div class="solution">It is given that:<br/>$$<br/>y\left(x_1 t\right)=8.0 \sin \left(0.5 \pi x-4 \pi t-\frac{\lambda}{9}\right)<br/>$$<br/>Compare this equation with standard equation<br/>$$<br/>y=a \sin \left(\frac{2 \pi x}{\lambda}-\frac{2 \pi t}{\mathrm{~T}}+\phi\right)<br/>$$<br/>we have<br/>$$<br/>\begin{aligned}<br/>\frac{2 \pi}{\lambda} &amp; =0.5 \pi \\<br/>\Rightarrow \quad \lambda &amp; =\frac{2 \pi}{0.5 \pi}=4 \mathrm{~m} \\<br/>\frac{2 \pi}{T} &amp; =4 \pi \\<br/>\Rightarrow \quad T &amp; =\frac{1}{2} \sec \\<br/>U=\frac{1}{T} &amp; =\frac{1}{y_2}=2 \mathrm{H}_2 .<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Waves and Sound', 'AP EAMCET', 'AP EAMCET 2005']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0.48</span> </div>
source_db: MarksBatch1_P1.db
title:
a-transverse-wave-propagating-on-a-stretched-string-of-linear-density-3-1-0-4-kg-m-1-is-represented-by-the-equation-y-02-sin-15-x-60-t-where-x-is-in-m-1

slug:
a-transverse-wave-propagating-on-a-stretched-string-of-linear-density-3-1-0-4-kg-m-1-is-represented-by-the-equation-y-02-sin-15-x-60-t-where-x-is-in-m-1-50555

question:
<div class="question">A transverse wave propagating on a stretched string of linear density $3 \times 10^{-4} \mathrm{~kg} \mathrm{~m}^{-1}$ is represented by the equation $y=0.2 \sin (15 x+60 t)$<br/>where $x$ is in metres and $t$ is in seconds. The tension in the string (in newton) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0.24</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">0.48</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1.20</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1.80</span> </li> </ul>

answer:
<div class="solution">Equation of wave, $y=0.2 \sin (1.5 x+60 t)$ Comparing with standard equation,<br/>$\begin{aligned}<br/>&amp; y=A \sin (k x+\omega t) \\<br/>&amp; k=1.5, \omega=60 \mathrm{rad} / \mathrm{s}<br/>\end{aligned}$<br/>$\therefore$ Velocity of wave, $v=\frac{\omega}{k}=\frac{60}{1.5}=40 \mathrm{~m} / \mathrm{s}$<br/>Velocity of wave in a stretched string,<br/>$v=\sqrt{\frac{T}{m}}$<br/>where $m=$ linear density<br/>$T=\text { tension in the string }$<br/>So,<br/>$\begin{aligned}<br/>T &amp; =v^2 m \\<br/>&amp; =(40)^2 \times 3 \times 10^{-4}=0.48<br/>\end{aligned}$</div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0.48</span> </div>
source_db: MarksBatch1_P1.db
title:
a-transverse-wave-propagating-on-a-stretched-string-of-linear-density-3-1-0-4-kg-m-1-is-represented-by-the-equation-y-02-sin-15-x-60-t-where-x-is-in-m-2

slug:
a-transverse-wave-propagating-on-a-stretched-string-of-linear-density-3-1-0-4-kg-m-1-is-represented-by-the-equation-y-02-sin-15-x-60-t-where-x-is-in-m-2-20190

question:
<div class="question">A transverse wave propagating on a stretched string of linear density $3 \times 10^{-4} \mathrm{~kg} \mathrm{~m}^{-1}$ is represented by the equation $y=0.2 \sin (15 x+60 t)$<br/>where $x$ is in metres and $t$ is in seconds. The tension in the string (in newton) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0.24</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">0.48</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1.20</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1.80</span> </li> </ul>

answer:
<div class="solution">Equation of wave, $y=0.2 \sin (1.5 x+60 t)$ Comparing with standard equation,<br/>$\begin{aligned}<br/>&amp; y=A \sin (k x+\omega t) \\<br/>&amp; k=1.5, \omega=60 \mathrm{rad} / \mathrm{s}<br/>\end{aligned}$<br/>$\therefore$ Velocity of wave, $v=\frac{\omega}{k}=\frac{60}{1.5}=40 \mathrm{~m} / \mathrm{s}$<br/>Velocity of wave in a stretched string,<br/>$v=\sqrt{\frac{T}{m}}$<br/>where $m=$ linear density<br/>$T=\text { tension in the string }$<br/>So,<br/>$\begin{aligned}<br/>T &amp; =v^2 m \\<br/>&amp; =(40)^2 \times 3 \times 10^{-4}=0.48<br/>\end{aligned}$</div>


tags: ['Physics', 'Waves and Sound', 'TS EAMCET', 'TS EAMCET 2005']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0.48</span> </div>
source_db: MarksBatch1_P1.db
title:
a-transverse-wave-propagating-on-a-stretched-string-of-linear-density-3-1-0-4-kg-m-1-is-represented-by-the-equation-y-02-sin-15-x-60-t-where-x-is-in-m

slug:
a-transverse-wave-propagating-on-a-stretched-string-of-linear-density-3-1-0-4-kg-m-1-is-represented-by-the-equation-y-02-sin-15-x-60-t-where-x-is-in-m-29481

question:
<div class="question">A transverse wave propagating on a stretched string of linear density $3 \times 10^{-4} \mathrm{~kg} \mathrm{~m}^{-1}$ is represented by the equation $y=0.2 \sin (15 x+60 t)$<br/>where $x$ is in metres and $t$ is in seconds. The tension in the string (in newton) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0.24</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">0.48</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1.20</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1.80</span> </li> </ul>

answer:
<div class="solution">Equation of wave, $y=0.2 \sin (1.5 x+60 t)$ Comparing with standard equation,<br/>$\begin{aligned}<br/>&amp; y=A \sin (k x+\omega t) \\<br/>&amp; k=1.5, \omega=60 \mathrm{rad} / \mathrm{s}<br/>\end{aligned}$<br/>$\therefore$ Velocity of wave, $v=\frac{\omega}{k}=\frac{60}{1.5}=40 \mathrm{~m} / \mathrm{s}$<br/>Velocity of wave in a stretched string,<br/>$v=\sqrt{\frac{T}{m}}$<br/>where $m=$ linear density<br/>$T=\text { tension in the string }$<br/>So,<br/>$\begin{aligned}<br/>T &amp; =v^2 m \\<br/>&amp; =(40)^2 \times 3 \times 10^{-4}=0.48<br/>\end{aligned}$</div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-transverse-wave-propagating-on-a-stretched-string-of-linear-density-3-10-4-kgm-1-is-represented-by-the-equation-y-0-2-sin-1-5-x-60-t-where-x-in-metr-1

slug:
a-transverse-wave-propagating-on-a-stretched-string-of-linear-density-3-10-4-kgm-1-is-represented-by-the-equation-y-0-2-sin-1-5-x-60-t-where-x-in-metr-1-11902

question:
<div class="question"><p>A transverse wave propagating on a stretched string of linear density <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup><mo> </mo><msup><mi>kgm</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> is represented by the equation</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><mi>sin</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>60</mn><mi>t</mi><mo>)</mo></math></p><p>where, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> in metres and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is in seconds. The tension in the string (in Newton) is</p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>24</mn></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>48</mn></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">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>20</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>80</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>48</mn></math></span> </div>

answer:
<div class="solution"><p>Equation of wave, </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><mi>sin</mi><mo>[</mo><mn>1</mn><mo>.</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>60</mn><mi>t</mi><mo>]</mo></math></p><p>Comparing with standard equation, we get </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>A</mi><mi>sin</mi><mo>[</mo><mi>k</mi><mi>x</mi><mo>+</mo><mi>ω</mi><mi>t</mi><mo>]</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mi>λ</mi></mfrac></math></p><p>and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>=</mo><mn>60</mn><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mi>T</mi></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Velocity of wave, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfrac><mi>ω</mi><mi>k</mi></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>60</mn><mrow><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfrac><mo>=</mo><mn>40</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p>Velocity of wave in stretched string, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msqrt><mfrac><mi>T</mi><mi>m</mi></mfrac></msqrt></math></p><p>where, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> is the linear density, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> is tension in the string.</p><p>So, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><msup><mi>v</mi><mn>2</mn></msup><mi>m</mi><mo>=</mo><mo>(</mo><mn>40</mn><msup><mo>)</mo><mn>2</mn></msup><mo>×</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>48</mn><mo> </mo><mi mathvariant="normal">N</mi></math></p></div>


tags: ['Physics', 'Waves and Sound', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P1.db
title:
a-transverse-wave-propagating-on-a-stretched-string-of-linear-density-3-10-4-kgm-1-is-represented-by-the-equation-y-0-2-sin-1-5-x-60-t-where-x-in-metr

slug:
a-transverse-wave-propagating-on-a-stretched-string-of-linear-density-3-10-4-kgm-1-is-represented-by-the-equation-y-0-2-sin-1-5-x-60-t-where-x-in-metr-12814

question:
<div class="question"><p>A transverse wave propagating on a stretched string of linear density <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup><mo> </mo><msup><mi>kgm</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> is represented by the equation</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><mi>sin</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>60</mn><mi>t</mi><mo>)</mo></math></p><p>where, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> in metres and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is in seconds. The tension in the string (in Newton) is</p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>24</mn></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>48</mn></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">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>20</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>80</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>48</mn></math></span> </div>

answer:
<div class="solution"><p>Equation of wave, </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><mi>sin</mi><mo>[</mo><mn>1</mn><mo>.</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>60</mn><mi>t</mi><mo>]</mo></math></p><p>Comparing with standard equation, we get </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>A</mi><mi>sin</mi><mo>[</mo><mi>k</mi><mi>x</mi><mo>+</mo><mi>ω</mi><mi>t</mi><mo>]</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mi>λ</mi></mfrac></math></p><p>and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>=</mo><mn>60</mn><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mi>T</mi></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Velocity of wave, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfrac><mi>ω</mi><mi>k</mi></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>60</mn><mrow><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfrac><mo>=</mo><mn>40</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p>Velocity of wave in stretched string, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msqrt><mfrac><mi>T</mi><mi>m</mi></mfrac></msqrt></math></p><p>where, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> is the linear density, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> is tension in the string.</p><p>So, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><msup><mi>v</mi><mn>2</mn></msup><mi>m</mi><mo>=</mo><mo>(</mo><mn>40</mn><msup><mo>)</mo><mn>2</mn></msup><mo>×</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>48</mn><mo> </mo><mi mathvariant="normal">N</mi></math></p></div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2023 (11 May Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-transverse-wave-y-2-sin-001-x-30-t-moves-on-a-stretched-string-from-one-end-to-another-end-in-05-second-if-x-and-y-are-in-cm-and-t-in-second-then-th

slug:
a-transverse-wave-y-2-sin-001-x-30-t-moves-on-a-stretched-string-from-one-end-to-another-end-in-05-second-if-x-and-y-are-in-cm-and-t-in-second-then-th-49239

question:
<div class="question">A transverse wave $\mathrm{Y}=2 \sin (0.01 \mathrm{x}+30 \mathrm{t})$ moves on a stretched string from one end to another end in 0.5 second. If $x$ and $y$ are in $\mathrm{cm}$ and $\mathrm{t}$ in second, then the length of the string is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$10 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$15 \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$20 \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$15 \mathrm{~m}$</span> </div>

answer:
<div class="solution">Given $Y=2 \sin (0.01 \mathrm{x}+30 \mathrm{t})$<br/>Comparing with standard equation,<br/>$$<br/>\begin{aligned}<br/>\mathrm{Y} &amp; =\mathrm{A} \sin (\mathrm{kx}+\omega \mathrm{t}), \\<br/>\therefore \quad \mathrm{k} &amp; =0.01 / \mathrm{cm} \\<br/>\omega &amp; =30 \mathrm{rad} / \mathrm{s}<br/>\end{aligned}<br/>$$<br/>$$<br/>\begin{aligned}<br/>\text { Velocity } \mathrm{v} &amp; =\frac{\omega}{\mathrm{k}}=\frac{30}{0.01}=3000 \mathrm{~cm} / \mathrm{s} \\<br/>\therefore \quad \text { Length } \mathrm{L} &amp; =\mathrm{v} \times \mathrm{t}=30 \times 0.5 \\<br/>&amp; =15 \mathrm{~m}<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Waves and Sound']
options: None
correct_option: None
source_db: MarksBatch1_P1.db
title:
a-travelling-harmonic-wave-on-a-string-is-described-by-y-x-t-75-sin-00050-x-12-t-4-i-wha-t-a-re-t-h-e-d-i-s-pl-a-ce-m-e-n-t-an-d-v-e-l-oc-i-t-yo-f-osc

slug:
a-travelling-harmonic-wave-on-a-string-is-described-by-y-x-t-75-sin-00050-x-12-t-4-i-wha-t-a-re-t-h-e-d-i-s-pl-a-ce-m-e-n-t-an-d-v-e-l-oc-i-t-yo-f-osc-31075

question:
<div class="question">A travelling harmonic wave on a string is described by<br/>$$<br/>y(x, t)=7.5 \sin \left(0.0050 x+12 t+\frac{\pi}{4}\right)<br/>$$<br/>(i) What are the displacement and velocity of oscillation of a point at $x=1 \mathrm{~cm}$, and $t=1 \mathrm{~s}$ ? Is this velocity equal to the velocity of wave propagation?<br/>(ii) Locate the points of the string, which have the same transverse displacement and velocity as the $x=1 \mathrm{~cm}$ point at $t=2 \mathrm{~s}, 5 \mathrm{~s}$ and $11 \mathrm{~s}$.</div>

answer:
<div class="solution">Given, $y(x, t)=7.5 \sin (0.0050 x+12 t+\pi / 4)$ $=7.5 \sin \left[0.0050\left\{\frac{12}{0.0050} t+x\right\}+\pi / 4\right] \ldots(1)$<br/>Comparing it with standard equation of travelling wave<br/>$$<br/>y=a \sin \left[\frac{2 \pi}{\lambda}\{v t+x\}+\phi\right]<br/>$$<br/>Comparing equations (1) and (2), we get $a=7.5 \mathrm{~cm}, v=\frac{12}{0.0050} \mathrm{~cm} \mathrm{~s}^{-1}$ and $\frac{2 \pi}{\lambda}=0.0050 \mathrm{~cm}^{-1}$<br/>(i) At $x=1 \mathrm{~cm}$ and $t=1 \mathrm{~s}$, displacement is $y=7.5 \sin (0.0050 \times 1+12 \times 1+\pi / 4)$ $=7.5 \sin 12.79$<br/>$=7.5 \times 0.2222=1.67 \mathrm{~cm}$.<br/>Velocity of oscillation of the particle is<br/>$$<br/>\begin{aligned}<br/>&amp;u=\frac{d y}{d t}=\frac{d}{d t}[7.5 \sin (0.0050 x+12 t+\pi / 4)] \\<br/>&amp;=7.5 \times 12 \cos (0.0050 x+12 t+\pi / 4) \\<br/>&amp;=90 \cos \left(0.0050 x+12 t+\frac{\pi}{4}\right) \\<br/>&amp;\text { At } x=1 \mathrm{~cm} \text { and } t=1 \mathrm{~s}, \\<br/>&amp;u=90 \cos (0.000050 \times 1+12 \times 1+\pi / 4) \\<br/>&amp;=90 \cos 12.79 \\<br/>&amp;=90 \times 0.9751=87.76 \mathrm{~cm} \mathrm{~s}^{-1}<br/>\end{aligned}<br/>$$<br/>Velocity of wave propagation is $v=\frac{12}{0.0050}=2400 \mathrm{~cm} \mathrm{~s}^{-1}$<br/>$\therefore$ Velocity of oscillation of a point is not equal to the velocity of wave propagation.<br/>(ii) As $\frac{2 \pi}{\lambda}-0.0050$<br/>$$<br/>\therefore \lambda=\frac{2 \pi}{0.0050}=1256.64 \mathrm{~cm}<br/>$$<br/>All points located at distance $n \lambda$ (where $n$ is an integer) from the point $x=1 \mathrm{~cm}$ have the same transverse displacement and velocity.</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-triangular-plane-abc-with-centroid-1-2-3-cuts-the-coordinate-axes-at-a-b-crespectively-what-are-the-intercepts-made-by-the-plane-a-bc-on-the-axes

slug:
a-triangular-plane-abc-with-centroid-1-2-3-cuts-the-coordinate-axes-at-a-b-crespectively-what-are-the-intercepts-made-by-the-plane-a-bc-on-the-axes-92001

question:
<div class="question">A triangular plane $\mathrm{ABC}$ with centroid $(1,2,3)$ cuts the coordinate axes at $A, B$, Crespectively. What are the intercepts made by the plane $A B C$ on the axes?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$3,6,9$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1,2,3$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1,4,9$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2,4,6$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3,6,9$</span> </div>

answer:
<div class="solution">Centroid $=(1,2,3)$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/e2MNrUgS3ImKvIhcEEXxbg5AwZhCEVHWR4hNq-IBfJU.original.fullsize.png"/><br/><br/>$(1,2,3)=\left(\frac{x+0+0}{3}, \frac{0+y+0}{3}, \frac{0+0+z}{3}\right)$<br/>$x=3, y=6$ and $z=9$<br/>Intercept made by plane on the axes are 3,6 and 9 . respectively.<br/>$\therefore$ Option (a) is correct.</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-triangular-plane-abc-with-centroid-1-2-3-cuts-the-coordinate-axes-at-a-b-crespectively-what-is-the-equation-of-plane-a-bc

slug:
a-triangular-plane-abc-with-centroid-1-2-3-cuts-the-coordinate-axes-at-a-b-crespectively-what-is-the-equation-of-plane-a-bc-78567

question:
<div class="question">A triangular plane $\mathrm{ABC}$ with centroid $(1,2,3)$ cuts the coordinate axes at $A, B$, Crespectively. What is the equation of plane $A B C$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$x+2 y+3 z=1$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3 x+2 y+z=3$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2 x+3 y+6 z=18$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$6 x+3 y+2 z=18$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$6 x+3 y+2 z=18$</span> </div>

answer:
<div class="solution">The plane passes through the point $\mathrm{A}(3,0,0), \mathrm{B}(0,6,0)$ and $\mathrm{C}(0,0,9)$. So, it should satisfy the equation given in option for all the three points. From option (a) For point $\mathrm{A}(3,0,0)$<br/>$x+2 y+3 z=1$<br/>$\Rightarrow 3+0+0 \neq 1$<br/>option (a) is wrong. From option (b) For point $\mathrm{A}(3,0,0)$<br/>$3 x+2 y+z=3$<br/>$\therefore 3(3)+0+0 \neq 3$<br/>$\therefore \quad$ option (b) is wrong. From option (c) For point $\mathrm{A}(3,0,0)$<br/>$2 x+3 y+6 z=18$<br/>$\therefore \quad 2(3)+0+0 \neq 18$<br/>of option (c) is wrong. From option (d) For point $\mathrm{A}(3,0,0)$ $6 x+3 y+2 z=18$<br/>$\Rightarrow 6(3)+0+0=18$<br/>For point $\mathrm{B}(0,6,0)$<br/>$6 x+3 y+2 z=18$<br/>$\therefore \quad 0+3(6)+0=18$<br/>For point $\mathrm{C}(0,0,9)$<br/>$6 x+3 y+2 z=18$<br/>$0+0+2 \times 9=18$<br/>$\therefore \quad$ Option $(\mathrm{d})$ is correct.</div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">50</span> </div>
source_db: MarksBatch1_P1.db
title:
a-tunning-fork-of-frequency-340-hz-resonates-in-the-fundamental-mode-with-an-air-column-of-length-125-cm-in-a-cylindrical-tube-closed-at-one-end-when--1

slug:
a-tunning-fork-of-frequency-340-hz-resonates-in-the-fundamental-mode-with-an-air-column-of-length-125-cm-in-a-cylindrical-tube-closed-at-one-end-when-1-87304

question:
<div class="question">A tunning fork of frequency <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>340</mn><mo> </mo><mi>Hz</mi></math> resonates in the fundamental mode with an air column of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>125</mn><mo> </mo><mi>cm</mi></math> in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is _____ <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cm</mi></math>.<br/>(Velocity of sound in air is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>340</mn><msup><mrow><mo> </mo><mi>ms</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>)</div>

answer:
<div class="solution"><p>We know that, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>λ</mi><mi>f</mi></math>, then, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mfrac><mi>v</mi><mi>f</mi></mfrac><mo>=</mo><mfrac><mrow><mn>340</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mrow><mn>340</mn><mo> </mo><mi>Hz</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>340</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mrow><mn>340</mn><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></mfrac><mo>=</mo><mn>1</mn><mo> </mo><mi mathvariant="normal">m</mi></math></p><p>First resonating length, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>l</mi><mn>1</mn></msub><mo>=</mo><mfrac><mi>λ</mi><mn>4</mn></mfrac><mo>=</mo><mfrac><mn>100</mn><mn>4</mn></mfrac><mo>=</mo><mn>25</mn><mo> </mo><mi>cm</mi></math></p><p>Second resonating length, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>l</mi><mn>2</mn></msub><mo>=</mo><mfrac><mrow><mn>3</mn><mi>λ</mi></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mo>×</mo><mn>100</mn></mrow><mn>4</mn></mfrac><mo>=</mo><mn>75</mn><mo> </mo><mi>cm</mi></math></p><p>Third resonating length, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>l</mi><mn>3</mn></msub><mo>=</mo><mfrac><mrow><mn>5</mn><mi>λ</mi></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mrow><mn>5</mn><mo>×</mo><mn>100</mn></mrow><mn>4</mn></mfrac><mo>=</mo><mn>125</mn><mo> </mo><mi>cm</mi></math></p><p>So third resonance is not possible since the length of the tube is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>125</mn><mo> </mo><mi>cm</mi></math></p><p>Thus, minimum height of water necessary for resonance <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>125</mn><mo>−</mo><mn>75</mn><mo>=</mo><mn>50</mn><mo> </mo><mi>cm</mi></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/b50d34b3-6d9f-458c-a072-38fa0d1e087e-image.png" style="width: 220px; height: 153px;"/></p></div>


tags: ['Physics', 'Waves and Sound', 'JEE Main', 'JEE Main 2022 (28 Jun Shift 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">50</span> </div>
source_db: MarksBatch1_P1.db
title:
a-tunning-fork-of-frequency-340-hz-resonates-in-the-fundamental-mode-with-an-air-column-of-length-125-cm-in-a-cylindrical-tube-closed-at-one-end-when-

slug:
a-tunning-fork-of-frequency-340-hz-resonates-in-the-fundamental-mode-with-an-air-column-of-length-125-cm-in-a-cylindrical-tube-closed-at-one-end-when-87276

question:
<div class="question">A tunning fork of frequency <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>340</mn><mo> </mo><mi>Hz</mi></math> resonates in the fundamental mode with an air column of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>125</mn><mo> </mo><mi>cm</mi></math> in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is _____ <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cm</mi></math>.<br/>(Velocity of sound in air is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>340</mn><msup><mrow><mo> </mo><mi>ms</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>)</div>

answer:
<div class="solution"><p>We know that, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>λ</mi><mi>f</mi></math>, then, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mfrac><mi>v</mi><mi>f</mi></mfrac><mo>=</mo><mfrac><mrow><mn>340</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mrow><mn>340</mn><mo> </mo><mi>Hz</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>340</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mrow><mn>340</mn><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></mfrac><mo>=</mo><mn>1</mn><mo> </mo><mi mathvariant="normal">m</mi></math></p><p>First resonating length, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>l</mi><mn>1</mn></msub><mo>=</mo><mfrac><mi>λ</mi><mn>4</mn></mfrac><mo>=</mo><mfrac><mn>100</mn><mn>4</mn></mfrac><mo>=</mo><mn>25</mn><mo> </mo><mi>cm</mi></math></p><p>Second resonating length, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>l</mi><mn>2</mn></msub><mo>=</mo><mfrac><mrow><mn>3</mn><mi>λ</mi></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mo>×</mo><mn>100</mn></mrow><mn>4</mn></mfrac><mo>=</mo><mn>75</mn><mo> </mo><mi>cm</mi></math></p><p>Third resonating length, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>l</mi><mn>3</mn></msub><mo>=</mo><mfrac><mrow><mn>5</mn><mi>λ</mi></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mrow><mn>5</mn><mo>×</mo><mn>100</mn></mrow><mn>4</mn></mfrac><mo>=</mo><mn>125</mn><mo> </mo><mi>cm</mi></math></p><p>So third resonance is not possible since the length of the tube is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>125</mn><mo> </mo><mi>cm</mi></math></p><p>Thus, minimum height of water necessary for resonance <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>125</mn><mo>−</mo><mn>75</mn><mo>=</mo><mn>50</mn><mo> </mo><mi>cm</mi></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/b50d34b3-6d9f-458c-a072-38fa0d1e087e-image.png" style="width: 220px; height: 153px;"/></p></div>


tags: ['Physics', 'Nuclear Physics']
options: None
correct_option: None
source_db: MarksBatch1_P1.db
title:
a-two-stable-isotopes-of-lithium-3-6-li-and-3-7-li-have-respective-abundances-of-75-and-925-these-isotopes-have-masses-601512-u-and-701600-u-respectiv

slug:
a-two-stable-isotopes-of-lithium-3-6-li-and-3-7-li-have-respective-abundances-of-75-and-925-these-isotopes-have-masses-601512-u-and-701600-u-respectiv-39657

question:
<div class="question">(a) Two stable isotopes of lithium ${ }_3^6 \mathrm{Li}$ and ${ }_3^7 \mathrm{Li}$ have respective abundances of $7.5 \%$ and $92.5 \%$. These isotopes have masses $6.01512 \mathrm{u}$ and $7.01600 \mathrm{u}$ respectively. Find the atomic mass of lithium.<br/>(b) Boron has two stable isotopes, ${ }_5^{10} \mathrm{~B}$ and ${ }_5^{11} \mathrm{~B}$. Their respective masses are $10.01294 \mathrm{u}$ and $11.00931 \mathrm{u}$, and the atomic mass of boron is $10.811 \mathrm{u}$. Find the abundances of ${ }_5^{10} \mathrm{~B}$ and ${ }_5^{11} \mathrm{~B}$.</div>

answer:
<div class="solution">(a) The isotope ${ }_3^6 \mathrm{Li}$ has abundance $7.5 \%$ and ${ }_3^7 \mathrm{Li}$ has $92.5 \% . \mathrm{m}\left({ }_3^6 \mathrm{Li}\right)=6.01512 \mathrm{u} \mathrm{m}\left({ }_3^7 \mathrm{Li}\right)=7.01600 \mathrm{u}$ Average mass of Li $=\frac{6.01512 \times 7.5+7.01600 \times 92.5}{7.5+92.5}$ $=\frac{45.1140+648.98}{7.5+92.5}$ $=\frac{694.094}{100}=6.94000 \mathrm{u}$.<br/>(b) $\mathrm{m}\left({ }_5^{10} \mathrm{~B}\right)=10.01294 \mathrm{u} ; \mathrm{m}\left({ }_5^{11} \mathrm{~B}\right)=11.00931 \mathrm{u} ; \mathrm{m}$ (B) $=10.811 \mathrm{u}$.<br/>Let abundance of ${ }_5^{10} \mathrm{~B}$ be $\mathrm{x} \%$ thus abundance of ${ }_5^{11} \mathrm{~B}$ will be $(100-\mathrm{x}) \%$<br/>Average mass of Boron<br/>$$<br/>\begin{aligned}<br/>&amp;=\frac{10.01294 \mathrm{x}+11.00931(100-\mathrm{x})}{100} \\<br/>&amp;=10.811 \mathrm{u}<br/>\end{aligned}<br/>$$<br/>$\Rightarrow 10.01294 \mathrm{x}+1100.931-11.00931 \mathrm{x}=1081.1$<br/>$\Rightarrow \quad 0.996 \mathrm{x}=19.831$<br/>$\Rightarrow \mathrm{x}=19.91 \%=$ abundance of ${ }_5^{10} \mathrm{~B}$<br/>$\quad$ and $(100-\mathrm{x})$<br/>$\quad=(100-19.91)=80.1 \%$ abundance of ${ }_5^{11} \mathrm{~B}$</div>


tags: ['Biology', 'Body Fluids and Circulation', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-type-of-granulocyte-i-and-agranulocyte-ii-are-phagocytic-cells-that-destroy-foreign-organisms-entering-the-body-iii-secrete-histamine-serotonin-hepa

slug:
a-type-of-granulocyte-i-and-agranulocyte-ii-are-phagocytic-cells-that-destroy-foreign-organisms-entering-the-body-iii-secrete-histamine-serotonin-hepa-69234

question:
<div class="question"><div> <p align="left" style="text-align:left;">A type of granulocyte (i) and agranulocyte (ii) are phagocytic cells that destroy foreign organisms entering the body. (iii) secrete histamine, serotonin, heparin, etc., and are involved in inflammatory reactions. (iv) resist infections and are also associated with allergic reactions. (v) are responsible for the immune responses of the body.</p> </div> </div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><table border="1" cellpadding="1" cellspacing="1" style="width:100%;"> <tbody> <tr> <td>(i)</td> <td>(ii)</td> <td>(iii)</td> <td>(iv)</td> <td>(v)</td> </tr> <tr> <td>Monocytes</td> <td>Neutrophils</td> <td>Basophils</td> <td>Eosinophils</td> <td>Lymphocytes</td> </tr> </tbody></table><p align="left" style="text-align:left;"> </p></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><table border="1" cellpadding="1" cellspacing="1" style="width: 368px;"> <tbody> <tr> <td>(i)</td> <td>(ii)</td> <td>(iii)</td> <td>(iv)</td> <td>(v)</td> </tr> <tr> <td>Neutrophils</td> <td>Monocytes</td> <td>Basophils</td> <td>Eosinophils</td> <td>Lymphocytes</td> </tr> </tbody></table><p align="left"> </p></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><table border="1" cellpadding="1" cellspacing="1" style="width: 368px;"> <tbody> <tr> <td>(i)</td> <td>(ii)</td> <td>(iii)</td> <td>(iv)</td> <td>(v)</td> </tr> <tr> <td>Neutrophils</td> <td>Monocytes</td> <td>Eosinophils</td> <td>Basophils</td> <td>Lymphocytes</td> </tr> </tbody></table></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><table border="1" cellpadding="1" cellspacing="1" style="width: 368px;"> <tbody> <tr> <td>(i)</td> <td>(ii)</td> <td>(iii)</td> <td>(iv)</td> <td>(v)</td> </tr> <tr> <td>Monocytes</td> <td>Neutrophils</td> <td>Eosinophils</td> <td>Basophils</td> <td>Lymphocytes</td> </tr> </tbody></table></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><table border="1" cellpadding="1" cellspacing="1" style="width: 368px;"> <tbody> <tr> <td>(i)</td> <td>(ii)</td> <td>(iii)</td> <td>(iv)</td> <td>(v)</td> </tr> <tr> <td>Neutrophils</td> <td>Monocytes</td> <td>Basophils</td> <td>Eosinophils</td> <td>Lymphocytes</td> </tr> </tbody></table><p align="left"> </p></span> </div>

answer:
<div class="solution"><div><p align="left" style="text-align:left;">Neutrophils, eosinophils, and basophils are different types of granulocytes, while lymphocytes and monocytes are the agranulocytes. Neutrophils are the most abundant cells (60-65 percent) of the total WBCs and basophils are the least (0.5-1 percent) among them. Neutrophils and monocytes (6-8 percent) are phagocytic cells that destroy foreign organisms entering the body. Basophils secrete histamine, serotonin, heparin, etc., and are involved in inflammatory reactions. Eosinophils (2-3 percent) resist infections and are also associated with allergic reactions. Lymphocytes (20-25 percent) are of two major types â âBâ and âTâ forms. Both B and T lymphocytes are responsible for immune responses of the body.</p></div></div>


title: a-typical-monocotyledonous-root-is-characterized-by
slug: a-typical-monocotyledonous-root-is-characterized-by-98111
question: <div class="question">A typical monocotyledonous root is characterized by ___________.</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">usually more than six xylem bundles.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">large and well developed pith.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">no secondary growth.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">All of the above</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">All of the above</span> </div>

answer:
<div class="solution">Monocotyledonous plants are subgroup of Angiosperms characterized by having one embryonic leaf or one cotyledon in their seed. Anatomically the root system of monocots has certain distinguishing feature even though it is similar to that of dicot plant root system.<br/><br/>The root lacks cambium in it and has no secondary growth. The number of xylem bundles are more than dicot, having higher than six. The pith region of monocots is larger in size and better developed than dicots.</div>


tags: ['Physics', 'Waves and Sound', 'AIIMS', 'AIIMS 2010']
source_db: MarksBatch1_P1.db
title:
a-uniform-string-is-vibrating-with-a-fundamental-frequency-f-the-new-frequency-if-radius-length-both-are-doubled-would-be

slug:
a-uniform-string-is-vibrating-with-a-fundamental-frequency-f-the-new-frequency-if-radius-length-both-are-doubled-would-be-70580

question:
<div class="question">A uniform string is vibrating with a fundamental frequency ' $f$ '. The new frequency, if radius \&amp; length both are doubled would be</div>

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

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

answer:
<div class="solution">Fundamental frequency of a vibrating string is expressed as<br/>$$<br/>f=\frac{1}{2 L} \sqrt{\frac{T}{\mu}}=\frac{1}{L D} \sqrt{\frac{T}{\pi \rho}}<br/>$$<br/>where,<br/>$$<br/>\begin{aligned}<br/>&amp; D= \text { diameter of string } \\<br/>&amp; \rho= \text { density of the } \\<br/>&amp; \text { material of string }<br/>\end{aligned}<br/>$$<br/>As length $L$ and radius are doubled, the new frequency<br/>$$<br/>f^{\prime}=\frac{1}{(2 L)(2 D)} \sqrt{\frac{T}{\pi \rho}}=\frac{1}{4} f<br/>$$</div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2023 (12 May Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-uniform-string-is-vibrating-with-a-fundamental-frequency-n-if-radius-and-length-of-string-both-are-doubled-keeping-tension-constant-then-the-new-fre

slug:
a-uniform-string-is-vibrating-with-a-fundamental-frequency-n-if-radius-and-length-of-string-both-are-doubled-keeping-tension-constant-then-the-new-fre-17642

question:
<div class="question">A uniform string is vibrating with a fundamental frequency ' $n$ '. If radius and length of string both are doubled keeping tension constant then the new frequency of vibration is</div>

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

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

answer:
<div class="solution">$\begin{aligned} &amp; l_2=2 l_1, \mathrm{R}_2=2 \mathrm{R}_1, \mathrm{~T}_1=\mathrm{T}_2 \\ &amp; \mathrm{n}=\frac{1}{2 l} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}} \\ &amp; \quad \text { Where, } \mathrm{m}=\text { mass per unit length }=\frac{\left(\mathrm{nR}^2 l\right) \rho}{l} \\ &amp; \therefore \quad \mathrm{m} \propto \mathrm{R}^2 \\ &amp; \therefore \quad \frac{\mathrm{n}_2}{\mathrm{n}_1}=\frac{l_1}{l_2} \times \frac{\mathrm{R}_1}{\mathrm{R}_2} \\ &amp; \therefore \quad \frac{\mathrm{n}_2}{\mathrm{n}_1}=\frac{l_1}{2 l_1} \times \frac{\mathrm{R}_1}{2 \mathrm{R}_1} \\ &amp; \therefore \quad \mathrm{n}_2=\frac{\mathrm{n}_1}{4}=\frac{\mathrm{n}}{4}\end{aligned}$</div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-uniform-wire-of-length-l-and-diameter-d-and-density-is-stretched-under-a-tension-t-the-correct-relation-between-its-fundamental-frequency-f-the-leng

slug:
a-uniform-wire-of-length-l-and-diameter-d-and-density-is-stretched-under-a-tension-t-the-correct-relation-between-its-fundamental-frequency-f-the-leng-44410

question:
<div class="question">A uniform wire of length <math><mi>L</mi></math> and diameter <math><mi>D</mi></math> and density <math><mi>Ï</mi></math> is stretched under a tension <math><mi>T</mi></math>. The correct relation between its fundamental frequency <math><mi>f</mi><mo>,</mo></math> the length <math><mi>L</mi></math> and the diameter <math><mi>D</mi></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mi>f</mi><mo>â</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>L</mi><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mi>f</mi><mo>â</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math><mi>f</mi><mo>â</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>L</mi><mi>D</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"><math><mi>f</mi><mo>â</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>L</mi><msqrt><mi>D</mi></msqrt></mrow></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mi>f</mi><mo>â</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>L</mi><mi>D</mi></mrow></mfrac></math> </span> </div>

answer:
<div class="solution">Since, we know,<br/><br/>Frequency, <math><mi>f</mi><mo>=</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn><mi>L</mi></mrow></mfrac><mi> </mi><msqrt><mfrac><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></mfrac></msqrt></math><br/><br/>Where, <math><mi>T</mi><mo>=</mo></math> tension in the string,<br/><br/><math><mi>L</mi><mo>=</mo></math> Length of the string<br/><br/>And <math><mi>m</mi><mo>=</mo></math> linear mass density of the string.<br/><br/><math><mo>â´</mo><mi>m</mi><mo>=</mo><mfrac><mrow><mi>M</mi></mrow><mrow><mi>L</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>Ï</mi><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msup><mo>â</mo><mi>L</mi><mo>â</mo><mi>Ï</mi></mrow><mrow><mi>L</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>Ï</mi><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>Ï</mi></mrow><mrow><mn>4</mn></mrow></mfrac></math><br/><br/>Thus, <math><mi>f</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>L</mi></mrow></mfrac><mo>â</mo><msqrt><mfrac><mrow><mi>T</mi></mrow><mrow><mfrac><mrow><mi>Ï</mi><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>Ï</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfrac></msqrt></math><br/><br/>For fundamental frequency, <math><mi>n</mi><mo>=</mo><mn>1</mn></math><br/><br/><math><mi>f</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>L</mi><mfrac><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mfrac><mi> </mi><msqrt><mfrac><mrow><mi>T</mi></mrow><mrow><mi>Ïâ</mi><mi>Ï</mi></mrow></mfrac></msqrt><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>L</mi><mi>D</mi></mrow></mfrac><mo>â</mo><msqrt><mfrac><mrow><mi>T</mi></mrow><mrow><mi>Ïâ</mi><mi>Ï</mi></mrow></mfrac></msqrt></math><br/><br/><math><mi>f</mi><mo>â</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>L</mi><mi>D</mi></mrow></mfrac></math></div>


tags: ['Physics', 'Waves and Sound', 'KCET', 'KCET 2010']
source_db: MarksBatch1_P1.db
title:
a-uniform-wire-of-length-l-diameter-d-and-density-is-stretched-under-a-tension-t-the-correct-relation-between-its-fundamental-frequency-f-the-length-l

slug:
a-uniform-wire-of-length-l-diameter-d-and-density-is-stretched-under-a-tension-t-the-correct-relation-between-its-fundamental-frequency-f-the-length-l-47391

question:
<div class="question">A uniform wire of length $\mathrm{L}$, diameter $\mathrm{D}$ and density $\rho$ is stretched under a tension T. The correct relation between its fundamental frequency $f$, the length $L$ and the diameter $D$ is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$f \propto \frac{1}{L D}$</span> </div>

answer:
<div class="solution">The fundamental frequency is $f=\frac{1}{2 L} \sqrt{\frac{T}{\mu}}$<br/>$$<br/>f=\frac{1}{2 L} \sqrt{\frac{T}{\rho \pi \frac{D^{2}}{4}}}=\frac{1}{L D} \sqrt{\frac{T}{\pi \rho}}<br/>$$<br/>$\therefore$<br/>$$<br/>f \propto \frac{1}{L D}<br/>$$</div>


title: a-unit-vector-perpendicular-to-each-of-the-vectors-2-i-j-k-and-3-i-4-j-k-is
slug: a-unit-vector-perpendicular-to-each-of-the-vectors-2-i-j-k-and-3-i-4-j-k-is-81913
tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch1_P1.db
question:
<div class="question">A unit vector perpendicular to each of the vectors<br/>$2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}-\hat{\mathrm{k}}$ is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{\sqrt{3}} \hat{\mathrm{i}}+\frac{1}{\sqrt{3}} \hat{\mathrm{j}}-\frac{1}{\sqrt{3}} \hat{\mathrm{k}}$</span> </div>

answer:
<div class="solution">$\left|\begin{array}{ccc}\hat{i} &amp; \hat{j} &amp; \hat{k} \\ 2 &amp; -1 &amp; 1 \\ 3 &amp; -4 &amp; -1\end{array}\right|$<br/>$=\hat{i}(1+4)-\hat{j}(-2-3)+\hat{k}(-8+3)$<br/>$=5 \hat{i}+5 \hat{j}-5 \hat{k}$<br/>Unit vector $=\frac{5}{5 \sqrt{3}} \hat{i}+\frac{5}{5 \sqrt{3}} \hat{j}-\frac{5}{5 \sqrt{3}} \hat{k}$<br/>$\quad=\frac{1}{\sqrt{3}} \hat{i}+\frac{1}{\sqrt{3}} \hat{j}-\frac{1}{\sqrt{3}} \hat{k}$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-variable-plane-passes-through-a-fixed-point-a-b-c-and-cuts-the-axes-in-a-b-and-c-respectively-the-locus-of-the-centre-of-the-sphere-oabc-o-being-the

slug:
a-variable-plane-passes-through-a-fixed-point-a-b-c-and-cuts-the-axes-in-a-b-and-c-respectively-the-locus-of-the-centre-of-the-sphere-oabc-o-being-the-21856

question:
<div class="question">A variable plane passes through a fixed point $(a, b, c)$ and cuts the axes in $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ respectively. The locus of the centre of the sphere $\mathrm{OABC}$, $\mathrm{O}$ being the origin $\mathrm{k}$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=2$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/P93OfQAbHt-KdzynOxy0HKL6r6pDNm_YkR0zQUEX_6Q.original.fullsize.png"/><br/><br/>Equation of plane passing through points<br/>$(\mathrm{p}, 0,0),(0, \mathrm{q}, 0)$ and $(0,0, \mathrm{r})$ is $\frac{\mathrm{x}}{\mathrm{p}}+\frac{\mathrm{y}}{\mathrm{q}}+\frac{\mathrm{z}}{\mathrm{r}}=1$<br/>Given that this plane passes through $(\mathrm{a}, \mathrm{b}, \mathrm{c})$.<br/>$\therefore \frac{a}{p}+\frac{b}{q}+\frac{c}{r}=1$<br/>Equation of sphere is $\mathrm{x}^{2}+\mathrm{y}^{2}+\mathrm{z}^{2}-\mathrm{px}-\mathrm{q} y-\mathrm{rz}=0$.<br/>Centre of the sphere $=(1, \mathrm{~m}, \mathrm{n})=\left(\frac{\mathrm{p}}{2}, \frac{\mathrm{q}}{2}, \frac{\mathrm{r}}{2}\right)$<br/>$\Rightarrow \mathrm{p}=2 \ell, \mathrm{q}=2 \mathrm{~m}, \mathrm{r}=2 \mathrm{n}$<br/>$\therefore$ locus of the centre $\Rightarrow \frac{\mathrm{a}}{\mathrm{x}}+\frac{\mathrm{b}}{\mathrm{y}}+\frac{\mathrm{c}}{\mathrm{z}}=2$.</div>


title: a-variate-x-takes-values-2-3-4-2-5-4-3-2-1-what-is-the-mode
slug: a-variate-x-takes-values-2-3-4-2-5-4-3-2-1-what-is-the-mode-31519
tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2011 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch1_P1.db
question:
<div class="question">A variate $X$ takes values $2,3,4,2,5,4,3,2,1$. What is the mode? $\quad$</div>

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

answer:
<div class="solution">Given data is $2,3,4,2,5,4,3,2,1$<br/>Mode $=2$<br/>$[\because 2$ occurs maximum number of times].</div>


title: a-variate-x-takes-values-3-7-5-4-3-2-10-what-is-the-median
slug: a-variate-x-takes-values-3-7-5-4-3-2-10-what-is-the-median-22921
tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2012 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch1_P1.db
question:
<div class="question">A variate $\mathrm{X}$ takes values $3,7,5,4,3,2,10$. What is the median?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-2$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">4</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">7</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">9</span> </li> </ul>

answer:
<div class="solution">First we arrange the data in ascending order $2,2,3,3,4,5,7,9,10$<br/>Since number of observation is odd<br/>$:$ median $=\left(\frac{9+1}{2}\right)^{\mathrm{th}}$ observation $=5$ th observation</div>


title: a-vascular-bundle-which-lacks-cambium-is-called
slug: a-vascular-bundle-which-lacks-cambium-is-called-30653
question: <div class="question">A vascular bundle which lacks cambium is called</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Conjoint, and collateral</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Conjoint, but not collateral</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Closed, and collateral</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Bicollateral</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Conjoint, but not collateral</span> </div>

answer:
<div class="solution">Vascular bundles having cambium in between xylem and phloem are called open bundles, due to cambium they carries secondary growth. Vascular bundles which lacks cambium are called closed bundles. Open bundles occurs in dicot and closed bundles occurs in monocots.</div>


tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-vector-b-is-collinear-with-the-vector-a-2-1-1-and-satisfies-the-condition-a-b-3-what-is-b-equal-to

slug:
a-vector-b-is-collinear-with-the-vector-a-2-1-1-and-satisfies-the-condition-a-b-3-what-is-b-equal-to-68589

question:
<div class="question">A vector $\vec{b}$ is collinear with the vector $\vec{a}=(2,1,-1)$ and<br/>satisfies the condition $\vec{a} \cdot \vec{b}=3 .$ What is $\vec{b}$ equal to?</div>

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

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

answer:
<div class="solution">Let $\vec{b}=x \vec{i}+y \vec{j}+z \vec{k}$<br/>Since, $\vec{b}$ is collinear with vetor $\vec{a}$<br/>therefore $\vec{a}=k \vec{b}$ where $k$ is a scalar.<br/>Given $\vec{a}=(2,1,-1)$<br/>$\therefore \quad(2,1,-1)=k(x, y, z)$<br/>$\Rightarrow x=\frac{2}{k}, y=\frac{1}{k}, z=\frac{-1}{k}$<br/>Also, $\vec{a} \cdot \vec{b}=3$<br/>$\Rightarrow 2 x+y-z=3$<br/>$\Rightarrow \quad 2\left(\frac{2}{k}\right)+\frac{1}{k}+\frac{1}{k}=3$<br/>$\Rightarrow \frac{4}{k}+\frac{1}{k}+\frac{1}{k}=3$<br/>$\Rightarrow \frac{6}{k}=3 \Rightarrow k=2$<br/>$\therefore \quad x=1, y=\frac{1}{2}$ and $z=\frac{-1}{2}$<br/>Hence $\vec{b}=\left(1, \frac{1}{2}, \frac{-1}{2}\right)$</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2006 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">120 m</span> </div>
source_db: MarksBatch1_P1.db
title:
a-vertical-pole-with-height-more-than-100-m-consists-of-two-parts-the-lower-being-onethird-of-the-whole-at-a-point-on-a-horizontal-plane-through-the-f

slug:
a-vertical-pole-with-height-more-than-100-m-consists-of-two-parts-the-lower-being-onethird-of-the-whole-at-a-point-on-a-horizontal-plane-through-the-f-22610

question:
<div class="question">A vertical pole with height more than $100 \mathrm{~m}$ consists of two parts, the lower being one-third of the whole. At a point on a horizontal plane through the foot and $40 \mathrm{~m}$ fromit, the upper<br/>part subtends an angle uhose tangent is $\frac{1}{2}$. What is the height of the pole ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$110 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$200 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">120 m</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">150 m</span> </li> </ul>

answer:
<div class="solution">Let h be the height of pole, upper portion CD subtend angle $\theta$ at $A$.<br/>Then, $\tan \theta=\frac{1}{2}$<br/>Let lower part $\mathrm{BC}$ subtend angle $\phi$ at A then $\operatorname{In} \Delta \mathrm{ABC}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/Zfv-txGolcueSJoww9XmXGuxj7iBANKj-xjUY_GxfCk.original.fullsize.png"/><br/><br/>$\tan \phi=\frac{\mathrm{BC}}{\mathrm{AB}}=\frac{\mathrm{h} / 3}{40}=\frac{\mathrm{h}}{120}$<br/>$\operatorname{In} \Delta \mathrm{ABD}$,<br/>$\tan (\theta+\phi)=\frac{\mathrm{BD}}{\mathrm{AB}}$<br/>$\Rightarrow \frac{\tan \theta+\tan \phi}{1-\tan \theta \tan \phi}=\frac{\mathrm{h}}{40}$<br/>$\Rightarrow \frac{\frac{1}{2}+\frac{\mathrm{h}}{120}}{1-\frac{\mathrm{h}}{240}}=\frac{\mathrm{h}}{40}$<br/>$\Rightarrow \frac{2(60+\mathrm{h})}{(240-\mathrm{h})}=\frac{\mathrm{h}}{40}$<br/>$\Rightarrow 80(60+\mathrm{h})=240 \mathrm{~h}-\mathrm{h}^{2} \Rightarrow 4800+80 \mathrm{~h}=240 \mathrm{~h}-\mathrm{h}^{2}$<br/>$\Rightarrow \mathrm{h}^{2}-160 \mathrm{~h}+4800=0 \quad \Rightarrow(\mathrm{h}-120)(\mathrm{h}-40)=0$<br/>$\Rightarrow \mathrm{h}=120$<br/>$[\mathrm{h}=40$ is discarded, since $\mathrm{h}&gt;100$ is given]</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-vertical-tower-standing-on-a-levelled-field-is-mounted-with-a-vertical-flag-staff-of-length-3-m-from-a-point-on-the-field-the-angles-of-elevation-of

slug:
a-vertical-tower-standing-on-a-levelled-field-is-mounted-with-a-vertical-flag-staff-of-length-3-m-from-a-point-on-the-field-the-angles-of-elevation-of-48953

question:
<div class="question">A vertical tower standing on a levelled field is mounted with a vertical flag staff of length $3 \mathrm{~m}$. From a point on the field. the angles of elevation of the bottom and tip of the flag staff are $30^{\circ}$ and $45^{\circ}$ respectively. Which one of the following gives the best approximation to the height of the tower?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$3.90 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$4.00 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$4.10 \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4.25 \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4.10 \mathrm{~m}$</span> </div>

answer:
<div class="solution">as $\angle \mathrm{CPA}=45^{\circ}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/Gckbx6_DYe7RPBGXv2mOC5nep0Y8AYTGxXSReH5QZt8.original.fullsize.png"/><br/><br/>so $\mathrm{AC}=\mathrm{AP}=\mathrm{x}+3$<br/>$\tan 30^{\circ}=\frac{\mathrm{AB}}{\mathrm{AP}}=\frac{\mathrm{x}}{\mathrm{x}+3}$<br/>$\frac{1}{\sqrt{3}}=\frac{\mathrm{x}}{\mathrm{x}+3}$<br/>$x+3=\sqrt{3} x$<br/>$\mathrm{x}=\frac{3}{\sqrt{3}-1} \times \frac{(\sqrt{3}+1)}{(\sqrt{3}+1)}$<br/>$\mathrm{x}=\frac{3 \times 2.73}{2}=\frac{8.19}{2}=4.095 \mathrm{~m} \approx 4 . \mathrm{lm}$</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-vertical-tower-stands-on-a-horizontal-plane-and-is-surmounted-by-a-vertical-flag-staff-of-height-h-at-a-point-p-on-the-plane-the-angle-of-elevation-

slug:
a-vertical-tower-stands-on-a-horizontal-plane-and-is-surmounted-by-a-vertical-flag-staff-of-height-h-at-a-point-p-on-the-plane-the-angle-of-elevation-21614

question:
<div class="question">A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height $h$. At a point $P$ on the plane, the angle of elevation of the bottom of the flag staff is $\beta$ and that of the top is $\alpha$. What is the height of the tower?</div>

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

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/O9NhdwxEZmjbntm_CFUmIEWuwG9HBjRuG4c79nv6_7I.original.fullsize.png"/><br/><br/>Let $\mathrm{BC}$ be the vertical tower and $\mathrm{CD}$ be the flagstaff so that $\mathrm{CD}=h$<br/>Let $\mathrm{P}$ be the point of observation on the plane. Then, $\angle \mathrm{BPC}=\beta$ and $\angle \mathrm{BPD}=\alpha$<br/>Let $\mathrm{BC}=x$<br/>Now, $\frac{\mathrm{PB}}{x}=\cot \beta \Rightarrow \mathrm{PB}=x \cot \beta$<br/>and $\frac{\mathrm{PB}}{x+h}=\cot \alpha \Rightarrow \mathrm{PB}=(x+h) \cot \alpha$<br/>From (1) and (2), we get $x \cot \beta=(\mathrm{x}+\mathrm{h}) \cot \alpha \Rightarrow x(\cot \beta-\cot \alpha)=h \cot \alpha$<br/>$\therefore$ Height of the tower,<br/>$\mathrm{x}=\frac{h \cot \alpha}{\cot \beta-\cot \alpha}=\frac{h \tan \beta}{\tan \alpha-\tan \beta}$</div>


tags: ['Physics', 'Kinetic Theory of Gases', 'JEE Main', 'JEE Main 2022 (29 Jun Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-vessel-contains-16-g-of-hydrogen-and-128-g-of-oxygen-at-standard-temperature-and-pressure-the-volume-of-the-vessel-in-cm-3-is

slug:
a-vessel-contains-16-g-of-hydrogen-and-128-g-of-oxygen-at-standard-temperature-and-pressure-the-volume-of-the-vessel-in-cm-3-is-39608

question:
<div class="question">A vessel contains <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of hydrogen and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>128</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of oxygen at standard temperature and pressure. The volume of the vessel in <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>cm</mi><mn>3</mn></msup></math> is :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn><mo>×</mo><msup><mn>10</mn><mn>4</mn></msup></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"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>54</mn><mo>×</mo><msup><mn>10</mn><mn>4</mn></msup></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn><mo>×</mo><msup><mn>10</mn><mn>4</mn></msup></math></span> </div>

answer:
<div class="solution"><p>Number of moles of Hydrogen <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub></mfenced><mo>=</mo><mfrac><mi>m</mi><mi>M</mi></mfrac><mo>=</mo><mfrac><mn>16</mn><mn>2</mn></mfrac><mo>=</mo><mn>8</mn></math></p><p>Number of moles of oxygen <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi mathvariant="normal">O</mi><mn>2</mn></msub></mfenced><mo>=</mo><mfrac><mn>128</mn><mn>32</mn></mfrac><mo>=</mo><mn>4</mn></math></p><p>Using ideal gas equation, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi><mo>=</mo><mi>n</mi><mi>R</mi><mi>T</mi></math>,</p><p>Where pressure <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mn>1</mn><mo> </mo><mi>atm</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>01</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup><mo> </mo><mi>Pa</mi><mo> </mo><mfenced><mi>STP</mi></mfenced></math></p><p>Putting the values, </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>01</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup><mo> </mo><mi mathvariant="normal">V</mi><mo>=</mo><mfenced><mrow><mn>8</mn><mo>+</mo><mn>4</mn></mrow></mfenced><mo>×</mo><mn>8</mn><mo>.</mo><mn>314</mn><mo>×</mo><mn>273</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfrac><mrow><mn>12</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>314</mn><mo>×</mo><mn>273</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>01</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup></mrow></mfrac><msup><mrow><mo> </mo><mi mathvariant="normal">m</mi></mrow><mn>3</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>27</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><msup><mrow><mo> </mo><mi>cm</mi></mrow><mn>3</mn></msup><mo>=</mo><mn>27</mn><mo>×</mo><msup><mn>10</mn><mn>4</mn></msup><msup><mrow><mo> </mo><mi>cm</mi></mrow><mn>3</mn></msup></math></p></div>


tags: ['Physics', 'Waves and Sound', 'AIIMS', 'AIIMS 2016']
source_db: MarksBatch1_P1.db
title:
a-wave-is-represented-by-the-equation-y-05-sin-10-t-x-metre-it-is-a-travelling-wave-propagating-along-x-direction-with-velocity

slug:
a-wave-is-represented-by-the-equation-y-05-sin-10-t-x-metre-it-is-a-travelling-wave-propagating-along-x-direction-with-velocity-96603

question:
<div class="question">A wave is represented by the equation $y=0.5 \sin (10 t-x)$ metre<br/>It is a travelling wave propagating along $+x$ direction with velocity</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$10 \mathrm{~m} \mathrm{~s}^{-1}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$20 \mathrm{~m} \mathrm{~s}^{-1}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$5 \mathrm{~m} \mathrm{~s}^{-1}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$10 \mathrm{~m} \mathrm{~s}^{-1}$</span> </div>

answer:
<div class="solution">Compare the given eqn $y=0.5 \sin (10 t-x)$ with the standard form<br/>$\begin{aligned} &amp; y=r \sin \left[\frac{2 \pi t}{T}+\frac{2 \pi x}{\lambda}\right] \\ &amp; \frac{2 \pi}{T}=10, \frac{2 \pi}{\lambda}=1 \\ &amp; v=\frac{\lambda}{T}=\frac{10}{1}=10 \mathrm{~m} / \mathrm{s}\end{aligned}$</div>


tags: ['Physics', 'Waves and Sound', 'JEE Main', 'JEE Main 2008']
source_db: MarksBatch1_P1.db
title:
a-wave-travelling-along-the-x-axis-is-described-by-the-equation-y-x-t-0005-cos-x-t-if-the-wavelength-and-the-time-period-of-the-wave-are-008-m-and-20-

slug:
a-wave-travelling-along-the-x-axis-is-described-by-the-equation-y-x-t-0005-cos-x-t-if-the-wavelength-and-the-time-period-of-the-wave-are-008-m-and-20-13321

question:
<div class="question">A wave travelling along the $x$-axis is described by the equation $y(x, t)=0.005 \cos (\alpha x-\beta t)$. If the wavelength and the time period of the wave are $0.08 \mathrm{~m}$ and $2.0 \mathrm{~s}$, respectively, then $\alpha$ and $\beta$ in appropriate units are</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\alpha=25.00 \pi, \beta=\pi$<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/>$\alpha=\frac{0.08}{\pi}, \frac{2.0}{\pi}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\alpha=\frac{0.04}{\pi}, \beta=\frac{1.0}{\pi}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\alpha=12.50 \pi, \beta=\frac{\pi}{2.0}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\alpha=25.00 \pi, \beta=\pi$<br/></span> </div>

answer:
<div class="solution">$$<br/>y=0.005 \cos (\alpha x-\beta \mathrm{t})<br/>$$<br/>comparing the equation with the standard form,<br/>$$<br/>\begin{aligned}<br/>&amp; y=A \cos \left[\left(\frac{\mathrm{x}}{\lambda}-\frac{\mathrm{t}}{\mathrm{T}}\right) 2 \pi\right] \\<br/>&amp; 2 \pi / \lambda=\alpha \text { and } 2 \pi / T=\beta \\<br/>&amp; \alpha=2 \pi / 0.08=25.00 \pi \\<br/>&amp; \beta=\pi<br/>\end{aligned}<br/>$$</div>


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

slug:
a-whistle-whose-air-column-is-open-at-both-ends-has-a-fundamental-frequency-of-5100-hz-if-the-speed-of-sound-in-air-is-340-ms-1-the-length-of-the-whis-1-82212

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

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

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

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


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

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

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

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

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

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


tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2007 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-wire-34-cm-long-is-to-be-bent-in-the-form-of-a-quadrilateral-of-which-each-angle-is-9-0-what-is-the-maximum-area-which-can-be-enclosed-inside-the-qu

slug:
a-wire-34-cm-long-is-to-be-bent-in-the-form-of-a-quadrilateral-of-which-each-angle-is-9-0-what-is-the-maximum-area-which-can-be-enclosed-inside-the-qu-67849

question:
<div class="question">A wire $34 \mathrm{~cm}$ long is to be bent in the form of a quadrilateral of which each angle is $90^{\circ}$. What is the maximum area which can be enclosed inside the quadrilateral?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$68 \mathrm{~cm}^{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$70 \mathrm{~cm}^{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$71.25 \mathrm{~cm}^{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\begin{array}{lll}\text {  } &amp; 72.25 \mathrm{~cm}^{2} &amp; {}\end{array}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$\begin{array}{lll}\text {  } &amp; 72.25 \mathrm{~cm}^{2} &amp; {}\end{array}$</span> </div>

answer:
<div class="solution">Let one side of quadrilateral be $x$ and another side be $y$ so, $2(x+y)=34$<br/>or, $(\mathrm{x}+\mathrm{y})=17$<br/>We know from the basic principle that for a given perimeter square has the maximum area, so, $x=y$ and putting this value in equation (i)<br/>$\mathrm{x}=\mathrm{y}=\frac{17}{2}$<br/>Area $=\mathrm{x} \cdot \mathrm{y}=\frac{17}{2} \times \frac{17}{2}=\frac{289}{4}=72.25$</div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2016']
source_db: MarksBatch1_P1.db
title:
a-wire-having-tension-225-n-produces-six-beats-per-second-when-it-vibrates-with-some-tuning-fork-when-the-tension-changes-to-256-n-it-vibrates-with-th-1

slug:
a-wire-having-tension-225-n-produces-six-beats-per-second-when-it-vibrates-with-some-tuning-fork-when-the-tension-changes-to-256-n-it-vibrates-with-th-1-52429

question:
<div class="question">A wire having tension <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>225</mn><mo> </mo><mi mathvariant="normal">N</mi></math> produces six beats per second when it vibrates with some tuning fork. When the tension changes to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>256</mn><mo> </mo><mi mathvariant="normal">N</mi></math>, it vibrates with the same fork with the number of beats remaining unchanged. The frequency of the fork will be</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>186</mn><mo> </mo><mi>Hz</mi></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">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>225</mn><mo> </mo><mi>Hz</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>256</mn><mo> </mo><mi>Hz</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>280</mn><mo> </mo><mi>Hz</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>186</mn><mo> </mo><mi>Hz</mi></math></span> </div>

answer:
<div class="solution">For wire vibrating under tension, the fundamental frequency is given by<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">f</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi mathvariant="normal">L</mi></mrow></mfrac><mroot><mfrac><mi mathvariant="normal">T</mi><mi mathvariant="normal">μ</mi></mfrac><mi mathvariant="normal"> </mi></mroot></math>, Where T is tension and <math> <mi>μ</mi> </math> linear mass density of string<br/>It is given that, when it is sounded with a tuning fork of frequency <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> beats per second were heard<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mi mathvariant="normal"> </mi><mfenced separators="|"><mrow><mi mathvariant="normal">x</mi><mo>-</mo><mi mathvariant="normal">f</mi></mrow></mfenced><mo>=</mo><mn>6</mn></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">f</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi mathvariant="normal">L</mi></mrow></mfrac><msqrt><mfrac><mn>225</mn><mi mathvariant="normal">μ</mi></mfrac></msqrt></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">f</mi><mn>2</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi mathvariant="normal">L</mi></mrow></mfrac><msqrt><mfrac><mn>256</mn><mi mathvariant="normal">μ</mi></mfrac></msqrt></math> undefined<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mi mathvariant="normal"> </mi><mfenced separators="|"><mrow><mi mathvariant="normal">x</mi><mo>+</mo><mn>6</mn></mrow></mfenced><mo>=</mo><mfrac><mn>16</mn><mn>15</mn></mfrac><mo>(</mo><mi mathvariant="normal">x</mi><mo>-</mo><mn>6</mn><mo>)</mo></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mi mathvariant="normal"> </mi><mn>15</mn><mi mathvariant="normal">x</mi><mo>+</mo><mn>90</mn><mo>=</mo><mn>16</mn><mi mathvariant="normal">x</mi><mo>-</mo><mn>96</mn></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mi mathvariant="normal"> </mi><mi mathvariant="normal">x</mi><mo>=</mo><mn>186</mn><mi mathvariant="normal"> </mi><mn>H</mn><mn>z</mn></math></div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-wire-having-tension-225-n-produces-six-beats-per-second-when-it-vibrates-with-some-tuning-fork-when-the-tension-changes-to-256-n-it-vibrates-with-th

slug:
a-wire-having-tension-225-n-produces-six-beats-per-second-when-it-vibrates-with-some-tuning-fork-when-the-tension-changes-to-256-n-it-vibrates-with-th-63524

question:
<div class="question">A wire having tension <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>225</mn><mo> </mo><mi mathvariant="normal">N</mi></math> produces six beats per second when it vibrates with some tuning fork. When the tension changes to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>256</mn><mo> </mo><mi mathvariant="normal">N</mi></math>, it vibrates with the same fork with the number of beats remaining unchanged. The frequency of the fork will be</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>186</mn><mo> </mo><mi>Hz</mi></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">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>225</mn><mo> </mo><mi>Hz</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>256</mn><mo> </mo><mi>Hz</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>280</mn><mo> </mo><mi>Hz</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>186</mn><mo> </mo><mi>Hz</mi></math></span> </div>

answer:
<div class="solution">For wire vibrating under tension, the fundamental frequency is given by<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">f</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi mathvariant="normal">L</mi></mrow></mfrac><mroot><mfrac><mi mathvariant="normal">T</mi><mi mathvariant="normal">μ</mi></mfrac><mi mathvariant="normal"> </mi></mroot></math>, Where T is tension and <math> <mi>μ</mi> </math> linear mass density of string<br/>It is given that, when it is sounded with a tuning fork of frequency <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> beats per second were heard<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mi mathvariant="normal"> </mi><mfenced separators="|"><mrow><mi mathvariant="normal">x</mi><mo>-</mo><mi mathvariant="normal">f</mi></mrow></mfenced><mo>=</mo><mn>6</mn></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">f</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi mathvariant="normal">L</mi></mrow></mfrac><msqrt><mfrac><mn>225</mn><mi mathvariant="normal">μ</mi></mfrac></msqrt></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">f</mi><mn>2</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi mathvariant="normal">L</mi></mrow></mfrac><msqrt><mfrac><mn>256</mn><mi mathvariant="normal">μ</mi></mfrac></msqrt></math> undefined<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mi mathvariant="normal"> </mi><mfenced separators="|"><mrow><mi mathvariant="normal">x</mi><mo>+</mo><mn>6</mn></mrow></mfenced><mo>=</mo><mfrac><mn>16</mn><mn>15</mn></mfrac><mo>(</mo><mi mathvariant="normal">x</mi><mo>-</mo><mn>6</mn><mo>)</mo></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mi mathvariant="normal"> </mi><mn>15</mn><mi mathvariant="normal">x</mi><mo>+</mo><mn>90</mn><mo>=</mo><mn>16</mn><mi mathvariant="normal">x</mi><mo>-</mo><mn>96</mn></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mi mathvariant="normal"> </mi><mi mathvariant="normal">x</mi><mo>=</mo><mn>186</mn><mi mathvariant="normal"> </mi><mn>H</mn><mn>z</mn></math></div>


tags: ['Physics', 'Electromagnetic Induction', 'TS EAMCET', 'TS EAMCET 2018 (04 May Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-wire-loop-enclosing-a-semicircle-of-radius-r-is-located-on-the-boundary-of-a-uniform-magnetic-field-of-induction-b-at-time-t-0-the-loop-is-set-into-

slug:
a-wire-loop-enclosing-a-semicircle-of-radius-r-is-located-on-the-boundary-of-a-uniform-magnetic-field-of-induction-b-at-time-t-0-the-loop-is-set-into-78379

question:
<div class="question"><p>A wire loop enclosing a semi-circle of radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> is located on the boundary of a uniform magnetic field of induction <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>B</mi><mo mathvariant="italic">→</mo></mover><mo>.</mo></math> At time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math>, the loop is set into rotation with velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi></math>? about its axis <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math>, coinciding with a line of vector <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>B</mi><mo>→</mo></mover></math> on the boundary as shown in the figure. The emf induced in the loop is</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/ff7ff817-903f-4e86-aae9-c50030d2c482-image.png" style="width: 231px; height: 270px;"/></p></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>B</mi><msup><mi>R</mi><mn>2</mn></msup></mrow><mn>2</mn></mfrac><mi>ω</mi></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">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mi>R</mi><mi>ω</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><msup><mi>R</mi><mn>2</mn></msup><mi>ω</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>B</mi><msup><mi>R</mi><mn>2</mn></msup></mrow><mrow><mn>2</mn><mi>ω</mi></mrow></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>B</mi><msup><mi>R</mi><mn>2</mn></msup></mrow><mn>2</mn></mfrac><mi>ω</mi></math></span> </div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>ϕ</mi><mo>=</mo><mover><mi>B</mi><mo>→</mo></mover><mo>·</mo><mover><mrow><mi>d</mi><mi>s</mi></mrow><mo>→</mo></mover><mo>=</mo><mi>B</mi><mi>d</mi><mi>s</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>B</mi><mfenced><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>ϕ</mi><msup><mi>R</mi><mn>2</mn></msup></mrow></mfenced></math>                (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi><mo>=</mo></math>Sector angle)</p><p>Magnitude of induced emf <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>-</mo><mfenced close="|" open="|"><mfrac><mrow><mi>d</mi><mi>ϕ</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>B</mi><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>R</mi><mn>2</mn></msup><mfenced close="|" open="|"><mfrac><mrow><mi>d</mi><mi>ϕ</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mi>B</mi><msup><mi>R</mi><mn>2</mn></msup><mi>ω</mi></mrow><mn>2</mn></mfrac></math></p></div>


tags: ['Physics', 'Waves and Sound', 'JEE Main', 'JEE Main 2023 (11 Apr Shift 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">80</span> </div>
source_db: MarksBatch1_P1.db
title:
a-wire-of-density-8-10-3-kg-m-3-is-stretched-between-two-clamps-0-5-m-apart-the-extension-developed-in-the-wire-is-3-2-10-4-m-if-y-8-10-10-n-m-2-the-f

slug:
a-wire-of-density-8-10-3-kg-m-3-is-stretched-between-two-clamps-0-5-m-apart-the-extension-developed-in-the-wire-is-3-2-10-4-m-if-y-8-10-10-n-m-2-the-f-61619

question:
<div class="question">A wire of density <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo> </mo><mi>kg</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></math> is stretched between two clamps <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">m</mi></math> apart. The extension developed in the wire is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math>. If <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>=</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>10</mn></msup><mo> </mo><mi mathvariant="normal">N</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math>, the fundamental frequency of vibration in the wire will be _____ <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Hz</mi></math></div>

answer:
<div class="solution"><p>Using the relation of Young's modulus,</p><p> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>T</mi><mi>A</mi></mfrac><mo>=</mo><mi>Y</mi><mfenced><mfrac><mrow><mi>Δ</mi><mi>L</mi></mrow><mi>L</mi></mfrac></mfenced><mo> </mo><mo> </mo></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>T</mi><mo>=</mo><mfenced><mrow><mfrac><mrow><mi>Y</mi><mi>Δ</mi><mi>L</mi></mrow><mi>L</mi></mfrac><mo>×</mo><mi>A</mi></mrow></mfenced></math></p><p>The linear mass density is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mi>μ</mi><mo>=</mo><mfenced><mfrac><mi>m</mi><mi>L</mi></mfrac></mfenced></math>.</p><p>So,<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>T</mi><mi>μ</mi></mfrac><mo>=</mo><mfrac><mrow><mi>Y</mi><mi>Δ</mi><mi>L</mi><mi>A</mi></mrow><mrow><mi>L</mi><mfenced><mfrac><mi>m</mi><mi>L</mi></mfrac></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>Y</mi><mo>(</mo><mi>Δ</mi><mi>L</mi><mo>)</mo><mo>×</mo><mi>L</mi><mi>A</mi></mrow><mrow><mi>L</mi><mo>(</mo><mi>m</mi><mo>)</mo></mrow></mfrac><mo>=</mo><mfenced><mfrac><mrow><mi>Y</mi><mi>Δ</mi><mi>L</mi></mrow><mi>L</mi></mfrac></mfenced><mo>×</mo><mfenced><mfrac><mn>1</mn><mi>ρ</mi></mfrac></mfenced></math></p><p>Substituting the values,<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>T</mi><mi>μ</mi></mfrac><mo>=</mo><mfrac><mrow><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>10</mn></msup><mo>×</mo><mn>3</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfrac><mo>×</mo><mfenced><mfrac><mn>1</mn><mrow><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow></mfrac></mfenced><mo>=</mo><mn>6</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mi>T</mi><mi>μ</mi></mfrac><mo>=</mo><mn>64</mn><mo>×</mo><msup><mn>10</mn><mn>2</mn></msup></math></p><p>The fundamental frequency is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>L</mi></mrow></mfrac><msqrt><mfrac><mi>T</mi><mi>μ</mi></mfrac></msqrt></math>.<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msqrt><mfrac><mi>T</mi><mi>μ</mi></mfrac></msqrt><mo>=</mo><mn>8</mn><mo>×</mo><mn>10</mn><mo>=</mo><mn>80</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><br/>Therefore,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfenced><mfrac><mn>80</mn><mn>1</mn></mfrac></mfenced><mo>=</mo><mn>80</mn><mo> </mo><mi>Hz</mi></math></p></div>


tags: ['Physics', 'Mechanical Properties of Solids', 'JEE Main', 'JEE Main 2020 (02 Sep Shift 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">35</span> </div>
source_db: MarksBatch1_P1.db
title:
a-wire-of-density-9-10-3-kg-cm-3-is-stretched-between-two-clamps-1-m-apart-the-resulting-strain-in-the-wire-is-4-9-10-4-the-lowest-frequency-of-the-tr

slug:
a-wire-of-density-9-10-3-kg-cm-3-is-stretched-between-two-clamps-1-m-apart-the-resulting-strain-in-the-wire-is-4-9-10-4-the-lowest-frequency-of-the-tr-49672

question:
<div class="question">A wire of density <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>–</mo><mn>3</mn></mrow></msup><mo> </mo><mi>kg</mi><mo> </mo><msup><mi>cm</mi><mrow><mo>–</mo><mn>3</mn></mrow></msup></math> is stretched between two clamps <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">m</mi></math> apart. The resulting strain in the wire is  <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>9</mn><mo> </mo><mo>×</mo><mo> </mo><msup><mn>10</mn><mrow><mo>–</mo><mn>4</mn></mrow></msup></math>. The lowest frequency of the transverse vibrations in the wire (Young's modulus of wire  <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo> </mo><mo>=</mo><mo> </mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>10</mn></msup><mo> </mo><msup><mi>Nm</mi><mrow><mo>–</mo><mn>2</mn></mrow></msup></math> ), (to the nearest integer),_______</div>

answer:
<div class="solution"><blockquote><p>Fundamental frequency in the string</p></blockquote><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">f</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi mathvariant="normal">ℓ</mi></mrow></mfrac><msqrt><mfrac><mi mathvariant="normal">T</mi><mi mathvariant="normal">μ</mi></mfrac></msqrt><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi mathvariant="normal">ℓ</mi></mrow></mfrac><msqrt><mfrac><mi mathvariant="normal">T</mi><mi>ρA</mi></mfrac></msqrt><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi mathvariant="normal">ℓ</mi></mrow></mfrac><mfrac><msqrt><mi>YΔℓ</mi></msqrt><mi>ρℓ</mi></mfrac></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">f</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi mathvariant="normal">ℓ</mi></mrow></mfrac><msqrt><mfrac><mi>YΔℓ</mi><mi>ρℓ</mi></mfrac></msqrt></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msqrt><mfrac><mrow><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>10</mn></msup><mo>×</mo><mn>4</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup></mrow><mrow><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfrac></msqrt><mo>=</mo><mn>35</mn></math></p></div>


tags: ['Physics', 'Waves and Sound', 'JEE Main', 'JEE Main 2020 (09 Jan Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-wire-of-length-l-and-mass-per-unit-length-60-10-3-k-g-m-1-is-put-under-tension-of-540-n-two-consecutive-frequencies-that-it-resonates-at-are-420-h-z

slug:
a-wire-of-length-l-and-mass-per-unit-length-60-10-3-k-g-m-1-is-put-under-tension-of-540-n-two-consecutive-frequencies-that-it-resonates-at-are-420-h-z-99508

question:
<div class="question">A wire of length <math><mi>L</mi></math> and mass per unit length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6.0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mi mathvariant="normal">k</mi><mi mathvariant="normal">g</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> is put under tension of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>540</mn><mo> </mo><mi mathvariant="normal">N</mi><mo>.</mo></math> Two consecutive frequencies that it resonates at are: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>420</mn><mo> </mo><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>490</mn><mo> </mo><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi><mo>.</mo></math> Then <math><mi>L</mi></math> in meters is :</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math><mn>2.1</mn><mi mathvariant="normal">m</mi></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">B</span> <span class="option-data"><math><mn>1.1</mn><mi mathvariant="normal">m</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mn>8.1</mn><mi mathvariant="normal">m</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mn>5.1</mn><mi mathvariant="normal">m</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>2.1</mn><mi mathvariant="normal">m</mi></math></span> </div>

answer:
<div class="solution">Fundamental frequency <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>490</mn><mo>-</mo><mn>420</mn><mo>=</mo><mn>70</mn><mo> </mo><mi>H</mi><mi>z</mi></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>L</mi></mrow></mfrac><msqrt><mfrac><mi>T</mi><mi>μ</mi></mfrac></msqrt></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mn>70</mn><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>L</mi></mrow></mfrac><msqrt><mfrac><mn>540</mn><mrow><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfrac></msqrt></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>L</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mo>×</mo><mn>70</mn></mrow></mfrac><msqrt><mn>90</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></msqrt><mo>=</mo><mfrac><mn>300</mn><mn>140</mn></mfrac></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>L</mi><mo>≈</mo><mn>2.14</mn><mo> </mo><mi>m</mi></math></div>


tags: ['Physics', 'Waves and Sound']
options: None
correct_option: None
source_db: MarksBatch1_P1.db
title:
a-wire-stretched-between-two-rigid-supports-vibrates-in-its-fundamental-mode-with-a-frequency-of-45-hz-the-mass-of-the-wire-is-35-1-0-2-kg-and-its-lin

slug:
a-wire-stretched-between-two-rigid-supports-vibrates-in-its-fundamental-mode-with-a-frequency-of-45-hz-the-mass-of-the-wire-is-35-1-0-2-kg-and-its-lin-88326

question:
<div class="question">A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45 \mathrm{~Hz}$. The mass of the wire is $3.5 \times 10^{-2} \mathrm{~kg}$ and its linear mass density is $4 \times 10^{-2} \mathrm{~kg} / \mathrm{m}$. What is (a) the speed of the transverse wave on the string and (b) the tension in the string?</div>

answer:
<div class="solution">(a) Given, $v=45 \mathrm{~Hz}, M=3.5 \times 10^{-2} \mathrm{~kg}$,<br/>$$<br/>\begin{aligned}<br/>&amp;m=4 \times 10^{-2} \mathrm{~kg} / \mathrm{m} \\<br/>&amp;\therefore l=\frac{M}{m}=\frac{3.5 \times 10^{-2}}{4 \times 10^{-2}}=\frac{7}{8} \mathrm{~m}<br/>\end{aligned}<br/>$$<br/>As it is vibrating in fundamental mode<br/>$$<br/>\frac{\lambda}{2}=l=\frac{7}{8} \quad \therefore \quad \lambda=\frac{7}{4}=1.75 \mathrm{~m} .<br/>$$<br/>Speed $=v=v \lambda=45 \times 1.75=78.75 \mathrm{~m} / \mathrm{s}$<br/>(b)<br/>$$<br/>\begin{aligned}<br/>v &amp;=\sqrt{\frac{T}{m}} \Rightarrow T=v^2 \times m \\<br/>&amp;=(78.5)^2 \times 4 \times 10^{-2}=248.06 \mathrm{~N}<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Waves and Sound', 'KCET', 'KCET 2011']
source_db: MarksBatch1_P1.db
title:
a-wire-under-tension-vibrates-with-a-fundamental-frequency-of-600-hz-if-the-length-of-the-wire-is-doubled-the-radius-is-halved-and-the-wire-is-made-to

slug:
a-wire-under-tension-vibrates-with-a-fundamental-frequency-of-600-hz-if-the-length-of-the-wire-is-doubled-the-radius-is-halved-and-the-wire-is-made-to-86321

question:
<div class="question">A wire under tension vibrates with a fundamental frequency of $600 \mathrm{~Hz}$. If the length of the wire is doubled, the radius is halved and the wire is made to vibrate under one-ninth the tension. Then the fundamental frequency will become</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$200 \mathrm{~Hz}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$300 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$600 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$400 \mathrm{~Hz}$</span> </li> </ul>

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

answer:
<div class="solution">Frequency of wire, $f=\frac{1}{2 l r} \sqrt{\frac{T}{\pi \rho}}$<br/>So here,<br/>$$<br/>\begin{aligned}<br/>\frac{f_{1}}{f_{2}} &amp;=\frac{l_{2}}{l_{1}} \times \frac{r_{2}}{r_{1}} \times \sqrt{\frac{T_{1}}{T_{2}}} \\<br/>\frac{600}{f_{2}} &amp;=\frac{2}{1} \times \frac{1}{2} \times \sqrt{\frac{T}{T / 9}} \\<br/>\frac{600}{f_{2}} &amp;=3 \\<br/>f_{2} &amp;=\frac{600}{3} \\<br/>f_{2} &amp;=200 \mathrm{~Hz}<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Waves and Sound', 'TS EAMCET', 'TS EAMCET 2021 (06 Aug Shift 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1.02</span> </div>
source_db: MarksBatch1_P1.db
title:
a-wire-vibrates-at-a-fundamental-frequency-of-500-hz-a-second-identical-wire-produces-5-beats-per-second-with-it-when-the-tension-in-the-first-wire-is

slug:
a-wire-vibrates-at-a-fundamental-frequency-of-500-hz-a-second-identical-wire-produces-5-beats-per-second-with-it-when-the-tension-in-the-first-wire-is-58463

question:
<div class="question">A wire vibrates at a fundamental frequency of $500 \mathrm{~Hz}$. A second identical wire produces 5 beats per second with it when the tension in the first wire is slightly decreased. The ratio of the tension in the second wire to the tension in the first wire is approximately equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1.04</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1.01</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1.05</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">1.02</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">(d) Given that, fundamental frequency of first wire, $f_1=500 \mathrm{~Hz}$<br/>Let frequency of 2 nd wire be $f_2$.<br/>Beat frequency, $f_b=5$<br/>$$<br/>\begin{aligned}<br/>&amp; f_b=f_2-f_1 \\<br/>&amp; f_2=f_b+f_1=500+5=505 \mathrm{~Hz}<br/>\end{aligned}<br/>$$<br/>Using, expression for fundamental frequency of wire,<br/>$$<br/>\begin{aligned}<br/>f &amp; =\frac{1}{2 L} \sqrt{\frac{T}{\mu}} \Rightarrow f \propto \sqrt{T} \\<br/>\Rightarrow \quad \frac{f_2}{f_1} &amp; =\sqrt{\frac{T_2}{T_1}} \Rightarrow \frac{505}{500}=\sqrt{\frac{T_2}{T_1}} \\<br/>\Rightarrow \quad \frac{T_2}{T_1} &amp; =\left(\frac{505}{500}\right)^2=1.02<br/>\end{aligned}<br/>$$</div>


title: a-x-y-x-y-x-y-b-3-2-and-c-4-2-if-ab-c-then-what-is-a-2-equal-to
slug: a-x-y-x-y-x-y-b-3-2-and-c-4-2-if-ab-c-then-what-is-a-2-equal-to-21270
tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2017 (Phase 1)']
source_db: MarksBatch1_P1.db
question:
<div class="question">$\mathrm{A}=\left[\begin{array}{cc}\mathrm{x}+\mathrm{y} &amp; \mathrm{y} \\ \mathrm{x} &amp; \mathrm{x}-\mathrm{y}\end{array}\right], \mathrm{B}=\left[\begin{array}{l}3 \\ -2\end{array}\right]$ and $\mathrm{C}=\left[\begin{array}{l}4 \\ -2\end{array}\right]$.<br/>If $\mathrm{AB}=\mathrm{C}$, then what is $\mathrm{A}^{2}$ equal to?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left[\begin{array}{cc}4 &amp; 8 \\ -4 &amp; -16\end{array}\right]$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left[\begin{array}{cc}4 &amp; -4 \\ 8 &amp; -16\end{array}\right]$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left[\begin{array}{cc}-4 &amp; -8 \\ 4 &amp; 12\end{array}\right]$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\left[\begin{array}{cc}-4 &amp; -8 \\ 8 &amp; 12\end{array}\right]$</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">$\left[\begin{array}{cc}-4 &amp; -8 \\ 8 &amp; 12\end{array}\right]$</span> </div>

answer:
<div class="solution">$A=\left[\begin{array}{cc}x+y &amp; y \\ x &amp; x-y\end{array}\right], B=\left[\begin{array}{c}3 \\ -2\end{array}\right], c=\left[\begin{array}{c}4 \\ -2\end{array}\right]$<br/>$A B=C$<br/>$\Rightarrow\left[\begin{array}{l}3 x+3 y-2 y \\ 3 x-2 x+2 y\end{array}\right]=\left[\begin{array}{c}4 \\ -2\end{array}\right]$<br/>$\Rightarrow 3 x+y=4 ; x+2 y=-2$<br/>Solving these equations, <br/>\begin{array}{l}<br/>3 x+y=4 \\<br/>3 x+6 y=-6 \\<br/>(-)(-) \quad(+) \\<br/>\hline-5 y=10<br/>\end{array}<br/>$\Rightarrow \mathrm{y}=-2$<br/>So, $3 \mathrm{x}-2=4 \Rightarrow 3 \mathrm{x}=6 \Rightarrow \mathrm{x}=2$<br/>$\therefore \mathrm{A}=\left[\begin{array}{cc}0 &amp; -2 \\ 2 &amp; 4\end{array}\right], \quad \mathrm{A}^{2}=\left[\begin{array}{cc}0 &amp; -2 \\ 2 &amp; 4\end{array}\right]\left[\begin{array}{cc}0 &amp; -2 \\ 2 &amp; 4\end{array}\right]$<br/>$=\left[\begin{array}{cc}-4 &amp; -8 \\ 8 &amp; 12\end{array}\right]$</div>


title: aand-b-are-two-matrices-such-that-ab-a-and-ba-b-then-what-is-b-2-equal-to
slug: aand-b-are-two-matrices-such-that-ab-a-and-ba-b-then-what-is-b-2-equal-to-23390
tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch1_P1.db
question:
<div class="question">Aand $\mathrm{B}$ are two matrices such that $\mathrm{AB}=\overline{\mathrm{A}}$ and $\mathrm{BA}=\mathrm{B}$ then what is $\mathrm{B}^{2}$ equal to?</div>

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

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

answer:
<div class="solution">Given $\mathrm{AB}=\mathrm{A}$ and $\mathrm{BA}=\mathrm{B}$<br/>Consider $\mathrm{B}=\mathrm{BA}=\mathrm{B}(\mathrm{AB})(\because \mathrm{AB}=\mathrm{A})$<br/>$=(\mathrm{BA}) \cdot \mathrm{B}=\mathrm{B} \cdot \mathrm{B}=\mathrm{B}^{2}$<br/>Hence, $\mathrm{B}^{2}=\mathrm{B}$</div>


tags: ['Mathematics', 'Properties of Triangles', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
abc-is-a-triangle-inscribed-in-a-circle-with-centre-o-let-bac-where-4-5-9-0-let-boc-which-one-of-the-following-is-correct

slug:
abc-is-a-triangle-inscribed-in-a-circle-with-centre-o-let-bac-where-4-5-9-0-let-boc-which-one-of-the-following-is-correct-68855

question:
<div class="question">$\mathrm{ABC}$ is a triangle inscribed in a circle with centre $\mathrm{O}$. Let $\alpha=$ $\angle \mathrm{BAC}$, where $45^{\circ}   &lt; \alpha &lt; 90^{\circ} .$ Let $\beta=\angle \mathrm{BOC}$. Which one of<br/>the following is correct?</div>

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

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

answer:
<div class="solution">$\angle \mathrm{BAC}=\alpha, \angle \mathrm{BOC}=\beta$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/uk7aIUrAFgZMD1Fo4EY33zRe38VjAlvb5-LEgjHNCcg.original.fullsize.png"/><br/><br/>We know, from figure, $\beta=2 \alpha$<br/>$\therefore \cos \beta=\cos 2 \alpha$<br/>$=\frac{1-\tan ^{2} \alpha}{1+\tan ^{2} \alpha}$</div>


tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
abcd-is-a-parallelogram-and-p-is-the-point-of-intersection-of-the-diagonals-if-o-is-the-origin-then-oa-ob-oc-od-is-equal-to

slug:
abcd-is-a-parallelogram-and-p-is-the-point-of-intersection-of-the-diagonals-if-o-is-the-origin-then-oa-ob-oc-od-is-equal-to-24883

question:
<div class="question">ABCD is a parallelogram and P is the point of intersection of the diagonals. If $\mathrm{O}$ is the origin, then $\overrightarrow{\mathrm{OA}}+\overrightarrow{\mathrm{OB}}+\overrightarrow{\mathrm{OC}}+\overrightarrow{\mathrm{OD}}$ is equal to</div>

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

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/dJQfC70xzIuW4fUTYfIawotvJ55UhhM2SfDQhHWJet8.original.fullsize.png"/><br/><br/>$\because \overrightarrow{\mathrm{OA}}=\overrightarrow{\mathrm{OP}}-\overrightarrow{\mathrm{AP}} ; \overrightarrow{\mathrm{OB}}=\overrightarrow{\mathrm{OP}}+\overrightarrow{\mathrm{PB}}$<br/>$\overrightarrow{\mathrm{OC}}=\overrightarrow{\mathrm{OP}}+\overrightarrow{\mathrm{PC}} \&amp; \overrightarrow{\mathrm{OD}}=\overrightarrow{\mathrm{OP}}-\overrightarrow{\mathrm{DP}}$<br/>Also, $\overrightarrow{\mathrm{AP}}=\overrightarrow{\mathrm{PC}} \&amp; \overrightarrow{\mathrm{DP}}=\overrightarrow{\mathrm{PB}}$<br/>$\therefore \overrightarrow{\mathrm{OA}}+\overrightarrow{\mathrm{OB}}+\overrightarrow{\mathrm{OC}}+\overrightarrow{\mathrm{OD}}=4 \overrightarrow{\mathrm{OP}}$</div>


title: abcd-is-a-parallelogram-if-ab-a-bc-b-then-what-is-bd-equal-to
slug: abcd-is-a-parallelogram-if-ab-a-bc-b-then-what-is-bd-equal-to-64974
tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch1_P1.db
question:
<div class="question">$\mathrm{ABCD}$ is a parallelogram. If $\overrightarrow{\mathrm{AB}}=\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{BC}}=\overrightarrow{\mathrm{b}}$, then what is<br/>$\overrightarrow{\mathrm{BD}}$ equal to ?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad-\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/YcNk_DEXgpOug16XRe5MWoifGjbobzJQZLTNY3P6cPA.original.fullsize.png"/><br/><br/>$\overrightarrow{\mathrm{BD}}=-\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}$</div>


title: abcd-is-a-quadrilateral-forces-ab-cb-cd-and-da-act-along-its-sides-what-is-their-resultant
slug: abcd-is-a-quadrilateral-forces-ab-cb-cd-and-da-act-along-its-sides-what-is-their-resultant-42694
tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2010 (Phase 2)']
source_db: MarksBatch1_P1.db
question:
<div class="question">$\mathrm{ABCD}$ is a quadrilateral. Forces $\overrightarrow{\mathbf{A B}}, \overrightarrow{\mathbf{C B}}, \overrightarrow{\mathbf{C D}}$ and $\overrightarrow{\mathbf{D A}}$ act along its sides. What is their resultant?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \overrightarrow{\mathbf{C B}}$</span> </div>

answer:
<div class="solution">Let $\mathrm{ABCD}$ be a quadrilateral<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/2hZNjNDm7WctMXsUyryG5Kyj_LH4tXEXzPR7c9SlTOY.original.fullsize.png"/><br/><br/>$\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{CB}}+\overrightarrow{\mathrm{CD}}+\overrightarrow{\mathrm{DA}}$<br/>$=\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{CB}}+\overrightarrow{\mathrm{CA}}(\because \overrightarrow{\mathrm{CD}}+\overrightarrow{\mathrm{DA}}=\overrightarrow{\mathrm{CA}})$<br/>$=\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{CA}}+\overrightarrow{\mathrm{CB}}$<br/>$=\overrightarrow{\mathrm{CB}}+\overrightarrow{\mathrm{CB}} \quad(\because \overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{CA}}=\overrightarrow{\mathrm{CB}})$<br/>$=2 \overline{\mathrm{CB}}$</div>


title: abcd-is-a-quadrilateral-whose-diagonals-are-ac-and-bd-which-one-of-the-following-is-correct
slug: abcd-is-a-quadrilateral-whose-diagonals-are-ac-and-bd-which-one-of-the-following-is-correct-40422
tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2017 (Phase 1)']
source_db: MarksBatch1_P1.db
question:
<div class="question">$\mathrm{ABCD}$ is a quadrilateral whose diagonals are $\mathrm{AC}$ and $\mathrm{BD}$. Which one of the following is correct?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\overrightarrow{\mathrm{BA}}+\overrightarrow{\mathrm{CD}}=\overrightarrow{\mathrm{BD}}+\overline{\mathrm{CA}}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/Aql9wsJ5B-Oq01bKkPgRdL3SQCr2YYa7Ir41UJaWlAQ.original.fullsize.png"/><br/><br/>$\overrightarrow{\mathrm{BA}}+\overrightarrow{\mathrm{AD}}=\overrightarrow{\mathrm{BD}}$...(i)<br/>$\overrightarrow{\mathrm{CD}}+\overrightarrow{\mathrm{DA}}=\overrightarrow{\mathrm{CA}}$...(ii)<br/>$(\mathrm{i})+(\mathrm{ii}) \Rightarrow \overrightarrow{\mathrm{BA}}+\overrightarrow{\mathrm{CD}}=\overrightarrow{\mathrm{BD}}+\overrightarrow{\mathrm{CA}}(\because \overrightarrow{\mathrm{AD}}, \overrightarrow{\mathrm{DA}}$ cancel $)$</div>


title: accessory-sexual-character-in-female-is-promoted-by
slug: accessory-sexual-character-in-female-is-promoted-by-11261
question: <div class="question">Accessory sexual character in female is promoted by</div>
tags: ['Biology', 'Cell - The Unit of Life', 'JIPMER', 'JIPMER 2008']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">androgen</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">progesterone</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">estrogen</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">testosterone</span> </li> </ul>

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

answer:
<div class="solution">Estrogens are secreted by cells of Graafian follicles. Estradiol is the principal feminizing estrogen. It stimulates the development of female secondary sex characteristics during puberty and maintains them through the reproductive years of adult life.</div>


title: according-to-hesss-law-the-heat-of-reaction-depends-upon-2
slug: according-to-hesss-law-the-heat-of-reaction-depends-upon-2-90360
question: <div class="question">According to Hess's law, the heat of reaction depends upon</div>
tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Main']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Initial condition of reactants</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Initial and final conditions of reactants</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Intermediate path of the reaction</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">End conditions of reactants</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">End conditions of reactants</span> </div>

answer:
<div class="solution">According to Hess's law, the heat of reaction depends upon Initial and final conditions of reactants. The the heat of reaction is independant of the intermediate path of the reaction. For example, the heat of the reaction for the reaction \(\mathrm{A} \rightarrow \mathrm{D}\) is equal to the sum of the heats of the reactions
<br/>\(\begin{aligned}
<br/>&amp; \mathrm{A} \rightarrow \mathrm{B} \\
<br/>&amp; \mathrm{B} \rightarrow \mathrm{C} \\
<br/>&amp; \mathrm{C} \rightarrow \mathrm{D}
<br/>\end{aligned}\)</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'NEET']
source_db: MarksBatch1_P1.db
title:
according-to-hesss-law-what-is-the-relationship-between-the-standard-reaction-enthalpy-of-a-reaction-that-occurs-in-several-steps-and-the-standard-ent

slug:
according-to-hesss-law-what-is-the-relationship-between-the-standard-reaction-enthalpy-of-a-reaction-that-occurs-in-several-steps-and-the-standard-ent-61748

question:
<div class="question">According to Hess's Law, what is the relationship between the standard reaction enthalpy of a reaction that occurs in several steps and the standard enthalpies of the intermediate reactions?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The standard reaction enthalpy is always equal to the sum of the standard enthalpies of the intermediate reactions.</span> </div>

answer:
<div class="solution">According to Hess's Law, the standard reaction enthalpy of a reaction that occurs in several steps is equal to the sum of the standard enthalpies of the intermediate reactions into which the overall reaction may be divided at the same temperature.</div>


title: according-to-iucn-red-list-what-is-the-status-of-red-panda-ailurus-fulgens
slug: according-to-iucn-red-list-what-is-the-status-of-red-panda-ailurus-fulgens-34196
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET', 'NEET 2005']
answer: <div class="solution">Red panda is listed as Endangered on the IUCN Red List.</div>
source_db: MarksBatch1_P1.db
question:
<div class="question">According to IUCN Red List, what is the status of Red Panda (Ailurus fulgens)?</div>

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


title: according-to-iucn-red-list-what-is-the-status-of-red-panda-athurus-fulgens
slug: according-to-iucn-red-list-what-is-the-status-of-red-panda-athurus-fulgens-52559
tags: ['Biology', 'Biodiversity and its Conservation', 'JIPMER', 'JIPMER 2007']
source_db: MarksBatch1_P1.db
question:
<div class="question">According to IUCN red list what is the status of red Panda (Athurus fulgens)?</div>

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

answer:
<div class="solution">Approximately 300 species and sub species of mammals are considered as endangered by the International Union for the Conservation of Nature and Natural Resources (IUCN). Red Panda is an endangered species because it is facing a very high risk of extinction in near future.</div>


title: according-to-iupac-system-the-compound-is-named-as
slug: according-to-iupac-system-the-compound-is-named-as-47026
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Main', 'JEE Main 2024 (29 Jan Shift 2)']
source_db: MarksBatch1_P1.db
question:
<div class="question"><p>According to IUPAC system, the compoundÂ Â <img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/79b782be-b540-41c0-be39-658bc99c20a6.png" style="width: 180px; height: 139px;"/>Â is named as:</p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cyclohex</mi><mo>-</mo><mn>1</mn><mo>-</mo><mi>en</mi><mo>-</mo><mn>2</mn><mo>-</mo><mi>ol</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mi>Hydroxyhex</mi><mo>-</mo><mn>2</mn><mo>-</mo><mi>ene</mi><mo>Â </mo></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cyclohex</mi><mo>-</mo><mn>1</mn><mo>-</mo><mi>en</mi><mo>-</mo><mn>3</mn><mo>-</mo><mi>ol</mi><mo>Â </mo></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cyclohex</mi><mo>-</mo><mn>2</mn><mo>-</mo><mi>en</mi><mo>-</mo><mn>1</mn><mo>-</mo><mi>ol</mi><mo>Â </mo></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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cyclohex</mi><mo>-</mo><mn>2</mn><mo>-</mo><mi>en</mi><mo>-</mo><mn>1</mn><mo>-</mo><mi>ol</mi><mo>Â </mo></math></span> </div>

answer:
<div class="solution"><p>The structure of the IUPAC compound is</p><p>Secondary prefix+ primary prefix + root word + Primary suffix + Secondary suffix</p><p>It is a cyclic compound, with oneÂ <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>OH</mi></math>Â group on positionÂ <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math>Â and double bond at positionÂ <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math>.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/ffec23be-84f4-4cf4-826c-c02e7391f3f1.png" style="width: 196px; height: 222px;"/></p><p>There is no secondary prefix in the above compound. primary prefix is cyclo. Root word is hex, primary suffix is en and secondary suffix is ol.</p><p>Hence, the name isÂ Cyclohex-2-en-1-ol.</p></div>


title: according-to-robert-constanza-the-accounts-for-about-50-in-ecosystem-services
slug: according-to-robert-constanza-the-accounts-for-about-50-in-ecosystem-services-19423
tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch1_P1.db
question:
<div class="question">According to Robert Constanza, the ________ accounts for about 50% in ecosystem services.</div>

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

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

answer:
<div class="solution">The product of ecosystem processes are called as ecosystem services. Robert Constanza and his colleagues have put a price tag of US <math><mi>$</mi></math> 33 trillion a year on these fundamental ecosystem services. Out of the total cost of various ecosystem services, the soil formation accounts for about 50%.</div>


tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch1_P1.db
title:
according-to-robert-constanza-what-percentage-of-the-total-cost-of-various-ecosystem-services-is-used-for-nutrient-recycling-and-recreation-activity

slug:
according-to-robert-constanza-what-percentage-of-the-total-cost-of-various-ecosystem-services-is-used-for-nutrient-recycling-and-recreation-activity-55247

question:
<div class="question">According to Robert Constanza, what percentage of the total cost of various ecosystem services is used for nutrient recycling and recreation activity?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><table border="1" cellpadding="1" cellspacing="1" style="width: 368px;"> <tbody> <tr> <td>Nutrient recycling</td> <td>Recreation</td> </tr> <tr> <td>Less than 10%</td> <td>More than 10%</td> </tr> </tbody></table></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><table border="1" cellpadding="1" cellspacing="1" style="width:100%;"> <tbody> <tr> <td>Nutrient recycling</td> <td>Recreation</td> </tr> <tr> <td>Less than 10%</td> <td>Less than 10%</td> </tr> </tbody></table></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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"><table border="1" cellpadding="1" cellspacing="1" style="width: 368px;"> <tbody> <tr> <td>Nutrient recycling</td> <td>Recreation</td> </tr> <tr> <td>More than 10%</td> <td>More than 10%</td> </tr> </tbody></table></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><table border="1" cellpadding="1" cellspacing="1" style="width: 368px;"> <tbody> <tr> <td>Nutrient recycling</td> <td>Recreation</td> </tr> <tr> <td>6%</td> <td>6%</td> </tr> </tbody></table></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><table border="1" cellpadding="1" cellspacing="1" style="width:100%;"> <tbody> <tr> <td>Nutrient recycling</td> <td>Recreation</td> </tr> <tr> <td>Less than 10%</td> <td>Less than 10%</td> </tr> </tbody></table></span> </div>

answer:
<div class="solution">Robert Constanza and his colleagues have very recently tried to put price tags on natureâs life-support services. Researchers have put an average price tag of USD 33 trillion a year on these fundamental ecosystem services, which are largely taken for granted because they are free. This is near twice the value of the global gross national product GNP which is USD 18 trillion.<br/><br/>Out of the total cost of various ecosystem services, the soil formation accounts for about 50%, and contributions of other services like recreation and nutrient cycling, are less than 10% each. The cost of climate regulation and habitat for wildlife is about 6% each.</div>


title: according-to-the-iucn-red-list-what-is-the-status-of-red-panda
slug: according-to-the-iucn-red-list-what-is-the-status-of-red-panda-51984
question: <div class="question">According to the IUCN Red List, what is the status of red panda?</div>
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Critically endangered species</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Vulnerable species</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Extinct species</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Endangered species</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Endangered species</span> </div>

answer:
<div class="solution">IUCN is the International Union of Conservation of Nature and Natural resources which are now called world conservation union (WCU). It maintains a red databook or red list which is a catalogue of taxa facing a risk of extinction.<br/>Endangered species are those facing a high risk of extinction in the wild in the near future due to a decrease in its habitat, excessive predation or poaching. The percentage of endangered species in the list of threatened ones is 19% mammals,17% birds, 21% reptiles, 22% amphibians and 19% angiosperms. In India, the number is 54 animals and 113 plants, e.g., red panda, <em>Bentinckia </em><em>nicobarica</em><em>.</em><br/><br/><strong>Critically Endangered:</strong> The taxon is facing a very high risk of extinction in the wild and can become extinct any moment in the immediate future, e.g., <em>Sus </em><em class="gr-progress">salvinus</em><em> </em>(Pigmy Hog), <em>Berberis </em><em>nilghiriensis, </em>Red panda.<br/><br/><strong>Vulnerable: </strong>Presently the population is sufficient but is undergoing depletion due to some factors so that it is facing a risk of extinction in medium-term future, e.g., <em>Antelope </em><em>cervi</em><em>carpa</em><em>.</em><br/><br/><strong>Extinct: </strong>The taxon has been completely eliminated or died out from earth, e.g., Dodo.</div>


title: according-to-the-recommendation-of-iupac-how-are-the-groups-in-the-periodic-table-numbered
slug: according-to-the-recommendation-of-iupac-how-are-the-groups-in-the-periodic-table-numbered-42777
tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'NEET']
source_db: MarksBatch1_P1.db
question:
<div class="question">According to the recommendation of IUPAC, how are the groups in the Periodic Table numbered?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">From 1 to 18</span> </div>

answer:
<div class="solution">According to the recommendation of International Union of Pure and Applied Chemistry (IUPA</div>


title: according-to-werner-which-type-of-valences-are-satisfied-by-neutral-molecules-or-negative-ions
tags: ['Chemistry', 'Coordination Compounds', 'NEET']
source_db: MarksBatch1_P1.db
slug:
according-to-werner-which-type-of-valences-are-satisfied-by-neutral-molecules-or-negative-ions-63223

question:
<div class="question">According to Werner, which type of valences are satisfied by neutral molecules or negative ions?</div>

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

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

answer:
<div class="solution">Secondary valences, as proposed by Werner, are satisfied by neutral molecules or negative ions.</div>


tags: ['Chemistry', 'Coordination Compounds', 'NEET']
source_db: MarksBatch1_P1.db
title:
according-to-werners-concept-what-is-the-term-used-for-the-number-of-groups-bound-directly-to-the-metal-ion

slug:
according-to-werners-concept-what-is-the-term-used-for-the-number-of-groups-bound-directly-to-the-metal-ion-30812

question:
<div class="question">According to Werner's concept, what is the term used for the number of groups bound directly to the metal ion?</div>

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

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

answer:
<div class="solution">Werner used the term "secondary valence" for the number of groups bound directly to the metal ion.</div>


tags: ['Chemistry', 'Coordination Compounds', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Two</span> </div>
source_db: MarksBatch1_P1.db
title:
according-to-werners-theory-how-many-types-of-linkages-valences-do-metals-show-in-coordination-compounds

slug:
according-to-werners-theory-how-many-types-of-linkages-valences-do-metals-show-in-coordination-compounds-31251

question:
<div class="question">According to Werner's theory, how many types of linkages (valences) do metals show in coordination compounds?</div>

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

answer:
<div class="solution">Werner's theory states that metals show two types of linkages (valences) in coordination compounds - primary and secondary.</div>


title: according-to-werners-theory-of-coordination-compounds
slug: according-to-werners-theory-of-coordination-compounds-52934
question: <div class="question">According to Werner's theory of coordination compounds,</div>
tags: ['Chemistry', 'Coordination Compounds', 'NEET']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">primary valency is ionisable</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">secondary valency is ionisable</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">primary and secondary valencies are ionisable</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">neither primary nor secondary valency is ionisable</span> </li> </ul>

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

answer:
<div class="solution">Primary valency is ionisable while secondary valency is non-ionisable according to Werner's theory of coordination compounds.</div>


title: according-to-werners-theory-the-geometry-of-the-complex-is-determined-by
slug: according-to-werners-theory-the-geometry-of-the-complex-is-determined-by-69588
tags: ['Chemistry', 'Coordination Compounds', 'MHT CET', 'MHT CET 2019 (Shift 2)']
source_db: MarksBatch1_P1.db
question:
<div class="question">According to Wernerâs theory the geometry of the complex is determined by</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Number and position of the secondary valences in space</span> </div>

answer:
<div class="solution">Wernerâs theory was used to describe the structure and formation of complex compounds or coordination compounds. According to this theory the primary valency gives the oxidation number and the secondary valency gives the coordination number. Also, the geometry of the complex is determined by number and position of secondary valences is space as the ligand satisfying secondary valences are always directed towards fixed position in space.</div>


tags: ['Chemistry', 'Coordination Compounds', 'TS EAMCET', 'TS EAMCET 2023 (13 May Shift 1)']
source_db: MarksBatch1_P1.db
title:
according-to-werners-theory-the-number-of-groups-bonded-to-the-central-metal-atomion-in-a-coordination-complex-represent

slug:
according-to-werners-theory-the-number-of-groups-bonded-to-the-central-metal-atomion-in-a-coordination-complex-represent-40375

question:
<div class="question">According to Werner's theory, the number of groups bonded to the central metal atom/ion in a coordination complex represent.</div>

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

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

answer:
<div class="solution">The secondary valency of a central metal atom/ ion in a complex represents the number of neutral or negatively charged groups called ligands.<br/>The primary valency represents the oxidation state of the metal.</div>


title: according-to-werners-theory
slug: according-to-werners-theory-48502
question: <div class="question">According to Werner's theory</div>
tags: ['Chemistry', 'Coordination Compounds', 'JEE Main']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Primary valency can be ionized</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Secondary valency can be ionized</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Primary and secondary valencies both cannot be ionized</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Only primary valency cannot be ionized</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Primary valency can be ionized</span> </div>

answer:
<div class="solution">According to Werner's theory, a coordination compound has two different types of valency, primary and secondary. The primary valency or the ionisable valency is satisfied by the negative charged ions in the solution.</div>


tags: ['Chemistry', 'Amines']
options: None
correct_option: None
source_db: MarksBatch1_P1.db
title:
account-for-the-following-i-mathrmpkmathrmb-of-aniline-is-more-than-that-of-methylamine-ii-ethylamine-is-soluble-in-water-whereas-aniline-is-not-iii-m

slug:
account-for-the-following-i-mathrmpkmathrmb-of-aniline-is-more-than-that-of-methylamine-ii-ethylamine-is-soluble-in-water-whereas-aniline-is-not-iii-m-28866

question:
<div class="question">Account for the following<br/>(i) \(\mathrm{pK}_{\mathrm{b}}\) of aniline is more than that of methylamine<br/>(ii) Ethylamine is soluble in water whereas aniline is not.<br/>(iii) Methylamine in water reacts with ferric chloride to precipitate hydrated ferric oxide.<br/>(iv) Although amino group is \(o\) and \(p\)-directing in aromatic electrophilic substitution reactions, aniline on nitration gives a substantial amount of \(m\) nitroaniline.<br/>(v) Aniline does not undergo Friedel-Crafts reaction.<br/>(vi) Diazonium salts of aromatic amines are more stable than those of aliphatic amines.<br/>(vii) Gabriel phthalimide synthesis is preferred for synthesising primary amines.</div>

answer:
<div class="solution">(i) In aniline, the lone pair of electrons on the \(\mathrm{N}\)-atom is delocalised over the benzene ring. As a result, electron density on the nitrogen atom decreases. Whereas in \(\mathrm{CH}_3 \mathrm{NH}_2,+\) I-effect of \(-\mathrm{CH}_3\) group increases the electron density on the \(\mathrm{N}\)-atom. Therefore, aniline is a weaker base than methylamine and hence its \(\mathrm{pK}_{\mathrm{b}}\) value is higher than that of methylamine.<br/>(ii) Ethylamine dissolves in water due to intermolecular H-bonding. However, in case of aniline, due to the large hydrophobic part, i.e., hydrocarbon part, the extent of \(\mathrm{H}\)-bonding is very less therefore aniline is insoluble in water.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/tHIQ5haL3jo0V38F94tie2r58WRO7rOnRoe03Fqe9Kc.original.fullsize.png"/><br/><br/>(iii) Methylamine being more basic than water, accepts a proton from water liberating \(\mathrm{OH}^{-}\)ions.<img src="https://cdn-question-pool.getmarks.app/modules/cbse/xnp5FqIuFh8PjMF8cQ-FzIB_SrhLaV6QE1KEsK2Ns78.original.fullsize.png"/><br/><br/>These \(\mathrm{OH}^{-}\)ions combine with \(\mathrm{Fe}^{3+}\) ions present in \(\mathrm{H}_2 \mathrm{O}\) to form brown precipitate of hydrated ferric oxide.<br/>\(\mathrm{FeCl}_3 \longrightarrow \mathrm{Fe}^{3+}+3 \mathrm{Cl}^{-}\)<br/>\(2 \mathrm{Fe}^{3+}+6 \mathrm{OH}^{-} \longrightarrow \underset{\text{(Brown ppt.)}}{2 \mathrm{Fe}(\mathrm{OH})_3 \text{ or } \mathrm{Fe}_2 \mathrm{O}_3 .3 \mathrm{H}_2 \mathrm{O}}\)<br/>(iv) Nitration is usually carried out with a mixture of conc \(\mathrm{HNO}_3+\) conc \(\mathrm{H}_2 \mathrm{SO}_4\). In presence of these acids, most of aniline gets protonated to form anilinium ion. Therefore, in presence of acids, the reaction mixture consist of aniline and anilinium ion. Now, \(-\mathrm{NH}_2\) group in aniline is activating and \(o, p\)-directing while the \(-\stackrel{+}{\mathrm{NH}_3}\) group in anilinium ion is deactivating and \(m\)-directing. Nitration of aniline (due to steric hindrance at \(o\)-position) mainly gives \(p\)-nitroaniline, the nitration of anilinium ion gives \(m\)-nitroaniline. In actual practice, approx a 1:1 mixture of \(p\)-nitroaniline and \(m\)-nitroaniline is obtained. Thus, nitration of aniline gives a substantial amount of \(m\)-nitroaniline due to protonation of the amino group.<img src="https://cdn-question-pool.getmarks.app/modules/cbse/oLXY4AzVkSpw9020t_IJMaYX6XJ7BZzYnDP5_FOkhBA.original.fullsize.png"/><br/><br/>(v) Aniline being a Lewis base reacts with Lewis acid \(\mathrm{AlCl}_3\) to form a salt.<br/>\(\mathrm{C}_6 \mathrm{H}_5 \mathrm{NH}_2+\mathrm{AlCl}_3 \longrightarrow \mathrm{C}_6 \mathrm{H}_5 \mathrm{NH}_2{ }^{+} \mathrm{AlCl}_3{ }^{-}\)<br/>As a result, \(\mathrm{N}\) of aniline acquires positive charge and hence it act as a strong deactivating group for electrophilic substitution reactions. Consequently, aniline does not undergo Fridel Crafts reaction.<br/>(vi) The diazonium salts of aromatic amines are more stable than those of aliphatic amines due to dispersal of the positive charge on benzene ring as a result of resonance.<img src="https://cdn-question-pool.getmarks.app/modules/cbse/WlzDOVbqyyOAPcKI82vMNSu2f5LEARaeqrkO7Zz1J4I.original.fullsize.png"/><br/><br/>(vii) Gabriel phthalimide reaction gives pure primary amines without any contamination of secondary and tertiary amines. Therefore, it is preferred for synthesising primaryamines.</div>


tags: ['Chemistry', 'Amines', 'NEET']
source_db: MarksBatch1_P1.db
title:
account-for-the-following-statement-gabriel-phthalimide-synthesis-is-preferred-for-synthesizing-primary-amines

slug:
account-for-the-following-statement-gabriel-phthalimide-synthesis-is-preferred-for-synthesizing-primary-amines-56892

question:
<div class="question">Account for the following statement-   Gabriel phthalimide synthesis is preferred for synthesizing primary amines.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">because Gabriel phthalimide synthesis is less expensive than other methods.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">because Gabriel phthalimide synthesis provides a high yield of primary amines.</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">because Gabriel phthalimide synthesis results in the formation of only 1<sup>0</sup>amines. Secondary and tertiary amines cannot be formed through this process.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">because Gabriel phthalimide synthesis is less sensitive to reaction conditions and is therefore more reliable for primary amine synthesis.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">because Gabriel phthalimide synthesis results in the formation of only 1<sup>0</sup>amines. Secondary and tertiary amines cannot be formed through this process.</span> </div>

answer:
<div class="solution">Correct Option is : (C)<br/>because Gabriel phthalimide synthesis results in the formation of only 1<sup>0</sup>amines. Secondary and tertiary amines cannot be formed through this process.</div>


title: accumulation-of-which-one-of-the-following-acids-results-in-the-closure-of-stomata
slug: accumulation-of-which-one-of-the-following-acids-results-in-the-closure-of-stomata-37112
tags: ['Biology', 'Transport in Plants', 'NEET']
source_db: MarksBatch1_P1.db
question:
<div class="question">Accumulation of which one of the following acids results in the closure of stomata.</div>

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

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

answer:
<div class="solution">According to <math><msup><mrow><mi mathvariant="normal">K</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>-</mo><msup><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mo>+</mo></mrow></msup></math> pump theory during the closure of stomata, ABA stops the energy dependant proton pump in guard cell, thus <math><msup><mrow><mi mathvariant="normal">K</mi></mrow><mrow><mo>+</mo></mrow></msup></math> diffuses out of the cell and <math><msup><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mo>+</mo></mrow></msup></math> enters inside, which combines with malate ion to form malic acid. OP of guard cells decreases thus stomata close.</div>


title: acid-catalyzed-hydration-of-alkenes-except-ethene-leads-to-the-formation-of-1
slug: acid-catalyzed-hydration-of-alkenes-except-ethene-leads-to-the-formation-of-1-85171
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Main']
source_db: MarksBatch1_P1.db
question:
<div class="question">Acid catalyzed hydration of alkenes except ethene leads to the formation of</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Secondary or tertiary alcohol</span> </div>

answer:
<div class="solution">Acid catalysed hydration of alkenes except ethene leads to the formation of secondary or tertiary alcohol. Acid catalysed hydration of ethene leads to the formation of primary alcohol. A molecule of water is added to $\mathrm{C}=\mathrm{C}$ double bond where $-\mathrm{OH}$ group is added to more substituted $\mathrm{C}$ atom.<br/><img src="https://cdn-question-pool.getmarks.app/modules/qc/4Ykf2jNcz6PUx378FDga4se3-kL1INSLFGhSbAseUbU.original.fullsize.png"/><br/></div>


title: acid-catalyzed-hydration-of-alkenes-except-ethene-leads-to-the-formation-of
slug: acid-catalyzed-hydration-of-alkenes-except-ethene-leads-to-the-formation-of-99317
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Main', 'JEE Main 2005']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch1_P1.db
question:
<div class="question">Acid catalyzed hydration of alkenes except ethene leads to the formation of</div>

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


tags: ['Chemistry', 'Chemical Kinetics', 'VITEEE', 'VITEEE 2013']
source_db: MarksBatch1_P1.db
title:
acid-hydrolysis-of-ester-is-first-order-reaction-and-rate-constant-is-given-by-k-t-2303-lo-g-v-v-t-v-v-0-where-v-0-v-t-and-v-are-the-volumle-of-standa

slug:
acid-hydrolysis-of-ester-is-first-order-reaction-and-rate-constant-is-given-by-k-t-2303-lo-g-v-v-t-v-v-0-where-v-0-v-t-and-v-are-the-volumle-of-standa-48804

question:
<div class="question">Acid hydrolysis of ester is first order reaction and rate constant is given by $k=\frac{2.303}{t} \log \frac{V_{\infty}-V_{0}}{V_{\infty}-V_{t}}$ where, $V_{0}, V_{t}$ and $V_{\infty}$ are the volumle of standard $\mathrm{NaOH}$ required to neutralise acid present at a given time, if ester is $50 \%$ neutralised then</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$V_{\infty}=2 V_{t}-V_{0}$</span> </div>

answer:
<div class="solution">$\mathrm{RCOOR}^{\prime}+\mathrm{H}_{2} \mathrm{O} \stackrel{\mathrm{H}^{+}}{\longrightarrow} \mathrm{RCOOH}+\mathrm{R}^{\prime} \mathrm{OH}$<br/>$\begin{array}{lccc}\text { At } \mathrm{t}=0, &amp; \text { a } &amp; 0 &amp; 0 \\ \text { At timet, } &amp; \mathrm{a}-\mathrm{x} &amp; \mathrm{x} &amp; \mathrm{x} \\ \text { At time } \infty, &amp; \mathrm{a}-\mathrm{a} &amp; \mathrm{a} &amp; \mathrm{a} \\ \text { At } \mathrm{t}=0, \mathrm{~V}_{0}=\text { volume } &amp; \mathrm{Va}_{\mathrm{t}}=\mathrm{x}+\mathrm{V}_{0} &amp; &amp; \text { (catalyst) }\end{array}$<br/>$\mathrm{V}_{\infty}=\mathrm{a}+\mathrm{V}_{0}$<br/>If ester is $50 \%$ hydrolysed then, $x=\frac{a}{2}$<br/>$\begin{array}{l}<br/>\text { or } \mathrm{V}_{\mathrm{t}}=\frac{\mathrm{a}}{2}+\mathrm{V}_{0} \\<br/>\text { or } \mathrm{a}=2 \mathrm{~V}_{\mathrm{t}}-2 \mathrm{~V}_{0} \\<br/>\therefore \mathrm{V}_{\infty}=2 \mathrm{~V}_{\mathrm{t}}-2 \mathrm{~V}_{0}+\mathrm{V}_{0} \\<br/>=2 \mathrm{~V}_{\mathrm{t}}-\mathrm{V}_{0}<br/>\end{array}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
acoin-is-tossed-if-a-head-is-observed-a-number-is-randomly-selected-from-the-set-1-2-3-and-if-a-tail-is-observed-number-is-randomly-selected-from-the-

slug:
acoin-is-tossed-if-a-head-is-observed-a-number-is-randomly-selected-from-the-set-1-2-3-and-if-a-tail-is-observed-number-is-randomly-selected-from-the-58047

question:
<div class="question">Acoin is tossed If a head is observed, a number is randomly selected from the set $\{1,2,3\}$ and if a tail is observed. number is randomly selected from the set $\{2,3,4,5\}$. If the selected number be denoted by $X$, what is the probability that $X=3$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">27</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1 / 5$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1 / 6$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$7 / 2 A$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$7 / 2 A$</span> </div>

answer:
<div class="solution">Probability that $(\mathrm{X}=3)=\frac{1}{2} \times \frac{1}{3}+\frac{1}{2} \times \frac{1}{4}=\frac{7}{24}$</div>


tags: ['Biology', 'Microbes in Human Welfare', 'NEET']
source_db: MarksBatch1_P1.db
title:
activated-sludge-is-a-formed-after-sequential-filtration-and-sedimentation-in-primary-setting-tank-b-bacterial-flocs-settling-after-secondary-treatmen

slug:
activated-sludge-is-a-formed-after-sequential-filtration-and-sedimentation-in-primary-setting-tank-b-bacterial-flocs-settling-after-secondary-treatmen-29080

question:
<div class="question"><p class="CxSpFirst" style="margin:0in; margin-bottom:.0001pt"><span style="line-height:normal">Activated sludge is</span></p> <p class="CxSpMiddle" style="margin:0in; margin-bottom:.0001pt"><span style="line-height:normal">A. formed after sequential filtration and sedimentation in primary setting tank.</span></p> <p class="CxSpMiddle" style="margin:0in; margin-bottom:.0001pt"><span style="line-height:normal">B. bacterial flocs settling after secondary treatment.</span></p> <p class="CxSpMiddle" style="margin:0in; margin-bottom:.0001pt"><span style="line-height:normal">C. passed into anaerobic sludge digester.</span></p> </div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Only (A) is incorrect</span> </div>

answer:
<div class="solution"><p>The effluent from the primary settling tank is taken for secondary treatment, where the primary effluent is passed into large-aeration tanks with constant agitation, and the air is pumped into it. Aeration tanks show vigorous growth of useful aerobic heterotrophic microbes into flocs (mass of bacterial and fungal filaments). The microbes consume a significant part of the organic matter and significantly reduce the BOD of the effluent. The effluent is passed into a secondary settling tank where bacterial flocs are allowed to sediment to form activated sludge.</p><p>A part of activated sludge is fed into anaerobic sludge digesters, where the anaerobic methanogenic bacteria digest the organic matter present in sludge to produce biogas, used as sources of energy.</p></div>


title: activated-sludge-should-have-the-ability-to-settle-quickly-so-that-it-can
slug: activated-sludge-should-have-the-ability-to-settle-quickly-so-that-it-can-47669
tags: ['Biology', 'Microbes in Human Welfare']
source_db: MarksBatch1_P1.db
question:
<div class="question">Activated sludge should have the ability to settle quickly so that it can</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>be rapidly pumped back from sedimentation tank to aeration tank<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/>absorb pathogenic bacteria present in waste water while sinking to the bottom of the settling tank<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>be discarded and anaerobically digested<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>absorb colloidal organic matter</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>be rapidly pumped back from sedimentation tank to aeration tank<br/></span> </div>

answer:
<div class="solution">$\ldots$ During secondary treatment of waste water, when $\mathrm{BOD}$ of sewage has reduced, the effluent is passed into setting tank. Here, the bacterial flocs settle and the sediment is called activated sludge.<br/>In the aeration tank a small part of the sludge is used as an inoculum and the remaining part is passed into large tanks called anaerobic sludge digesters. That's why activated sludge should have the ability to settle quickly.</div>


title: activation-energy-of-a-chemical-reaction-can-be-determined-by
slug: activation-energy-of-a-chemical-reaction-can-be-determined-by-83409
question: <div class="question">Activation energy of a chemical reaction can be determined by ...... .</div>
tags: ['Chemistry', 'Chemical Kinetics']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>determining the rate constant at standard temperature<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>determining the rate constant at two temperatures<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/>determining probability of collision<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>using catalyst</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>determining the rate constant at two temperatures<br/></span> </div>

answer:
<div class="solution">Arrhenius equation relates activation energy of a chemical reaction with rate constant of a reaction at two different temperatures.<br/>$\ln \left(\frac{k_1}{k_2}\right)=\frac{E_a}{R}\left[\frac{1}{T_1}-\frac{1}{T_2}\right]$</div>


title: activation-energy-of-any-chemical-reaction-can-be-calculated-if-one-knows-the-value-of
slug: activation-energy-of-any-chemical-reaction-can-be-calculated-if-one-knows-the-value-of-68301
tags: ['Chemistry', 'Chemical Kinetics', 'NEET', 'NEET 2024']
source_db: MarksBatch1_P1.db
question:
<div class="question">Activation energy of any chemical reaction can be calculated if one knows the value of</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">rate constant at two different temperatures</span> </div>

answer:
<div class="solution">To calculate value of $E_a$<br/>Equation used is<br/>$\log \left(\frac{k_2}{k_1}\right)=\frac{E_a}{2.303 R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)$<br/>Hence $E_a$ can be calculated if value of rate constant $k$ is known at two different temperatures $T_1$ and $\mathrm{T}_2$.</div>


title: addition-of-inert-gas-to-system-n-2-g-3-h-2-g-2-n-h-3-g-at-equilibrium-at-constant-volume-then
tags: ['Chemistry', 'Chemical Equilibrium', 'NEET']
source_db: MarksBatch1_P1.db
slug:
addition-of-inert-gas-to-system-n-2-g-3-h-2-g-2-n-h-3-g-at-equilibrium-at-constant-volume-then-54174

question:
<div class="question">Addition of inert gas to system<br/> <br/> <math><msub><mrow><mi mathvariant="normal">N</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi mathvariant="normal">g</mi><mo>)</mo><mo>+</mo><mn>3</mn><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi mathvariant="normal">g</mi><mo>)</mo><mo>â</mo><mn>2</mn><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>(</mo><mi mathvariant="normal">g</mi><mo>)</mo></math><br/> <br/>
at equilibrium at constant volume. Then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><msub><mrow><mi mathvariant="normal">N</mi></mrow><mrow><mn>2</mn></mrow></msub></math> and <math><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub></math> are formed in abundance</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><msub><mrow><mi mathvariant="normal">N</mi></mrow><mrow><mn>2</mn></mrow></msub></math> , <math><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub></math> and <math><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></math> will have the same molar concentration</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The production of ammonia increases</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">No change in the equilibrium</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">No change in the equilibrium</span> </div>

answer:
<div class="solution">At constant volume on adding inert gas partial pressure of all gases remain unchanged, hence no change in equilibrium constant.</div>


title: aerobic-bacteria-are-found-in
slug: aerobic-bacteria-are-found-in-85658
question: <div class="question">Aerobic bacteria are found in:</div>
tags: ['Biology', 'Microbes in Human Welfare', 'NEET']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Activated sludge sediment in settlement tanks of sewage treatment plant</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Stomach of ruminants and produce methane</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Biogas plant and produce biogas</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Both (A) and (B)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Activated sludge sediment in settlement tanks of sewage treatment plant</span> </div>

answer:
<div class="solution">In the secondary treatment of waste, flocs are used which are a mesh formed due to the association of fungal filament with the aerobic bacteria. These flocs for sediments are the treatment called as activated sludge. This sludge can be said to be rich with aerobic bacteria as it is formed of flocs. This activated sludge is later used in anaerobic sludge digestor. Methanogens present in stomach of ruminants and biogas plants are anaerobic bacteria. Mushrooms and truffles are fungi</div>


tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
aflower-in-the-form-of-a-sector-has-been-fenced-by-a-wire-of-40-m-length-if-the-flowerbed-has-the-greatest-possible-area-then-what-is-the-radius-of-th

slug:
aflower-in-the-form-of-a-sector-has-been-fenced-by-a-wire-of-40-m-length-if-the-flowerbed-has-the-greatest-possible-area-then-what-is-the-radius-of-th-72129

question:
<div class="question">Aflower in the form of a sector has been fenced by a wire of $40 \mathrm{~m}$ length. If the flower-bed has the greatest possible area, then what is the radius of the sector? $\quad$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$25 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$20 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$10 \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$5 \mathrm{~m}$</span> </li> </ul>

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

answer:
<div class="solution">$\quad \ell+2 r=40$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/MSqYISFevJBVUqh7j-m01oDmpcvXgn_7ywFl_jDSE50.original.fullsize.png"/><br/><br/>Area is maximum, when $\ell+2 r=20 \Rightarrow r=10$</div>


title: after-double-fertilisation-a-mature-ovule-has
slug: after-double-fertilisation-a-mature-ovule-has-69645
question: <div class="question">After double fertilisation, a mature ovule has</div>
tags: ['Biology', 'Sexual Reproduction in Flowering Plants', 'AIIMS', 'AIIMS 2017']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1 diploid and 1 haploid cell</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">1 diploid and 1 triploid cell</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2 haploid and 1 triploid cell</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1 haploid and 1 triploid cell.</span> </li> </ul>

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

answer:
<div class="solution">Double fertilisation is found only in angiosperms. In this group of plants, the pollen tube on entering the embryo sac bursts open in one of the two synergids to release the two male gametes. One male gamete fuses with the egg or oosphere to form a diploid zygote or oospore. It is called generative fertilisation. The second male gamete descends down and fuses with the diploid secondary nucleus of the central cell to form a triploid primary endosperm cell. It is known as vegetative fertilisation. Thus, after double fertilisation, a mature angiospermous ovule contains one diploid cell (zygote) and one triploid cell (primary endosperm cell). The haploid cells of the ovule such as antipodals and synergids degenerate after fertilisation.</div>


title: after-double-fertilization-a-mature-ovule-has
slug: after-double-fertilization-a-mature-ovule-has-32571
question: <div class="question">After double fertilization, a mature ovule has</div>
tags: ['Biology', 'Sexual Reproduction in Flowering Plants', 'AIIMS', 'AIIMS 2013']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1 diploid and 1 haploid cell</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">1 diploid and 1 triploid cell</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2 haploid and 1 triploid cell</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1 haploid and 1 triploid cell</span> </li> </ul>

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

answer:
<div class="solution">Double fertilization is the fusion of two male gametes brought about by a pollen tube fusing to two different cells of the same female gametophyte in order to produce two different structures. It is found only in angiosperms. In angiosperms, the pollen tube bursts open in one of the two synergids to release the two male gametes. One male gamete fuses with the egg or oosphere to form a diploid zygote or oospore. It is called generative fertilization. The second male gamete descends down and fuses with the diploid secondary nucleus of the central cell to form a triploid primary endosperm cell. It is known as vegetative fertilization. Thus, after double fertilization, a mature angiospermous ovule contains one diploid cell (zygote) and one triploid cell (endosperm). The haploid cells of the ovule such as antipodals and synergids degenerate after fertilization.</div>


title: after-fertilization-in-the-embryo-sac-which-will-grow-faster
slug: after-fertilization-in-the-embryo-sac-which-will-grow-faster-90109
question: <div class="question">After fertilization, in the embryo sac, which will grow faster?</div>
tags: ['Biology', 'Sexual Reproduction in Flowering Plants', 'NEET']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Nucellus</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Endosperm</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Pollen tube</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Synergids</span> </li> </ul>

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

answer:
<div class="solution">Double fertilization occurs in Angiosperm. In this fertilization, one male gamete enters to the ovule and fuse with the egg cell result into the formation of diploid zygote while another male gamete fuse with the polar nuclei (2n) or secondary nucleus present in the center results into the formation of primary endosperm nucleus(3n) and that will be triploid in nature. Endosperm will form from the primary endosperm nucleus. They provide nourishment to the developing embryo. So the correct answer is B. Embryo will be able to survive when endosperm grows faster. Synergids guide the pollen tube and it degenerates after fertilization.</div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2008 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
after-paying-30-out-of-40-installments-of-a-debt-of-rs-3600-one-third-of-the-debt-is-unpaid-if-the-installments-are-forming-an-arithmetic-series-then-

slug:
after-paying-30-out-of-40-installments-of-a-debt-of-rs-3600-one-third-of-the-debt-is-unpaid-if-the-installments-are-forming-an-arithmetic-series-then-30502

question:
<div class="question">After paying 30 out of 40 installments of a debt of Rs. 3600 , one third of the debt is unpaid. If the installments are forming an arithmetic series, then what is the first instalment?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\operatorname{Rs} 50$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\operatorname{Rs} 51$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\operatorname{Rs} 105$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\operatorname{Rs} 110$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\operatorname{Rs} 51$</span> </div>

answer:
<div class="solution">Let first instalement be Rs. $x$ and difference of consecutive instalments be Rs. $\mathrm{d}$.<br/>$\Rightarrow \frac{30}{2}[2 \mathrm{x}+29 \mathrm{~d}]=\frac{3600 \times 2}{3}$<br/>$\left(\because 1 / 3^{\mathrm{rd}}\right.$ amount is unpaid, $2 / 3^{\mathrm{rd}}$ amount is paid)<br/>$\Rightarrow 2 x+29 d=\frac{2400}{15}$<br/>$\Rightarrow 2 x+29 d=160$ ...(i)<br/>Since total amount was 3600 and it was to be paid $1 n 40$ installment.<br/>$\Rightarrow \frac{40}{2}[2 \mathrm{x}+39 \mathrm{~d}]=3600$<br/>$\Rightarrow 2 \mathrm{x}+39 \mathrm{~d}=180$ ...(ii)<br/>On solving eqs. (1) and (2), we get $\mathrm{x}=51$ and $\mathrm{d}=2$<br/>First instalment $=$ Rs. 51</div>


title: after-simplification-what-is-the-number-of-terms-in-the-expansion-of-3-x-y-5-4-3-x-y-4-5
slug: after-simplification-what-is-the-number-of-terms-in-the-expansion-of-3-x-y-5-4-3-x-y-4-5-25133
tags: ['Mathematics', 'Binomial Theorem', 'NDA', 'NDA 2007 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">10</span> </div>
source_db: MarksBatch1_P1.db
question:
<div class="question">After simplification, what is the number of terms in the expansion of $\left[(3 x+y)^{5}\right]^{4}-\left[(3 x-y)^{4}\right]^{5} ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">4</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">5</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">10</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">11</span> </li> </ul>

answer:
<div class="solution">Given expression is:<br/>$\left[(3 x+y)^{5}\right]^{4}-\left[(3 x-y)^{4}\right]^{5}=[(3 x+y)]^{20}-[(3 x-y)]^{20}$<br/>First and second expansion will have 21 terms each but odd terms in second expansion be Ist, $3 \mathrm{rd}$, 5 th.....21st will be equal and opposite to those of first expansion. Thus, the number of terms in the expansion of above expression is 10</div>


tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
after-subtending-an-angle-of-100-0-from-its-inital-position-the-revolving-line-will-be-situated-in-which-one-of-the-following-quadrants

slug:
after-subtending-an-angle-of-100-0-from-its-inital-position-the-revolving-line-will-be-situated-in-which-one-of-the-following-quadrants-90650

question:
<div class="question">After subtending an angle of $1000^{\circ}$ from its inital position, the revolving line will be situated in which one of the following quadrants?</div>

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

answer:
<div class="solution">$1000^{\circ}=2 \times 360^{\circ}+280^{\circ}$<br/>It is clear that the revolving live will be in fourth quadrant.</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0.00</span> </div>
source_db: MarksBatch1_P1.db
title:
ag-s-fe-3-aq-ag-aq-fe-2-aq-given-standard-electrode-potentials-e-fe-3-fe-2-o-0-7-7-v-and-e-ag-ag-s-o-0-8-0-v-if-the-reaction-is-feasible-enter-100-as-

slug:
ag-s-fe-3-aq-ag-aq-fe-2-aq-given-standard-electrode-potentials-e-fe-3-fe-2-o-0-7-7-v-and-e-ag-ag-s-o-0-8-0-v-if-the-reaction-is-feasible-enter-100-as-99675

question:
<div class="question"><math> <mrow> <mtext>Ag</mtext> <mfenced close=")" open="(" separators=","> <mrow> <mtext>s</mtext> </mrow> </mfenced> <mo>+</mo> <msup> <mtext>Fe</mtext> <mrow> <mn>3</mn> <mo>+</mo> </mrow> </msup> <mfenced close=")" open="(" separators=","> <mrow> <mtext>aq</mtext> </mrow> </mfenced> <mo>â¶</mo> <msup> <mtext>Ag</mtext> <mo>+</mo> </msup> <mfenced close=")" open="(" separators=","> <mrow> <mtext>aq</mtext> </mrow> </mfenced> <mo>+</mo> <msup> <mtext>Fe</mtext> <mrow> <mn>2</mn> <mo>+</mo> </mrow> </msup> <mfenced close=")" open="(" separators=","> <mrow> <mtext>aq</mtext> </mrow> </mfenced> </mrow> </math><br/>
Given standard electrode potentials- <math><mrow><mtable><mtr><mtd> </mtd></mtr><mtr><mtd><msubsup> <mtext>E</mtext> <mrow> <msup> <mtext>Fe</mtext> <mrow> <mn>3</mn> <mo>+</mo> </mrow> </msup> <mo>/</mo> <msup> <mtext>Fe</mtext> <mrow> <mn>2</mn> <mo>+</mo> </mrow> </msup> </mrow> <mtext>o</mtext> </msubsup> <mo>=</mo> <mo>+</mo> <mn>0</mn> <mtext>.</mtext> <mn>7</mn> <mn>7</mn> <mtext> V</mtext> </mtd> </mtr> <mtr> <mtd> </mtd> </mtr> </mtable> </mrow> </math> and <math> <mrow> <msubsup> <mtext>E</mtext> <mrow> <msup> <mtext>Ag</mtext> <mo>+</mo> </msup> <mo>/</mo> <mtext>Ag</mtext> <mfenced close=")" open="(" separators=","> <mrow> <mtext>s</mtext> </mrow> </mfenced> </mrow> <mtext>o</mtext> </msubsup> <mo>=</mo> <mo>+</mo> <mn>0</mn> <mtext>.</mtext> <mn>8</mn> <mn>0</mn> <mtext> V</mtext> </mrow> </math><br/>
If the reaction is feasible, enter 1.00 as answer elsewise enter 0.00.</div>

answer:
<div class="solution"><math> <mrow> <mtext>Ag</mtext> <mfenced close=")" open="(" separators=","> <mrow> <mtext>s</mtext> </mrow> </mfenced> <mo>+</mo> <msup> <mtext>Fe</mtext> <mrow> <mn>3</mn> <mo>+</mo> </mrow> </msup> <mfenced close=")" open="(" separators=","> <mrow> <mtext>aq</mtext> </mrow> </mfenced> <mo>â¶</mo> <msup> <mtext>Ag</mtext> <mo>+</mo> </msup> <mfenced close=")" open="(" separators=","> <mrow> <mtext>aq</mtext> </mrow> </mfenced> <mo>+</mo> <msup> <mtext>Fe</mtext> <mrow> <mn>2</mn> <mo>+</mo> </mrow> </msup> <mfenced close=")" open="(" separators=","> <mrow> <mtext>aq</mtext> </mrow> </mfenced> </mrow> </math><br/><br/>        <math> <mrow> <msubsup> <mtext>E</mtext> <mtext>cell</mtext> <mtext>o</mtext> </msubsup> <mo>=</mo> <msubsup> <mtext>E</mtext> <mfenced close=")" open="(" separators=","> <mrow> <msup> <mtext>Fe</mtext> <mrow> <mn>3</mn> <mo>+</mo> </mrow> </msup> <mo>/</mo> <msup> <mtext>Fe</mtext> <mrow> <mn>2</mn> <mo>+</mo> </mrow> </msup> </mrow> </mfenced> <mtext>o</mtext> </msubsup> <mo>-</mo> <msubsup> <mtext>E</mtext> <mfenced close=")" open="(" separators=","> <mrow> <msup> <mtext>Ag</mtext> <mo>+</mo> </msup> <mo>/</mo> <mtext>Ag</mtext> </mrow> </mfenced> <mtext>o</mtext> </msubsup> <mo>=</mo> <mn>0</mn> <mtext>.</mtext> <mn>7</mn> <mn>7</mn> <mo>-</mo> <mn>0</mn> <mtext>.</mtext> <mn>8</mn> <mn>0</mn> <mo>=</mo> <mo>-</mo> <mn>0</mn> <mtext>.</mtext> <mn>0</mn> <mn>3 </mn> <mtext>V</mtext> </mrow> </math><br/><br/>The reaction is not feasible.<br/><br/><math> <mrow> <msup> <mtext>Fe</mtext> <mrow> <mn>2</mn> <mo>+</mo> </mrow> </msup> <mo>+</mo> <msup> <mtext>Ag</mtext> <mo>+</mo> </msup> <mo>â¶</mo> <mtext>Ag</mtext> <mfenced close=")" open="(" separators=","> <mrow> <mtext>s</mtext> </mrow> </mfenced> <mo>+</mo> <msup> <mtext>Fe</mtext> <mrow> <mn>3</mn> <mo>+</mo> </mrow> </msup> <mfenced close=")" open="(" separators=","> <mrow> <mtext>aq</mtext> </mrow> </mfenced> </mrow> </math></div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2022 (05 Aug Shift 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$1: 2$</span> </div>
source_db: MarksBatch1_P1.db
title:
air-column-in-two-identical-tubes-is-vibrating-tube-a-has-one-end-closed-and-tube-b-has-both-ends-open-neglecting-end-correction-the-ratio-of-the-fund

slug:
air-column-in-two-identical-tubes-is-vibrating-tube-a-has-one-end-closed-and-tube-b-has-both-ends-open-neglecting-end-correction-the-ratio-of-the-fund-29140

question:
<div class="question">Air column in two identical tubes is vibrating. Tube A has one end closed and tube B has both ends open. Neglecting end correction, the ratio of the fundamental frequency of air column in tube A to that in tube B is</div>

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

answer:
<div class="solution">The correct option is (C).<br/>Consider the following diagram:<br/><img src="https://cdn-question-pool.getmarks.app/pyq/mht_cet/L_-2SGEJVagvAk0N7SrTS36VcYOVKdV-xy50kzCDzmk.original.fullsize.png"/><br/>Velocity of a wave $v$ in a given medium is fixed, as $v=\lambda \mathrm{f}$, where $\lambda$ is the wavelength and $f$ is the frequency.<br/>Therefore,<br/>$f \propto \frac{1}{\lambda}$<br/>The ratio of frequencies in case A and case B is given by,<br/>$\frac{\mathrm{f}_1}{\mathrm{f}_2}=\frac{\lambda_2}{\lambda_1}=\frac{1}{2}$</div>


title: air-pollutants-that-produce-photochemical-smog-include
slug: air-pollutants-that-produce-photochemical-smog-include-25028
question: <div class="question">Air pollutants that produce photochemical smog include</div>
tags: ['Biology', 'Environmental Issues', 'NEET']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">Â </mi><mi mathvariant="normal">C</mi><mi mathvariant="normal">O</mi><mo>,</mo><mi mathvariant="normal">Â </mi><msub><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">nitrous oxide and fluorocarbons</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">ozone, PAN and nitrogen oxides</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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"><math><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">Â </mi><mi mathvariant="normal">C</mi><mi mathvariant="normal">l</mi><mo>,</mo><mi mathvariant="normal">Â </mi><msub><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">ozone, PAN and nitrogen oxides</span> </div>

answer:
<div class="solution">Smog is a mixture of fog with dust particles and smoke in the air of the environment. When the UV rays react with the nitrous acid to form smog that is called as photochemical smog. It is observed as a brown haze and very prominent during morning and afternoon. It also contains PAN and other secondary pollutants.</div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
source_db: MarksBatch1_P1.db
title:
alcohols-react-with-active-metals-eg-na-k-etc-to-give-corresponding-alkoxides-what-is-the-decreasing-order-of-reactivity-of-sodium-metal-towards-prima

slug:
alcohols-react-with-active-metals-eg-na-k-etc-to-give-corresponding-alkoxides-what-is-the-decreasing-order-of-reactivity-of-sodium-metal-towards-prima-39505

question:
<div class="question">Alcohols react with active metals e.g. Na, K etc. to give corresponding alkoxides. What is the decreasing order of reactivity of sodium metal towards primary, secondary and tertiary alcohols?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Decreasing order of reactivity of sodium metal is : 1Â° &gt; 2Â° &gt; 3Â°</span> </div>

answer:
<div class="solution">Correct Option is : (B)<br/>Decreasing order of reactivity of sodium metal is : 1Â° &gt; 2Â° &gt; 3Â°</div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers']
options: None
correct_option: None
source_db: MarksBatch1_P1.db
title:
alcohols-react-with-active-metals-eg-na-k-etc-to-give-corresponding-alkoxides-write-down-the-decreasing-order-of-reactivity-of-sodium-metal-towards-pr

slug:
alcohols-react-with-active-metals-eg-na-k-etc-to-give-corresponding-alkoxides-write-down-the-decreasing-order-of-reactivity-of-sodium-metal-towards-pr-47430

question:
<div class="question">Alcohols react with active metals e.g., $\mathrm{Na}, \mathrm{K}$ etc., to give corresponding alkoxides. Write down the decreasing order of reactivity of sodium metal towards primary, secondary and tertiary alcohols.</div>

answer:
<div class="solution">Alcohols are acidic in nature while sodium metal is basic in nature. The reactivity of alcohol with sodium metal decreases with decrease in acidic strength of alcohol. The order of acidic strength of alcohol is as follows<br/>$1^{\circ}$ alcohol $&gt;2^{\circ}$ alcohol $&gt;3^{\circ}$ alcohol<br/>Therefore, the correct order of reactivity of sodium metal towards these alcohols will be as follows:<br/>$1^{\circ}$ alcohol $&gt;2^{\circ}$ alcohol $&gt;3^{\circ}$ alcohol</div>


title: alkali-metals-have-negative-reduction-potential-and-hence-they-behave-as
slug: alkali-metals-have-negative-reduction-potential-and-hence-they-behave-as-68198
tags: ['Chemistry', 'Electrochemistry', 'KCET', 'KCET 2013']
source_db: MarksBatch1_P1.db
question:
<div class="question">Alkali metals have negative reduction potential and hence they behave as</div>

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

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

answer:
<div class="solution">Standard reduction potential is a measure of tendency of an element to lose electron in aqueous solution. More negative is the reduction potential, higher is the ability of element to lose electrons and hence stronger is the reducing character. Therefore, alkali metals behave as reducing agents.</div>


title: alkyl-cyanides-undergo-stephen-reduction-to-produce-1
slug: alkyl-cyanides-undergo-stephen-reduction-to-produce-1-67766
question: <div class="question">Alkyl cyanides undergo Stephen reduction to produce</div>
tags: ['Chemistry', 'Aldehydes and Ketones', 'VITEEE', 'VITEEE 2008']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">aldehyde</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">secondary amine</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">primary amine</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">amide</span> </li> </ul>

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

answer:
<div class="solution">Stephen reduction is partial reduction of alkyl or aryl cyanides to give corresponding aldehydes with a suspension of anhydrous stannous chloride in ether.<br/>$\mathrm{SnCl}_{2}+2 \mathrm{HCl} \longrightarrow \mathrm{SnCl}_{4}+2[\mathrm{H}]$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/viteee/-w3BVgM43u22tBWhQc0mx-udys87iypUTxmmkvXnLQw.original.fullsize.png"/></div>


title: alkyl-cyanides-undergo-stephen-reduction-to-produce
slug: alkyl-cyanides-undergo-stephen-reduction-to-produce-70546
question: <div class="question">Alkyl cyanides undergo Stephen reduction to produce</div>
tags: ['Chemistry', 'Amines', 'NEET']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Aldehyde</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Secondary amine</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Primary amine</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Amide</span> </li> </ul>

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

answer:
<div class="solution">An alkyl cyanide is dissolved in ether or better in ethyl formate or ethyl acetate, and reduced with <math> <mrow> <msub> <mrow> <mtext>SnCl</mtext></mrow> <mtext>2</mtext> </msub> </mrow> </math> and <math><mi>HCl</mi></math> and then steam distilled. The whole process is called Stephen reaction. In this process, alkyl cyanide is reduced to aldehyde.<br/><br/><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/140asda.PNG" style="width: 350px; height: 149px;"/><br/><br/>There is no analogous method for the preparation of ketones.</div>


title: all-of-the-following-statements-are-correct-about-active-immunity-except
slug: all-of-the-following-statements-are-correct-about-active-immunity-except-21764
tags: ['Biology', 'Human Health and Diseases', 'NEET']
source_db: MarksBatch1_P1.db
question:
<div class="question">All of the following statements are correct about active immunity, except</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">It is slow and takes time to give its full effective response.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Memory cells are formed.</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Antibodies are not formed during primary response.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Exposure of antigen is a pre-requisite for the development of active immunity.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Antibodies are not formed during primary response.</span> </div>

answer:
<div class="solution">It is developed when a host is exposed to antigens (living or dead microbes/proteins) and antibodies are produced in the host body (both in primary and secondary immune response). Active immunity is slow and takes time to give its full effective response. It can be developed by injecting the microbes or by the natural entry of infectious organisms into the body.<br/><br/>Example: During Vaccination and Immunisation.</div>


tags: ['Biology', 'Breathing and Exchange of Gases', 'NEET']
source_db: MarksBatch1_P1.db
title:
all-of-the-following-structures-of-the-human-respiratory-system-contains-incomplete-cartilaginous-rings-except

slug:
all-of-the-following-structures-of-the-human-respiratory-system-contains-incomplete-cartilaginous-rings-except-28509

question:
<div class="question">All of the following structures of the human respiratory system contains incomplete cartilaginous rings, except:</div>

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

answer:
<div class="solution">The trachea, primary bronchi, secondary bronchi, tertiary bronchi and initial bronchioles are supported by incomplete cartilaginous rings.</div>


tags: ['Mathematics', 'Matrices', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
all-possible-values-of-scalar-mathrmk-so-that-the-matrix-mathrma1-mathrmki-is-singular-where-mathrmaleftbeginarraylll1-0-2-0-2-1-1-0-0endarrayright

slug:
all-possible-values-of-scalar-mathrmk-so-that-the-matrix-mathrma1-mathrmki-is-singular-where-mathrmaleftbeginarraylll1-0-2-0-2-1-1-0-0endarrayright-24989

question:
<div class="question">All possible values of scalar \( \mathrm{k} \) so that the matrix \( \mathrm{A}^{-1} \) - \( \mathrm{kI} \) is singular where \( \mathrm{A}=\left[\begin{array}{lll}1 &amp; 0 &amp; 2 \\ 0 &amp; 2 &amp; 1 \\ 1 &amp; 0 &amp; 0\end{array}\right] \)</div>

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

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

answer:
<div class="solution">|A<sup>-1</sup> - kI| = 0<br/>|A|A<sup>-1</sup> - kI| = 0 (|A| <mo>≠</mo> 0)<br/>|I - kA| = 0<br/><math> <mrow> <mfenced close="|" open="|" separators=","> <mrow> <mfrac> <mrow> <mtext>I</mtext> </mrow> <mrow> <mtext>k</mtext> </mrow> </mfrac> <mo>-</mo> <mtext>A</mtext> </mrow> </mfenced> <mo>=</mo> <mn>0</mn> <mo>⇒</mo> <mfenced close="|" open="|" separators=","> <mrow> <mtext>A</mtext> <mo>-</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mtext>k</mtext> </mrow> </mfrac> <mo>·</mo> <mtext>I</mtext> </mrow> </mfenced> <mo>=</mo> <mn>0</mn> </mrow> </math><br/><mo>⇒</mo> |A - <mi>λ</mi>I| = 0 where <math> <mrow> <mi>λ</mi> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mtext>k</mtext> </mrow> </mfrac> </mrow> </math><br/><math> <mrow> <mo>=</mo> <mfenced close="|" open="|" separators=","> <mrow> <mtable> <mtr> <mtd> <mn>1</mn> <mo>-</mo> <mi>λ</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>2</mn> <mo>-</mo> <mi>λ</mi> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>-</mo> <mi>λ</mi> </mtd> </mtr> </mtable> </mrow> </mfenced> <mo>=</mo> <mn>0</mn> </mrow> </math><br/>=(1 - <mi>λ</mi>) (-<mi>λ</mi>) (2 - <mi>λ</mi>) + 2(0 - (2 - <mi>λ</mi>)) = 0<br/>= -<mi>λ</mi><sup>3</sup> + 3<mi>λ</mi><sup>2</sup> - 2<mi>λ</mi> - 4 + 2<mi>λ</mi> = 0<br/><mi>= λ</mi><sup>3</sup> - 3<mi>λ</mi><sup>2</sup> + 4 = 0 <mo>⇒</mo> <mi>λ</mi> = 2, 2,-1 <mi>λ</mi> k = <math> <mrow> <mo>-</mo> <mn>1</mn> <mtext>,</mtext> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math></div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch1_P1.db
title:
all-the-energy-released-from-the-reaction-x-y-r-g-o-193-kj-mo-l-1-is-used-for-oxidizing-m-as-m-m-3-2-e-e-o-025-v-under-standard-conditions-the-number-

slug:
all-the-energy-released-from-the-reaction-x-y-r-g-o-193-kj-mo-l-1-is-used-for-oxidizing-m-as-m-m-3-2-e-e-o-025-v-under-standard-conditions-the-number-39617

question:
<div class="question">All the energy released from the reaction <math><mi mathvariant="normal">X</mi><mo>â</mo><mi mathvariant="normal">Y</mi><mo>,</mo><msub><mrow><mi mathvariant="normal">Î</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub><msup><mrow><mi mathvariant="normal">G</mi></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msup><mo>=</mo><mo>-</mo><mtext>193 kJ mo</mtext><msup><mrow><mtext>l</mtext></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> is used for oxidizing <math><msup><mrow><mi mathvariant="normal">M</mi></mrow><mrow><mo>+</mo></mrow></msup></math> as <math><msup><mrow><mi mathvariant="normal">M</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>â</mo><msup><mrow><mi mathvariant="normal">M</mi></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup><mo>+</mo><mn>2</mn><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mo>-</mo></mrow></msup><mo>,</mo><msup><mrow><mi mathvariant="normal">E</mi></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msup><mo>=</mo><mo>-</mo><mn>0.25</mn><mi mathvariant="normal">V</mi><mo>.</mo></math><br/>
Under standard conditions, the number of moles of <math><msup><mrow><mi mathvariant="normal">M</mi></mrow><mrow><mo>+</mo></mrow></msup></math> oxidized when one mole of X is converted to Y is [F = 96500 C <math><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><msup><mrow><mi mathvariant="normal">l</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> ]</div>

answer:
<div class="solution"><math><mi mathvariant="normal">Î</mi><msup><mrow><mi mathvariant="normal">G</mi></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msup><mo>=</mo><mo>-</mo><msup><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">F</mi><mi mathvariant="normal">E</mi></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msup></math><br/><br/><math><mo>-</mo><mi mathvariant="normal">n</mi><mo>=</mo><mfrac><mrow><mn>193</mn><mo>Ã</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>3</mn></mrow></msup></mrow><mrow><mn>96500</mn><mo>Ã</mo><mn>0.25</mn></mrow></mfrac><mo>=</mo><mn>8</mn></math><br/><br/>So No. of moles of <math><msup><mrow><mi mathvariant="normal">M</mi></mrow><mrow><mo>+</mo></mrow></msup></math> oxidized by 1 moles of <math><mi mathvariant="normal">X</mi><mo>=</mo><mfrac><mrow><mn>8</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>=</mo><mn>4</mn></math></div>


tags: ['Chemistry', 'Redox Reactions', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
all-the-following-species-are-strong-oxidizing-agents-their-strength-as-oxidizing-agents-in-acidic-solution-is-such-that

slug:
all-the-following-species-are-strong-oxidizing-agents-their-strength-as-oxidizing-agents-in-acidic-solution-is-such-that-27065

question:
<div class="question">All the following species are strong oxidizing agents. Their strength as oxidizing agents in acidic solution is such that</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><msub><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>2</mn></mrow></msub><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>8</mn></mrow><mrow><mn>2</mn><mo>-</mo></mrow></msubsup><mo>&gt;</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">r</mi></mrow><mrow><mn>2</mn></mrow></msub><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>7</mn></mrow><mrow><mn>2</mn><mo>-</mo></mrow></msubsup><mo>&gt;</mo><mi mathvariant="normal">M</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>4</mn></mrow><mrow><mo>-</mo></mrow></msubsup></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mi mathvariant="normal">M</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>4</mn></mrow><mrow><mo>-</mo></mrow></msubsup><mo>&gt;</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">r</mi></mrow><mrow><mn>2</mn></mrow></msub><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>7</mn></mrow><mrow><mn>2</mn><mo>-</mo></mrow></msubsup><mo>&gt;</mo><msub><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>2</mn></mrow></msub><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>8</mn></mrow><mrow><mn>2</mn><mo>-</mo></mrow></msubsup></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math><msub><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>2</mn></mrow></msub><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>8</mn></mrow><mrow><mn>2</mn><mo>-</mo></mrow></msubsup><mo>&gt;</mo><mi mathvariant="normal">M</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>4</mn></mrow><mrow><mo>-</mo></mrow></msubsup><mo>&gt;</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">r</mi></mrow><mrow><mn>2</mn></mrow></msub><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>7</mn></mrow><mrow><mn>2</mn><mo>-</mo></mrow></msubsup></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"><math><mi mathvariant="normal">M</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>4</mn></mrow><mrow><mo>-</mo></mrow></msubsup><mo>&gt;</mo><msub><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>2</mn></mrow></msub><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>8</mn></mrow><mrow><mn>2</mn><mo>-</mo></mrow></msubsup><mo>&gt;</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">r</mi></mrow><mrow><mn>2</mn></mrow></msub><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>7</mn></mrow><mrow><mn>2</mn><mo>-</mo></mrow></msubsup></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><msub><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>2</mn></mrow></msub><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>8</mn></mrow><mrow><mn>2</mn><mo>-</mo></mrow></msubsup><mo>&gt;</mo><mi mathvariant="normal">M</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>4</mn></mrow><mrow><mo>-</mo></mrow></msubsup><mo>&gt;</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">r</mi></mrow><mrow><mn>2</mn></mrow></msub><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>7</mn></mrow><mrow><mn>2</mn><mo>-</mo></mrow></msubsup></math></span> </div>

answer:
<div class="solution">The standard reduction potentials of the above species in acidic medium are as given below<br/><math><msub><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>2</mn></mrow></msub><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>8</mn></mrow><mrow><mn>2</mn><mo>-</mo></mrow></msubsup><mo>(</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">q</mi><mo>)</mo><mo>+</mo><mn>2</mn><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mo>-</mo></mrow></msup><mo>â</mo><mn>2</mn><mi mathvariant="normal">S</mi><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>4</mn></mrow><mrow><mn>2</mn><mo>-</mo></mrow></msubsup><mo>(</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">q</mi><mo>)</mo><mo>;</mo><mi mathvariant="normal">E</mi><mo>Â°</mo><mo>=</mo><mo>+</mo><mn>2.01</mn><mtext>V</mtext></math><br/><math><mi mathvariant="normal">M</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>4</mn></mrow><mrow><mo>-</mo></mrow></msubsup><mo>(</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">q</mi><mo>)</mo><mo>+</mo><mn>8</mn><msup><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>+</mo><mn>5</mn><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mo>-</mo></mrow></msup><mo>â</mo><mi mathvariant="normal">M</mi><msup><mrow><mi mathvariant="normal">n</mi></mrow><mrow><mn>2</mn><mo>+</mo></mrow></msup><mo>(</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">q</mi><mo>)</mo><mo>+</mo><mn>4</mn><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">O</mi><mo>;</mo><mi mathvariant="normal">E</mi><mo>Â°</mo><mo>=</mo><mo>+</mo><mn>1.77</mn><mtext>V</mtext></math><br/><math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">r</mi></mrow><mrow><mn>2</mn></mrow></msub><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>7</mn></mrow><mrow><mn>2</mn><mo>-</mo></mrow></msubsup><mo>(</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">q</mi><mo>)</mo><mo>+</mo><mn>14</mn><msup><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>+</mo><mn>6</mn><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mo>-</mo></mrow></msup><mo>â</mo><mn>2</mn><mi mathvariant="normal">C</mi><msup><mrow><mi mathvariant="normal">r</mi></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup><mo>+</mo><mn>7</mn><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">O</mi><mo>;</mo><mi mathvariant="normal">E</mi><mo>Â°</mo><mo>=</mo><mo>+</mo><mn>1.33</mn><mtext>V</mtext></math><br/>The more the standard reduction potential, the more the tendency of the species to undergo reduction and more strongly it (species) would work as oxidizing agent.<br/>As a result, their strength as oxidizing agent in acidic solution decreases in the following order<br/><math><msub><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>2</mn></mrow></msub><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>8</mn></mrow><mrow><mn>2</mn><mo>-</mo></mrow></msubsup><mo>&gt;</mo><mi mathvariant="normal">M</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>4</mn></mrow><mrow><mo>-</mo></mrow></msubsup><mo>&gt;</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">r</mi></mrow><mrow><mn>2</mn></mrow></msub><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>7</mn></mrow><mrow><mn>2</mn><mo>-</mo></mrow></msubsup></math></div>


title: all-the-given-properties-are-found-in-the-meristematic-cell-except
slug: all-the-given-properties-are-found-in-the-meristematic-cell-except-66498
question: <div class="question">All the given properties are found in the meristematic cell except </div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">It shows the ability to actively divide.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Vacuole is very large and maybe more than one.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">It shows prominent nucleus and abundant cytoplasm.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Meristematic cell has a thin cell wall of cellulose.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Vacuole is very large and maybe more than one.</span> </div>

answer:
<div class="solution">The meristematic cell has certain set of characteristic features. It is generally isodiametric in shape, has a prominent nucleus and abundant cytoplasm. Generally, these cells do not possess vacuoles. Their cell walls are composed of cellulose and are thin to facilitate cell division. The meristematic tissue contains compactly arranged cells.</div>


title: all-these-statements-about-trophic-levels-and-ecosystems-are-false-except
slug: all-these-statements-about-trophic-levels-and-ecosystems-are-false-except-22721
tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch1_P1.db
question:
<div class="question">All these statements about trophic levels and ecosystems are false except</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Trophic level represents a functional level, not a species as such</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">A given species never occupies more than one trophic level in the same ecosystem at the same            time</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">In most ecosystems, producers are less in number and biomass than the herbivores</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Pyramid of energy can never be upright.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Trophic level represents a functional level, not a species as such</span> </div>

answer:
<div class="solution">Organisms occupy a specific position in an ecosystem based on their source of food which is known as trophic levels. In trophic levels, the first level is occupied by producers second by herbivores and third level by carnivores. These levels do not depict the species but their functional level. A sparrow becomes a primary consumer when it eats seeds and secondary consumers when it feeds on worms. Hence a given specie can occupy more than one trophic level at the same time in the ecosystem. In the most ecosystem, the pyramid of energy and biomass is upright as producers more in number and biomass than herbivores and herbivores are more in number and biomass than carnivores.</div>


tags: ['Mathematics', 'Permutation Combination', 'JEE Main', 'JEE Main 2023 (13 Apr Shift 2)']
source_db: MarksBatch1_P1.db
title:
all-words-with-or-without-meaning-are-made-using-all-the-letters-of-the-word-m-o-n-d-a-y-these-words-are-written-as-in-a-dictionary-with-serial-number

slug:
all-words-with-or-without-meaning-are-made-using-all-the-letters-of-the-word-m-o-n-d-a-y-these-words-are-written-as-in-a-dictionary-with-serial-number-68188

question:
<div class="question">All words, with or without meaning, are made using all the letters of the word <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>O</mi><mi>N</mi><mi>D</mi><mi>A</mi><mi>Y</mi></math>. These words are written as in a dictionary with serial numbers. The serial number of the word <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>O</mi><mi>N</mi><mi>D</mi><mi>A</mi><mi>Y</mi></math> is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>327</mn></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">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>328</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>324</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>326</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>327</mn></math></span> </div>

answer:
<div class="solution"><blockquote><p>The given word is MONDAY</p><p>Arranging the letters alphabetically, we get</p><p>ADMNOY</p><p>When the word starts with any of the letters A/D, the number of possibilities<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>5</mn><mo>!</mo><mo>×</mo><mn>2</mn><mo>=</mo><mn>240</mn></math></p><p>Now when the word starts with MA, then the number of possibilities<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>4</mn><mo>!</mo><mo>=</mo><mn>24</mn></math></p><p>Now when the word starts with MD, then the number of possibilities <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>4</mn><mo>!</mo><mo>=</mo><mn>24</mn></math></p><p>Now when the word starts with MN, then the number of possibilities <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>4</mn><mo>!</mo><mo>=</mo><mn>24</mn></math></p><p>Now when the word starts with MOA, then the number of possibilities<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo>!</mo><mo>=</mo><mn>6</mn></math></p><p>Now when the word starts with MOD, then the number of possibilities <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo>!</mo><mo>=</mo><mn>6</mn></math></p><p>Now when the word starts with MONA, then the number of possibilities <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mo>!</mo><mo>=</mo><mn>2</mn></math></p><p>Now when the word starts with MONDAY, then the number of possibilities<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn></math></p><p>Rank <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>240</mn><mo>+</mo><mn>24</mn><mo>×</mo><mn>3</mn><mo>+</mo><mn>6</mn><mo>×</mo><mn>2</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>=</mo><mn>327</mn></math></p><p>Hence, rank of the word MONDAY is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>327</mn></math>.</p><p><strong>SHORTCUT METHOD</strong></p><p>Another method is a shortcut, first number the alphabet and then check how many number are there on right hand side less that number and then start number in factorial in decreasing order and then multiply and add them and in last add one to find rank, </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mn>3</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>4</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>6</mn></mtd></mtr><mtr><mtd><mi>M</mi></mtd><mtd><mi>O</mi></mtd><mtd><mi>N</mi></mtd><mtd><mi>D</mi></mtd><mtd><mi>A</mi></mtd><mtd><mi>Y</mi></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>5</mn><mo>!</mo></mtd><mtd><mn>4</mn><mo>!</mo></mtd><mtd><mn>3</mn><mo>!</mo></mtd><mtd><mn>2</mn><mo>!</mo></mtd><mtd><mn>1</mn><mo>!</mo></mtd><mtd><mn>0</mn><mo>!</mo></mtd></mtr></mtable></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Rank <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>(</mo><mn>2</mn><mo>×</mo><mn>5</mn><mo>!</mo><mo>+</mo><mn>3</mn><mo>×</mo><mn>4</mn><mo>!</mo><mo>+</mo><mn>2</mn><mo>×</mo><mn>3</mn><mo>!</mo><mo>+</mo><mn>1</mn><mo>×</mo><mn>2</mn><mo>!</mo><mo>)</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>240</mn><mo>+</mo><mn>72</mn><mo>+</mo><mn>12</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>=</mo><mn>327</mn></math></p></blockquote></div>


tags: ['Physics', 'Electrostatics', 'AP EAMCET', 'AP EAMCET 2006']
source_db: MarksBatch1_P1.db
title:
along-the-xaxis-three-charges-2-q-q-and-2-q-are-placed-at-x-0-x-a-and-x-2-a-respectively-the-resultant-electric-potential-at-x-a-r-if-a-r-is-0-is-the--1

slug:
along-the-xaxis-three-charges-2-q-q-and-2-q-are-placed-at-x-0-x-a-and-x-2-a-respectively-the-resultant-electric-potential-at-x-a-r-if-a-r-is-0-is-the-1-30512

question:
<div class="question">Along the X-axis, three charges $\frac{q}{2},-q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2 a$ respectively. The resultant electric potential at $x=a+r$ (if $a&lt; &lt; r)$ is : ( $\varepsilon_0$ is the permittivity of free space)</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{q a^2}{4 \pi \varepsilon_0 r^3}$</span> </div>

answer:
<div class="solution">We have to find the electric potential at point $P$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/bruE2nDAkEzpHYM1METlXZIOXrNpTSUUUiC4OGMJ5qM.original.fullsize.png"/><br/><br/>$V_P=\left[\frac{1}{4 \pi \varepsilon_0} \frac{q / 2}{(r+a)}-\frac{1}{4 \pi \varepsilon_0} \cdot \frac{q}{r}+\frac{1}{4 \pi \varepsilon_0} \cdot \frac{q / 2}{(r-a)}\right]$<br/>$=\frac{q}{4 \pi \varepsilon_0}\left[\frac{1}{2(r+a)}-\frac{1}{r}+\frac{1}{2(r-a)}\right]$<br/>$=\frac{q}{4 \pi \varepsilon_0}\left[\frac{r(r-a)-2\left(r^2-a^2\right)+(r+a) r}{2 r\left(r^2-a^2\right)}\right]$<br/>$=\frac{q}{4 \pi \varepsilon_0}\left[\frac{r^2-a r-2 r^2+2 a^2+r^2+a r}{2 r\left(r^2-a^2\right)}\right]$<br/>$=\frac{q a^2}{4 \pi \varepsilon_0 r\left(r^2-a^2\right)}$<br/>Since, $r&gt;&gt;a$, so we have $r^2-a^2 \approx r^2$<br/>$\therefore \quad V_P=\frac{q a^2}{4 \pi \varepsilon_0 r^3}$</div>


tags: ['Physics', 'Electrostatics', 'TS EAMCET', 'TS EAMCET 2006']
source_db: MarksBatch1_P1.db
title:
along-the-xaxis-three-charges-2-q-q-and-2-q-are-placed-at-x-0-x-a-and-x-2-a-respectively-the-resultant-electric-potential-at-x-a-r-if-a-r-is-0-is-the-

slug:
along-the-xaxis-three-charges-2-q-q-and-2-q-are-placed-at-x-0-x-a-and-x-2-a-respectively-the-resultant-electric-potential-at-x-a-r-if-a-r-is-0-is-the-51197

question:
<div class="question">Along the X-axis, three charges $\frac{q}{2},-q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2 a$ respectively. The resultant electric potential at $x=a+r$ (if $a&lt; &lt; r)$ is : ( $\varepsilon_0$ is the permittivity of free space)</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{q a^2}{4 \pi \varepsilon_0 r^3}$</span> </div>

answer:
<div class="solution">We have to find the electric potential at point $P$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/bruE2nDAkEzpHYM1METlXZIOXrNpTSUUUiC4OGMJ5qM.original.fullsize.png"/><br/><br/>$V_P=\left[\frac{1}{4 \pi \varepsilon_0} \frac{q / 2}{(r+a)}-\frac{1}{4 \pi \varepsilon_0} \cdot \frac{q}{r}+\frac{1}{4 \pi \varepsilon_0} \cdot \frac{q / 2}{(r-a)}\right]$<br/>$=\frac{q}{4 \pi \varepsilon_0}\left[\frac{1}{2(r+a)}-\frac{1}{r}+\frac{1}{2(r-a)}\right]$<br/>$=\frac{q}{4 \pi \varepsilon_0}\left[\frac{r(r-a)-2\left(r^2-a^2\right)+(r+a) r}{2 r\left(r^2-a^2\right)}\right]$<br/>$=\frac{q}{4 \pi \varepsilon_0}\left[\frac{r^2-a r-2 r^2+2 a^2+r^2+a r}{2 r\left(r^2-a^2\right)}\right]$<br/>$=\frac{q a^2}{4 \pi \varepsilon_0 r\left(r^2-a^2\right)}$<br/>Since, $r&gt;&gt;a$, so we have $r^2-a^2 \approx r^2$<br/>$\therefore \quad V_P=\frac{q a^2}{4 \pi \varepsilon_0 r^3}$</div>


tags: ['Physics', 'Alternating Current', 'MHT CET', 'MHT CET 2020 (15 Oct Shift 2)']
source_db: MarksBatch1_P1.db
title:
alternating-current-of-peak-value-2-a-flows-through-the-primary-coil-of-transformer-the-coefficient-of-mutual-inductance-between-primary-and-secondary

slug:
alternating-current-of-peak-value-2-a-flows-through-the-primary-coil-of-transformer-the-coefficient-of-mutual-inductance-between-primary-and-secondary-45710

question:
<div class="question">Alternating current of peak value $\left(\frac{2}{\pi}\right)$ A flows through the primary coil of transformer. The coefficient of mutual inductance between primary and secondary coil is $1 \mathrm{H}$. The peak e.m.f. induced in secondary coil is (Frequency of a.c. $=50 \mathrm{~Hz}$ )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$400 \mathrm{~V}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$200 \mathrm{~V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$300 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$100 \mathrm{~V}$</span> </li> </ul>

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

answer:
<div class="solution">Given \(: \mathrm{I}_{0}=\frac{2}{\pi}\) ampere \(v=50 \mathrm{~Hz} \mathrm{~L}=1 \mathrm{H}\)<br/>Thus \(w=2 \pi v=2 \pi(50)=100 \pi\)<br/>Alternating current flowing through the coil is given by \(I=I_{0} \sin w t\) <br/>Differentiating it wr.t. time we get \(\frac{\mathrm{dI}}{\mathrm{dt}}=\mathrm{I}_{0} \mathrm{w} \cos w \mathrm{t}\) \(\left.\therefore \frac{\mathrm{dI}}{\mathrm{dt}}\right|_{\max }=\mathrm{I}_{0} \mathrm{~W}=\frac{2}{\pi} \times 100 \pi=200\) ampere per second<br/>Peak e.m.f induced \(\mathcal{E}=\mathrm{L} \frac{\mathrm{dI}}{\mathrm{dt}}\)<br/>\(\Longrightarrow \mathcal{E}=1 \times 200=200 \mathrm{~V}\</div>


tags: ['Physics', 'Alternating Current', 'MHT CET', 'MHT CET 2016']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">200 V</span> </div>
source_db: MarksBatch1_P1.db
title:
alternating-current-of-peak-value-2-ampere-flows-through-the-primary-coil-of-the-transformer-the-coefficient-of-mutual-inductance-between-primary-and-

slug:
alternating-current-of-peak-value-2-ampere-flows-through-the-primary-coil-of-the-transformer-the-coefficient-of-mutual-inductance-between-primary-and-53509

question:
<div class="question">Alternating current of peak value <math><mfenced separators="|"><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mi>Ï</mi></mrow></mfrac></mrow></mfenced></math> ampere flows through the primary coil of the transformer. The coefficient of mutual inductance between primary and secondary coil is 1 henry. The peak emf induced in secondary coil is (Frequency of AC = 50 Hz)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">100 V</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">200 V</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">300 V</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">400 V</span> </li> </ul>

answer:
<div class="solution">Peak value of current <math><msub><mrow><mi>I</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>r</mi><mi>m</mi><mi>s</mi></mrow></msub><mo>Ã</mo><msqrt><mn>2</mn></msqrt><mo>=</mo><mfenced separators="|"><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mi>Ï</mi></mrow></mfrac></mrow></mfenced></math> Amp<br/>Co-efficient of mutual inductance is M = 1 henry<br/>Induced emf in secondary is given by<br/><math><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mi>M</mi><mo>â</mo><mfrac><mrow><mi>d</mi><mi>i</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></math> where <math><mi>i</mi><mo>=</mo><msub><mrow><mi>i</mi></mrow><mrow><mn>0</mn></mrow></msub><mi> </mi><mo>.</mo><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mi>Ï</mi><mi>t</mi><mo>+</mo><mi>Ï</mi></mrow></mfenced></mrow></mrow></math><br/>Here <math><mi>Ï=</mi><mn>2</mn><mi>Ï</mi><mi>n</mi><mo>=</mo><mn>100</mn><mi> </mi><mi>Ï</mi><mo>.</mo></math><br/><math><mo>â´</mo><msub><mrow><mi> </mi><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>1</mn><mo>Ã</mo><mfrac><mrow><mi>d</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>(</mo><msub><mrow><mi>i</mi></mrow><mrow><mn>0</mn></mrow></msub><mi> </mi><mo>.</mo><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>â¡</mo><mrow><mi> </mi><mi>Ï</mi><mi>t</mi></mrow></mrow><mo>)</mo></math><br/><math><msub><mrow><mi>i</mi></mrow><mrow><mn>0</mn></mrow></msub><mi> </mi><mo>.</mo><mi>Ï</mi><mi> </mi><mo>.</mo><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>â¡</mo><mrow><mi> </mi><mfenced separators="|"><mrow><mi>Ï</mi><mi>t</mi></mrow></mfenced><mo>=</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mi>Ï</mi></mrow></mfrac><mo>Ã</mo><mn>2</mn><mi>Ï</mi><mo>Ã</mo><mn>50</mn><mi> </mi><mo>.</mo><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>â¡</mo><mrow><mi> </mi><mo>(</mo><mn>100</mn><mi> </mi><mi>Ï</mi><mi>t</mi><mo>)</mo></mrow></mrow></mrow></mrow></math><br/>For, <math><mi>t</mi><mo>=</mo><mn>0</mn></math> , we have <math><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>4</mn><mo>Ã</mo><mn>50</mn><mo>=</mo><mn>200</mn><mi>V</mi></math> .</div>


title: amino-terminal-and-carboxyl-terminal-are-observed-in
slug: amino-terminal-and-carboxyl-terminal-are-observed-in-94763
question: <div class="question">Amino terminal and carboxyl terminal are observed in </div>
tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">primary structure of the protein</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">secondary structure of DNA</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">sugar molecule</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">primary structure of RNA</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">primary structure of the protein</span> </div>

answer:
<div class="solution"><p>The sequence of amino acids, i.e., the positional information in a protein â which is the first amino acid, which is second, and so on â is called the primary structure of a protein. A protein is imagined as a line, the left end represented by the first amino acid, and the right end represented by the last amino acid. The first amino acid is also called as N-terminal amino acid. The last amino acid is called the C-terminal amino acid. A protein thread does not exist throughout as an extended rigid rod. The thread is folded in the form of a helix (similar to a revolving staircase).</p></div>


