# questions

title: the-compound-on-dehydrogenation-gives-a-ketone-the-original-compound-is-1
slug: the-compound-on-dehydrogenation-gives-a-ketone-the-original-compound-is-1-96739
tags: ['Chemistry', 'Aldehydes and Ketones', 'COMEDK', 'COMEDK 2017']
source_db: MarksBatch2_P2.db
question:
<div class="question">The compound on dehydrogenation gives a ketone. The original compound is</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 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">tertiary alcohol</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">carboxylic acid</span> </li> </ul>

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

answer:
<div class="solution">Secondary alcohols gives ketones on dehydrogenation e.g.,<br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/comedk/Xv6EoC6rrgWQPvAsK2ACsObAMNyZSuMbGJpxJQ5XegA.original.fullsize.png"/><br/></div>


title: the-compound-on-dehydrogenation-gives-a-ketone-the-original-compound-is-2
slug: the-compound-on-dehydrogenation-gives-a-ketone-the-original-compound-is-2-96067
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'KCET', 'KCET 2008']
source_db: MarksBatch2_P2.db
question:
<div class="question">The compound on dehydrogenation gives a ketone. The original compound is</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 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">tertiary alcohol</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">carboxylic acid</span> </li> </ul>

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

answer:
<div class="solution">Secondary alcohols on dehydrogenation with $\mathrm{Cu}$ at $573 \mathrm{~K}$ give ketones.<br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/kcet/DZ21HMwyerm5ymmHR10FFEoaeYZyWswnERgrqyA-iOg.original.fullsize.png"/><br/></div>


title: the-compound-on-dehydrogenation-gives-a-ketone-the-original-compound-is
slug: the-compound-on-dehydrogenation-gives-a-ketone-the-original-compound-is-42150
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
source_db: MarksBatch2_P2.db
question:
<div class="question">The compound on dehydrogenation gives a ketone. The original compound is</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 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">Tertiary alcohol</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Carboxylic acid</span> </li> </ul>

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

answer:
<div class="solution">Secondary alcohols on dehydrogenation with Cu at 573 K give ketones.<br/><br/><br/><img alt="" object-fit:contain="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/ci/image40-1d09291b-f1bb-4e11-9197-0e4ef77a0d23.jpg" style="max-width:"/></div>


title: the-compound-that-forms-a-yellow-oily-liquid-with-nitrous-acid-is-1
slug: the-compound-that-forms-a-yellow-oily-liquid-with-nitrous-acid-is-1-90390
question: <div class="question">The compound that forms a yellow oily liquid with nitrous acid is</div>
tags: ['Chemistry', 'Amines', 'JEE Main']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2 -methyl aniline</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">methyl amine</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Benzyl amine</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">diethyl amine</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">diethyl amine</span> </div>

answer:
<div class="solution">Secondary amines (-NH group containing amines), when reacts with nitrous acid $\left(\mathrm{HNO}_{2}\right)$, a yellow oily nitroso compound is formed.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/mht_cet/XTyUNVZDgKGdam4YMVKgLMJYwz-zZo2VDUv1IjVolfI.original.fullsize.png"/></div>


tags: ['Chemistry', 'Amines', 'AIIMS', 'AIIMS 2010']
source_db: MarksBatch2_P2.db
title:
the-compound-which-on-reaction-with-aqueous-nitrous-acid-at-low-temperature-produces-an-oily-nitrosoamine-is

slug:
the-compound-which-on-reaction-with-aqueous-nitrous-acid-at-low-temperature-produces-an-oily-nitrosoamine-is-96038

question:
<div class="question">The compound which on reaction with aqueous nitrous acid at low temperature produces an oily nitrosoamine is</div>

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

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

answer:
<div class="solution">Secondary $\left(2^{\circ}\right)$ amines (aliphatic as well as aromatic) react with nitrous acid $\left(\mathrm{HNO}_2\right)$ to form N-nitrosoamines.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/aiims/kFeOfZXh4rSH8REebYjAf2opcV_xcl6K1p-nBWtaUXc.original.fullsize.png"/><br/></div>


tags: ['Mathematics', 'Straight Lines', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
the-condition-that-the-equation-l-xm-yn0-represents-the-equation-of-a-straight-line-in-the-normal-form-is

slug:
the-condition-that-the-equation-l-xm-yn0-represents-the-equation-of-a-straight-line-in-the-normal-form-is-52549

question:
<div class="question">The condition that the equation \( l x+m y+n=0 \) represents the equation of a straight line in the normal form, is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( l^{2}+m^{2}=1 ; n &lt; 0 \)</span> </div>

answer:
<div class="solution"><blockquote><p>Given,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>x</mi><mo>+</mo><mi>m</mi><mi>y</mi><mo>+</mo><mi>n</mi><mo>=</mo><mn>0</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>(</mo><mi mathvariant="normal">i</mi><mo>)</mo></math></p><p>Standard normal form of an equation of a line is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mi>cos</mi><mo>⁡</mo><mi>α</mi><mo>+</mo><mi>y</mi><mi>sin</mi><mo>⁡</mo><mi>α</mi><mo>=</mo><mi>p</mi><mo>,</mo><mo> </mo><mi>p</mi><mo>&gt;</mo><mn>0</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>(</mo><mi>ii</mi><mo>)</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> is the perpendicular distance from the origin to the line, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math> is an angle made by its perpendicular with the positive direction of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>)</mo></math></p><p>Comparing the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>ii</mi><mo>)</mo></math> with the given equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">i</mi><mo>)</mo></math>, we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mi>l</mi><mo>=</mo><mi>cos</mi><mi>α</mi><mo>,</mo><mo> </mo><mi>m</mi><mo>=</mo><mi>sin</mi><mi>α</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mo>-</mo><mi>p</mi></math>.</p><p>And <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>&lt;</mo><mn>0</mn></math>.</p><p>As <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>cos</mi><mn>2</mn></msup><mi>α</mi><mo>+</mo><msup><mi>sin</mi><mn>2</mn></msup><mi>α</mi><mo>=</mo><mn>1</mn><mo>⇒</mo><msup><mi>l</mi><mn>2</mn></msup><mo>+</mo><msup><mi>m</mi><mn>2</mn></msup><mo>=</mo><mn>1</mn><mo>,</mo><mo> </mo><mi>n</mi><mo>&lt;</mo><mn>0</mn></math></p></blockquote></div>


tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-condition-where-protoxylem-lies-towards-the-pith-and-metaxylem-towards-periphery-is-called-as-i-while-the-condition-where-protoxylem-lies-towards-

slug:
the-condition-where-protoxylem-lies-towards-the-pith-and-metaxylem-towards-periphery-is-called-as-i-while-the-condition-where-protoxylem-lies-towards-25876

question:
<div class="question">The condition where protoxylem lies towards the pith and metaxylem towards periphery is called as (i) while the condition where protoxylem lies towards periphery and metaxylem towards pith is known as (ii)</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">(i) endarch xylem (ii) exarch xylem.</span> </div>

answer:
<div class="solution">The primary xylem tissue is of two types : protoxylem and metaxylem. The protoxylem is formed first and the metaxylem is formed later. The primary xylem is called endarch when the protoxylem lies towards the centre(pith) and metaxylem lies towards the periphery. E.g in stem. When the protoxylem lies towards periphery and metaxylem towards the centre it is called exarch xylem, eg : in roots.</div>


tags: ['Chemistry', 'Surface Chemistry', 'JEE Main', 'JEE Main 2021 (20 Jul Shift 1)']
source_db: MarksBatch2_P2.db
title:
the-conditions-given-below-are-in-the-context-of-observing-tyndall-effect-in-colloidal-solutions-a-the-diameter-of-the-colloidal-particles-is-comparab

slug:
the-conditions-given-below-are-in-the-context-of-observing-tyndall-effect-in-colloidal-solutions-a-the-diameter-of-the-colloidal-particles-is-comparab-40858

question:
<div class="question">The conditions given below are in the context of observing Tyndall effect in colloidal solutions:<br/>(A) The diameter of the colloidal particles is comparable to the wavelength of light used.<br/>(B) The diameter of the colloidal particles is much smaller than the wavelength of light used.<br/>(C) The diameter of the colloidal particles is much larger than the wavelength of light used.<br/>(D) The refractive indices of the dispersed phase and the dispersion medium are comparable.<br/>(E) The dispersed phase has a very different refractive index from the dispersion medium. Choose the most appropriate conditions from the options given below:</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"><mo>(</mo><mi mathvariant="normal">A</mi><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">E</mi><mo>)</mo></math> only</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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"><mo>(</mo><mi mathvariant="normal">C</mi><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">D</mi><mo>)</mo></math> only</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">A</mi><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">D</mi><mo>)</mo></math> only</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">B</mi><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">E</mi><mo>)</mo></math> only</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"><mo>(</mo><mi mathvariant="normal">A</mi><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">E</mi><mo>)</mo></math> only</span> </div>

answer:
<div class="solution"><p>The phenomenon of scattering of light by colloidal particles as a result of which the path of the beam becomes visible is called a tyndall effect. Smaller the diameter and similar the magnitude of refractive indices, lesser is the scattering and hence the tyndall effect and viced-versa. The diameter of the dispersed phase particle should not be smaller than the wavelength of light used because they won't be able to scatter the light so, therefore, the diameter of the dispersed particles should be equal or not much smaller than the wavelength of the light used.<br/>2. The refractive indices (i.e. the ratio of the velocity of light in vacuum to the velocity of light in any medium) of the dispersed phase and the dispersion medium should differ greatly in magnitude than only the particles will be able to scatter the light and tyndall effect will be observed. On the other hand, if the refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude, then there will be no scattering of light and hence, therefore, no tyndall effect is observed.<br/>Hence answer <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">E</mi></math> are correct.</p></div>


title: the-connective-tissue-having-the-presence-of-abundant-fibroblasts-macrophages-and-mast-cells-is
tags: ['Biology', 'Structural Organisation in Animals', 'NEET']
source_db: MarksBatch2_P2.db
slug:
the-connective-tissue-having-the-presence-of-abundant-fibroblasts-macrophages-and-mast-cells-is-84673

question:
<div class="question">The connective tissue having the presence of abundant fibroblasts, macrophages and mast cells is:</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>Type of connective tissue</td> <td>Location</td> </tr> <tr> <td>Adipose tissue</td> <td>Beneath the skin</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: 368px;"> <tbody> <tr> <td>Type of connective tissue</td> <td>Location</td> </tr> <tr> <td>Areolar tissue</td> <td>Beneath the skin</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>Type of connective tissue</td> <td>Example</td> </tr> <tr> <td>Dense connective tissue</td> <td>Tendons</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>Type of connective tissue</td> <td>Location</td> </tr> <tr> <td>Specialised connective tissue</td> <td>Cartilage</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>Type of connective tissue</td> <td>Location</td> </tr> <tr> <td>Areolar tissue</td> <td>Beneath the skin</td> </tr> </tbody></table></span> </div>

answer:
<div class="solution">Areolar connective tissue: A type of connective tissue consisting of a gel-like matrix incorporating strands of protein fibres (collagen and elastin) and such cells as fibroblasts, mast cells, macrophages, and fat cells. This tissue is found throughout the body under the skin and linking organs and other tissues.</div>


tags: ['Mathematics', 'Determinants', 'KCET', 'KCET 2019']
source_db: MarksBatch2_P2.db
title:
the-constant-term-in-the-expansion-of-leftbeginarrayccc3-x1-2-x1-x2-5-x1-3-x2-x1-7-x2-3-x1-4-x1endarrayright-is

slug:
the-constant-term-in-the-expansion-of-leftbeginarrayccc3-x1-2-x1-x2-5-x1-3-x2-x1-7-x2-3-x1-4-x1endarrayright-is-99195

question:
<div class="question">The constant term in the expansion of \( \left|\begin{array}{ccc}3 x+1 &amp; 2 x-1 &amp; x+2 \\ 5 x-1 &amp; 3 x+2 &amp; x+1 \\ 7 x-2 &amp; 3 x+1 &amp; 4 x-1\end{array}\right| \) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\( 12 \)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\( 06 \)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">\( 00 \)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\( -10 \)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( 06 \)</span> </div>

answer:
<div class="solution">(B)<br/>Take \( x=0 \)<br/>\[<br/>\begin{array}{c}<br/>\left|\begin{array}{ccc}<br/>1 &amp; -1 &amp; 2 \\<br/>-1 &amp; 2 &amp; 1 \\<br/>-2 &amp; 1 &amp; -1<br/>\end{array}\right| \\<br/>=1(-3)+1(3)+2(3)=6<br/>\end{array}<br/>\]</div>


title: the-coordinates-of-foci-of-the-ellipse-16-x-2-9-y-2-144-are
slug: the-coordinates-of-foci-of-the-ellipse-16-x-2-9-y-2-144-are-51912
question: <div class="question">The co-ordinates of foci of the ellipse $16 x^{2}+9 y^{2}=144$ are</div>
tags: ['Mathematics', 'Ellipse', 'MHT CET', 'MHT CET 2020 (13 Oct Shift 1)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(\pm 7,0)$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$(0, \pm \sqrt{7})$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(\pm \sqrt{7}, 0)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$(0, \pm 7)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(0, \pm \sqrt{7})$</span> </div>

answer:
<div class="solution">Center is $(0,0)$, focii are $(0, \sqrt{7})$ and $(0,-\sqrt{7})$, major axis is along $y$-axis and is 8 , and minor axis is along $x$-axis and is 6 .<br/>Explanation:<br/>Note that equation $16 x^{2}+9 y^{2}=144$ by dividing each term by 144 can be written as $\frac{x^{2}}{9}+\frac{y^{2}}{16}=1$<br/>As the standard equation is of the form $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$, center is $(0,0)$.<br/>In this equation major axis is along $y$-axis and is $2 b=8$, and minor axis is along $x$ axis and is $2 a=6$.<br/>As $a=3$ and $b=4$, focii are given by $\pm \sqrt{4^{2}-3^{2}}=\pm \sqrt{7}$ i.e. $(0, \sqrt{7})$ and $(0,-\sqrt{7})$</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2007 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-coordinates-of-p-and-q-are-3-4-and-2-1-respectively-if-pq-is-extended-to-r-such-that-pr-2-qr-then-what-are-the-coordinates-of-r

slug:
the-coordinates-of-p-and-q-are-3-4-and-2-1-respectively-if-pq-is-extended-to-r-such-that-pr-2-qr-then-what-are-the-coordinates-of-r-97453

question:
<div class="question">The coordinates of $\mathrm{P}$ and $\mathrm{Q}$ are $(-3,4)$ and $(2,1)$, respectively. If $P Q$ is extended to $R$ such that $P R=2 Q R$, then what are the coordinates of $\mathrm{R} ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\quad(3,7)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(2,4)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left(-\frac{1}{2}, \frac{5}{2}\right)$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$(7,-2)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution">As given :<br/>Coordinates of $\mathrm{P}$ and $\mathrm{Q}$ are $(-3,4)$ and $(2,1)$ respectively. Let coordinates of $\mathrm{R}$ be $(\mathrm{x}, \mathrm{y})$. As given : $\mathrm{PR}=2 \mathrm{QR}$<br/>$\Rightarrow \quad \mathrm{PR}-\mathrm{QR}=\mathrm{QR} \Rightarrow \mathrm{PQ}=\mathrm{QR}$<br/>So, Q is the mid point of $P$ and $R$<br/>$\Rightarrow \quad 2=\frac{-3+\mathrm{x}}{2}$ and $1=\frac{4+\mathrm{y}}{2}$<br/>$\Rightarrow \quad \mathrm{x}=7$ and $\mathrm{y}=-2$<br/>$\therefore$ Coordinates of $\mathrm{R} \equiv(7,-2)$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-coordinates-of-the-vertices-p-q-and-r-of-a-triangle-por-are-1-1-1-3-2-2-and-0-2-6-respectively-if-rop-then-what-is-prq-equal-to

slug:
the-coordinates-of-the-vertices-p-q-and-r-of-a-triangle-por-are-1-1-1-3-2-2-and-0-2-6-respectively-if-rop-then-what-is-prq-equal-to-34559

question:
<div class="question">The coordinates of the vertices $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ of a triangle $\mathrm{POR}$ are $(1,-1,1),(3,-2,2)$ and $(0,2,6)$ respectively. If $\angle \mathrm{ROP}=\theta$. then what is $\angle P R Q$ equal to?</div>

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

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

answer:
<div class="solution">Given, $\mathrm{P}=(1,-1,1)$<br/>$\mathrm{Q}=(3,-2,2)$<br/>$\mathrm{R}=(0,2,6)$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/d5ZhUQtGLKa1RaJfGyc1NRGMEGzAZzNW1VdJegQZkQI.original.fullsize.png"/><br/><br/>Direction ratios of $\mathrm{PQ}\left(\mathrm{a}_{1}, \mathrm{~b}_{1}, \mathrm{c}_{1}\right)=(3-1,-2+1,2-1)$<br/>$=(2,-1,1)$<br/>Direction ratios of $\mathrm{PR}\left(\mathrm{a}_{2}, \mathrm{~b}_{2}, \mathrm{c}_{2}\right)=(0-1,2+1,6-1)$<br/>$=(-1,3,5)$<br/>Let us calculate, $\mathrm{a}_{1} \mathrm{a}_{2}+\mathrm{b}_{1} \mathrm{~b}_{2}+\mathrm{c}_{1} \mathrm{c}_{2}$<br/>$=(2)(-1)+(-1)(3)+(1)(5)$<br/>$=-2-3+5$<br/>$=0$<br/>$\therefore P Q \perp$ PRi.e., $\angle \overline{Q P R}=90^{\circ}$<br/>$\operatorname{In} \angle \mathrm{PQR}, \angle \mathrm{P}+\angle \mathrm{Q}+\angle \mathrm{R}=180^{\circ} \Rightarrow 90^{\circ}+\theta+\angle \mathrm{R}=180^{\circ}$<br/>$\Rightarrow \angle \mathrm{R}=90^{\circ}-\theta$</div>


title: the-coordination-number-of-a-metal-in-coordination-compounds-is
slug: the-coordination-number-of-a-metal-in-coordination-compounds-is-41785
question: <div class="question">The coordination number of a metal in coordination compounds is</div>
tags: ['Chemistry', 'Coordination Compounds', 'JEE Main']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Same as primary valency</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Sum of primary and secondary valencies</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Same as 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">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Same as secondary valency</span> </div>

answer:
<div class="solution">The secondary valency is equal to the coordination number the secondary valency are non ionizable valencies. These are satisfied by neutral molecules or negative ions.</div>


tags: ['Chemistry', 'Coordination Compounds', 'KCET', 'KCET 2020']
source_db: MarksBatch2_P2.db
title:
the-coordination-number-of-f-e-and-c-o-in-the-complex-ions-fe-c-2-o-4-3-3-and-co-scn-4-2-are-respectively

slug:
the-coordination-number-of-f-e-and-c-o-in-the-complex-ions-fe-c-2-o-4-3-3-and-co-scn-4-2-are-respectively-36753

question:
<div class="question">The coordination number of $F e$ and $C o$ in the complex ions, $\left.\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}$ and $\left[\mathrm{Co}(\mathrm{SCN})_{4}\right]^{2-}$ are respectively</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">3 and 4</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">6 and 8</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">4 and 6</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">6 and 4</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">6 and 4</span> </div>

answer:
<div class="solution">The coordination number of $\mathrm{Fe}$ in $\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3+}$ is 6 and Co in $\left[\mathrm{Co}(\mathrm{SCN})_{4}\right]^{2-}$ is 4 . It is because $\mathrm{C}_{2} \mathrm{O}_{4}$ is a bidentate ligand. So, $3 \times 2=6$<br/>SCN is a monodendate ligand $4 \times 1=4$<br/>So, depending upon the number of the ligands, we can calculate the coordination number of central metal atom.</div>


title: the-core-of-a-transformer-is-laminated-because-1
slug: the-core-of-a-transformer-is-laminated-because-1-86803
question: <div class="question">The core of a transformer is laminated because:</div>
tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">ratio of voltage in primary and secondary may be increased</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">energy losses due to eddy currents may be minimised</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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 weight of the transformer may be reduced</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">rusting of the core may be prevented</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">energy losses due to eddy currents may be minimised</span> </div>

answer:
<div class="solution">The core of a transformers is laminated to minimise the energy losses due to eddy currents.</div>


title: the-core-of-any-transformer-is-laminated-so-as-to-1
slug: the-core-of-any-transformer-is-laminated-so-as-to-1-33393
question: <div class="question">The core of any transformer is laminated so as $\mathrm{to}$</div>
tags: ['Physics', 'Alternating Current', 'AIIMS', 'AIIMS 2010']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">reduce the energy loss due to eddy currents</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">make it light weight</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">make it robust \&amp; strong</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">increase the secondary voltage</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">reduce the energy loss due to eddy currents</span> </div>

answer:
<div class="solution">The energy loss due to eddy currents is reduced by using laminated core in a transformer.</div>


title: the-core-of-any-transformer-is-laminated-so-as-to
slug: the-core-of-any-transformer-is-laminated-so-as-to-54890
question: <div class="question">The core of any transformer is laminated so as to</div>
tags: ['Physics', 'Alternating Current', 'JEE Main', 'JEE Main 2003']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>reduce the energy loss due to eddy currents<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/>make it light weight<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>make it robust and strong<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>increase the secondary voltage</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>reduce the energy loss due to eddy currents<br/></span> </div>


title: the-cork-cambium-cork-and-secondary-cortex-are-collectively-called-1
slug: the-cork-cambium-cork-and-secondary-cortex-are-collectively-called-1-50732
question: <div class="question">The cork cambium, cork and secondary cortex are collectively called</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET', 'NEET 2011 (Screening)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">phellogen</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">periderm</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">phellem</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">phelloderm</span> </li> </ul>

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

answer:
<div class="solution">The periderm is a secondary protective structure and is made up of cork cambium (phellogen), cork (phellem) and secondary cortex (phelloderm).</div>


title: the-cork-cambium-cork-and-secondary-cortex-are-collectively-called
slug: the-cork-cambium-cork-and-secondary-cortex-are-collectively-called-41502
question: <div class="question">The cork cambium, cork and secondary cortex are collectively called</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">phelloderm</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">phellogen</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">periderm</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">phellem.</span> </li> </ul>

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

answer:
<div class="solution">During secondary growth in extra stellar region hypodermis or outer cortical cells, a layer becomes meristematic which is known as cork cambium or phellogen. This phellogen also cuts off cells both on its outer side and inner side. The cells cut off on outer side are phellem or cork cells and cells cut off on inner side are phelloderm or secondary cortex. Phellem,  phellogen and phelloderm collectively constitute periderm.</div>


title: the-correct-option-representing-the-structures-forming-phellogen-phellem-and-phelloderm-is
slug: the-correct-option-representing-the-structures-forming-phellogen-phellem-and-phelloderm-is-22102
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P2.db
question:
<div class="question">The correct option representing the structures forming phellogen, phellem and phelloderm is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Phellogen: Cork cambium, Phellem: Cork and Phelloderm: Secondary cortex</span> </div>

answer:
<div class="solution">As the stem continues to increase in girth due to the activity of vascular cambium, the outer cortical and epidermis layers get broken and need to be replaced to provide new protective cell layers. Hence, sooner or later, another meristematic tissue called cork cambium or phellogen develops, usually in the cortex region. Phellogen is a couple of layers thick. It is made of narrow, thin-walled and nearly rectangular cells. Phellogen cuts off cells on both sides. The outer cells differentiate into cork or phellem while the inner cells differentiate into secondary cortex or phelloderm.</div>


title: the-correct-order-of-boiling-point-for-primary-1-secondary-2-and-tertiary-3-alcohols-is
slug: the-correct-order-of-boiling-point-for-primary-1-secondary-2-and-tertiary-3-alcohols-is-92715
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'MHT CET', 'MHT CET 2008']
source_db: MarksBatch2_P2.db
question:
<div class="question">The correct order of boiling point for primary $\left(1^{\circ}\right)$, secondary $\left(2^{\circ}\right)$ and tertiary $\left(3^{\circ}\right)$ alcohols is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1^{\circ}&gt;2^{\circ}&gt;3^{\circ}$</span> </div>

answer:
<div class="solution">Alcohols with same molecular weight are expected to have almost same boiling point however two more factors other than molecular weight are important, they are namely H-bonding and surface area of molecule. Both these factors are least in $3^{\circ}$ alcohols and maximum in $1^{\circ}$ alcohols. Hence, $3^{\circ}$ alcohols have least boiling point while $1^{\circ}$ alcohols have maximum boiling point.</div>


tags: ['Chemistry', 'Amines', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-correct-order-of-boiling-points-of-the-following-isomeric-amines-is-c-4-h-9-n-h-2-c-2-h-5-2-n-h-c-2-h-5-n-c-h-3-2

slug:
the-correct-order-of-boiling-points-of-the-following-isomeric-amines-is-c-4-h-9-n-h-2-c-2-h-5-2-n-h-c-2-h-5-n-c-h-3-2-14817

question:
<div class="question">The correct order of boiling points of the following isomeric amines is <br/><math><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>4</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>9</mn></mrow></msub><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>(</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi><mo>,</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><mi mathvariant="normal">N</mi><mo>(</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub></math></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><mi mathvariant="normal">N</mi><mo>(</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub><mo>&gt;</mo><mo>(</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi><mo>&gt;</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>4</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>9</mn></mrow></msub><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mo>(</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi><mo>&gt;</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><mi mathvariant="normal">N</mi><mo>(</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub><mo>&gt;</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>4</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>9</mn></mrow></msub><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math><mo>(</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>4</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>9</mn></mrow></msub><mo>)</mo><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>&gt;</mo><mo>(</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi><mo>&gt;</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><mi mathvariant="normal">N</mi><mo>(</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub></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><mo>(</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi><mo>&gt;</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>4</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>9</mn></mrow></msub><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>&gt;</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><mi mathvariant="normal">N</mi><mo>(</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mo>)</mo></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"><math><mo>(</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>4</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>9</mn></mrow></msub><mo>)</mo><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>&gt;</mo><mo>(</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi><mo>&gt;</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><mi mathvariant="normal">N</mi><mo>(</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub></math></span> </div>

answer:
<div class="solution">Primary and secondary amines are engaged in intermolecular association due to hydrogen bonding between nitrogen of one and hydrogen of another molecule. This intermolecular association is more in primary amines than in secondary amines as there are two hydrogen atoms available for hydrogen bond formation in it. Tertiary amines do not have intermolecular association due to the absence of hydrogen atom available for hydrogen bond formation. Therefore, the order of boiling points of amines is as follows. <br/><math><mo>(</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>4</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>9</mn></mrow></msub><mo>)</mo><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>&gt;</mo><mo>(</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi><mo>&gt;</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><mi mathvariant="normal">N</mi><mo>(</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub></math></div>


title: the-correct-order-of-chemical-reactivity-with-water-according-to-electrochemical-series
slug: the-correct-order-of-chemical-reactivity-with-water-according-to-electrochemical-series-35679
tags: ['Chemistry', 'Electrochemistry', 'JEE Main']
source_db: MarksBatch2_P2.db
question:
<div class="question">The correct order of chemical reactivity with water according to electrochemical series</div>

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

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

answer:
<div class="solution">The standard reduction potential of, $\mathrm{K}^{+} \mathrm{Mg}^{2+}, \mathrm{Zn}^{+2} \mathrm{Cu}^{2+}$ increase in this order.</div>


title: the-correct-order-of-rates-of-c-br-bond-ionisation-of-the-following-bromides-is
slug: the-correct-order-of-rates-of-c-br-bond-ionisation-of-the-following-bromides-is-83336
tags: ['Chemistry', 'General Organic Chemistry', 'TS EAMCET', 'TS EAMCET 2019 (06 May Shift 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The correct order of rates of $\mathrm{C}-\mathrm{Br}$ bond ionisation of the following bromides is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/JHCTBxIW26VyO-Oh8ysmtrPI9tvvMgeirNnJMnPzT4E.original.fullsize.png"/><br/></div>

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

answer:
<div class="solution">The more stables carbocation, the more is the<br/>rate of $\mathrm{C}-\mathrm{Br}$ ionisation.<br/>Among the given species,<br/>Specie (ii) shows aromatic nature along with resonance, thus gives most stable carbocation.<br/>Specie (i) shows less stable carbocation due to absence of aromatic nature, it only shows resonance effect.<br/>Specie (iii) is least stable because it is secondary carbocation which is stabilised by hyper conjugation. Hence, the correct order is $\mathrm{ii}&gt;\mathrm{i}&gt;\mathrm{iii}$</div>


title: the-correct-order-of-the-basis-strength-of-methyl-substituted-amines-in-aqueous-solution-is
slug: the-correct-order-of-the-basis-strength-of-methyl-substituted-amines-in-aqueous-solution-is-61675
tags: ['Chemistry', 'General Organic Chemistry', 'NEET', 'NEET 2019 (All India)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The correct order of the basis strength of methyl substituted amines in aqueous solution is:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math><msub><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi><mo>&gt;</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>&gt;</mo><msub><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">N</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><msub><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">N</mi><mo>&gt;</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>&gt;</mo><msub><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><msub><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">N</mi><mo>&gt;</mo><msub><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mi mathvariant="normal">Â </mi></mrow></msub><mo>&gt;</mo><msub><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>&gt;</mo><msub><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi><mo>&gt;</mo><msub><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">N</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><msub><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi><mo>&gt;</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>&gt;</mo><msub><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">N</mi></math></span> </div>

answer:
<div class="solution"><p>Combined effect of the inductive effect of Alkyl group <math><mfenced separators="|"><mrow><mo>+</mo><mi mathvariant="normal">I</mi></mrow></mfenced><mo>,</mo></math> steric hindrance and the salvation of Amines causes the basicity order to be Secondary Amine &gt; Primary Amine &gt; Tertiary Amine</p><p><math><msub><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi><mo>&gt;</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>&gt;</mo><msub><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">N</mi></math></p></div>


title: the-correct-sequence-of-base-strengths-in-aqueous-solution-is
slug: the-correct-sequence-of-base-strengths-in-aqueous-solution-is-54850
question: <div class="question">The correct sequence of base strengths in aqueous solution is</div>
tags: ['Chemistry', 'Amines', 'VITEEE', 'VITEEE 2007']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}&gt;\mathrm{CH}_{3} \mathrm{NH}_{2}&gt;\left(\mathrm{CH}_{3}\right)_{3} \mathrm{~N}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left(\mathrm{CH}_{3}\right)_{3} \mathrm{~N}&gt;\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}&gt;\mathrm{CH}_{3} \mathrm{NH}_{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left(\mathrm{CH}_{3}\right)_{3} \mathrm{~N}&gt;\mathrm{CH}_{3} \mathrm{NH}_{2}=\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left(\mathrm{CH}_{3}\right)_{2} \mathrm{~N} \mathrm{H}&gt;\left(\mathrm{CH}_{3}\right)_{3} \mathrm{~N}&gt;\mathrm{CH}_{3} \mathrm{NH}_{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}&gt;\mathrm{CH}_{3} \mathrm{NH}_{2}&gt;\left(\mathrm{CH}_{3}\right)_{3} \mathrm{~N}$</span> </div>

answer:
<div class="solution">It is expected that the basic nature of amines should be in order tertiary $&gt;$ secondary $&gt;$ primary but the observed order in the case of lower members is found to be as secondary $&gt;$ Primary $&gt;$ tetriary. This anomalous behaviour of tetriary amines is due to steric factors i.e crowding of alkyl groups cover nitrogen atom from all sides thus makes the approach and bonding by a proton relatively difficult which results the maximum steric strain in tetiary amines. The electrons are there but the path is blocked, resulting the reduction in basicity. Thus the correct order is $\mathrm{R}_{2} \mathrm{NH}&gt;\mathrm{R} \mathrm{NH}_{2}&gt;\mathrm{R}_{3} \mathrm{~N}$</div>


title: the-correct-sequence-of-organisms-during-hydrarch-succession-is
slug: the-correct-sequence-of-organisms-during-hydrarch-succession-is-26291
question: <div class="question">The correct sequence of organisms during hydrarch succession is:</div>
tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Phytoplankton-submerged plant-submersed free floating plant stage-reed swamp stage-marsh- meadow stage-scrub stages-forest</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Scrub stages-forest-reed swamp stage-marsh-meadow stage-submersed free floating plant                   stage-submerged plant-phytoplankton</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Submerged plant-marsh-meadow stage-scrub stages-forest-phytoplankton-submersed free                     floating plant stage-reed swamp stage</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Phytoplankton -red swamp stage-scrub stages-forest-submerged plant-submersed free floating              plant stage-marsh-meadow stage</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Phytoplankton-submerged plant-submersed free floating plant stage-reed swamp stage-marsh- meadow stage-scrub stages-forest</span> </div>

answer:
<div class="solution">Ecological succession is defined as the process of gradual and predictable change in the species composition of an area. Primary succession occurs in those areas where no organism ever existed whereas secondary succession takes place in those areas where organisms once existed but now have lost them due to some reason. In a primary succession of wetland into the forest the first to appear are the phytoplanktons. They are replaced by submerged plants and later submerged and floating plants both appear. Gradually it passes through the reed swamp and marsh meadow stages and lastly scrubs appear before forming it into a forest land.</div>


title: the-correct-sequence-of-processes-represented-by-a-b-and-c-are
slug: the-correct-sequence-of-processes-represented-by-a-b-and-c-are-71012
tags: ['Biology', 'Digestion and Absorption', 'NEET']
source_db: MarksBatch2_P2.db
question:
<div class="question">The correct sequence of processes represented by A, B, and C are:-<br/> <br/> <img alt="" object-fit:contain="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/asd_fkanvjknda_kvc.jpg" style="max-width:"/><br/>
 </div>

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

answer:
<div class="solution">The whole concept of nutrition is to obtain energy, food is digested and broken down into smaller molecules and stored. When there is need of energy these molecules are broken down through processes such as glycolysis, lipolysis Krebs cycle, and electron carrier carry these electrons and enter into cellular respiration or electron transfer chain where electron transfer generate ATP. ATP is used to carry out different tasks.</div>


tags: ['Biology', 'Human Reproduction', 'NEET', 'NEET 2009 (Screening)']
source_db: MarksBatch2_P2.db
title:
the-correct-sequence-of-spermatogenetic-stages-leading-to-the-formation-of-sperms-in-a-mature-human-testis-is-1

slug:
the-correct-sequence-of-spermatogenetic-stages-leading-to-the-formation-of-sperms-in-a-mature-human-testis-is-1-58843

question:
<div class="question">The correct sequence of spermatogenetic stages leading to the formation of sperms in a mature human testis is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">spermatogonia-spermatocyte-spermatid - sperms</span> </div>

answer:
<div class="solution">In spermatogenesis, during growth phase some spermatogonia either due to growth or due to food storage become 2 or 3 times larger of their original size and are known as primary spermatocytes, which undergo meiosis-I and as a result 2 haploid secondary spermatocytes are formed. Further, meiosis-II takes place that results in the formation of 4-spermatids. Then, these round, non-motile and haploid spermatids are transformed into thread-like motile, haploid sperms (four).</div>


title: the-correct-sequence-of-the-pathway-of-air-from-outside-to-inside-the-lungs-is
slug: the-correct-sequence-of-the-pathway-of-air-from-outside-to-inside-the-lungs-is-76665
tags: ['Biology', 'Breathing and Exchange of Gases', 'NEET']
source_db: MarksBatch2_P2.db
question:
<div class="question">The CORRECT sequence of the pathway of air from outside to inside the lungs is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Pharynx-larynx-trachea-bronchus-alveoli</span> </div>

answer:
<div class="solution">Air enters the air through the nose. The pathway followed is External nares- Nasal chambers- Pharynx- Larynx- Trachea- Primary Bronchi- Secondary bronchi- Tertiary bronchi- Bronchioles- Alveolar ducts- Atria- Alveoli.</div>


title: the-correct-statement-about-dialysis-is
slug: the-correct-statement-about-dialysis-is-10494
question: <div class="question">The correct statement about dialysis is:</div>
tags: ['Biology', 'Excretory Products and their Elimination', 'NEET']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">It acts as a permanent treatment solution to treat people with end-stage kidney disease.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">The dialysing unit into which the blood is drained contains heparin to prevent coagulation.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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 cellophane tube is surrounded by a dialysing fluid, which has the same concentration as plasma including the nitrogenous waste.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Dialysis replaces all of the functions of the kidney through diffusion, ultrafiltration and tubular secretion.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The dialysing unit into which the blood is drained contains heparin to prevent coagulation.</span> </div>

answer:
<div class="solution">Dialysis is used to provide an artificial replacement for lost kidney function in people with renal failure. Dialysis may be necessary in patients with acute kidney failure to bridge the time gap required for treating the fundamental causes and as a holding measure in patients with irreversible end stage chronic kidney disease (CKD) stage 5 until transplantation is performed. Sometimes Dialysis is the only supportive measure in patients with end stage CKD when transplantation is not possible.<br/>In this process, the blood is drained from a convenient artery and an anti-coagulant like heparin is added to prevent clotting of blood and the cleared blood is pumped back to the body through a vein after adding anti-heparin to it. Dialysis treatment replaces only some of the kidney functions like diffusion (waste removal) and ultrafiltration (fluid removal). Thus Dialysis is an imperfect treatment to replace kidney function because it does not correct the endocrine functions of the kidney.</div>


title: the-correct-statement-is
slug: the-correct-statement-is-38375
question: <div class="question">The correct statement is</div>
tags: ['Chemistry', 'd and f Block Elements', 'JEE Main']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Potassium dichromate is more soluble than sodium dichromate</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">All Cr-O bond lengths in dichromate ion are equal.</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Potassium dichromate is used as a primary standard in volumetric titrations</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">All are correct</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Potassium dichromate is used as a primary standard in volumetric titrations</span> </div>

answer:
<div class="solution">Potassium dichromate is widely used in redox titrations as primary standard.</div>


tags: ['Chemistry', 'Chemistry in Everyday Life', 'JEE Main', 'JEE Main 2019 (12 Jan Shift 2)']
source_db: MarksBatch2_P2.db
title:
the-correct-statements-among-i-to-iii-with-respect-to-potassium-ions-that-are-abundant-within-the-cell-fluids-isare-i-they-activate-many-enzymes-ii-th

slug:
the-correct-statements-among-i-to-iii-with-respect-to-potassium-ions-that-are-abundant-within-the-cell-fluids-isare-i-they-activate-many-enzymes-ii-th-91384

question:
<div class="question">The correct statement(s) among <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>III</mi></math> with respect to potassium ions that are abundant within the cell fluids, is/are<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi><mo>.</mo></math> They activate many enzymes.<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>II</mi><mo>.</mo></math> They participate in the oxidation of glucose to produce <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ATP</mi></math>.<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>III</mi><mo>.</mo></math> Along with sodium ions, they are responsible for the transmission of nerve signals.</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"><mi mathvariant="normal">I</mi><mo>, </mo><mi>II</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>III</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>III</mi></math> only</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>II</mi></math> only</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>III</mi></math> only</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"><mi mathvariant="normal">I</mi><mo>, </mo><mi>II</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>III</mi></math></span> </div>

answer:
<div class="solution"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi><mo>.</mo></math> They activate many enzymes.<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>II</mi><mo>.</mo></math> They participate in the oxidation of glucose to produce <math><mi>A</mi><mi>T</mi><mi>P</mi></math>.<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>III</mi><mo>.</mo></math> Along with sodium ions, they are responsible for the transmission of nerve signals.<br/>All are correct.</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2015 (Phase 1)']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch2_P2.db
title:
the-correlation-coefficient-between-two-variables-x-and-y-found-to-be-06-all-the-observations-on-x-and-y-are-transformed-using-the-transformations-u-2

slug:
the-correlation-coefficient-between-two-variables-x-and-y-found-to-be-06-all-the-observations-on-x-and-y-are-transformed-using-the-transformations-u-2-62566

question:
<div class="question">The correlation coefficient between two variables $X$ and $y$ found to be $0.6 .$ All the observations on $X$ and $Y$ are transformed using the transformations $U=2-3 X$ and $V=$. $Y+1$. The correlation coefficient between the transformed variables $U$ anc</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-0 \cdot f$</span> </div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2018 (Phase 2)']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch2_P2.db
title:
the-correlation-coefficient-computed-from-a-set-of-30-observations-is-08-then-the-percentage-of-variation-not-explained-by-linear-regression-is

slug:
the-correlation-coefficient-computed-from-a-set-of-30-observations-is-08-then-the-percentage-of-variation-not-explained-by-linear-regression-is-18142

question:
<div class="question">The correlation coefficient computed from a set of 30 observations is $0.8 .$ Then the percentage of variation not explained by linear regression is $\quad$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$80 \%$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$20 \%$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$64 \%$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$36 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$36 \%$</span> </div>


title: the-cumulative-frequency-of-the-largest-observed-value-must-always-be
slug: the-cumulative-frequency-of-the-largest-observed-value-must-always-be-39042
tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The cumulative frequency of the largest observed value must always be : $\quad$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Equal to total number of observations</span> </div>

answer:
<div class="solution">The cumulative frequency of the largest observed value must always be equal to the total number of observations</div>


tags: ['Physics', 'Current Electricity', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-current-of-a-conductor-flowing-through-a-conductor-in-terms-of-the-drift-speed-of-electrons-is-the-symbols-have-their-usual-meanings

slug:
the-current-of-a-conductor-flowing-through-a-conductor-in-terms-of-the-drift-speed-of-electrons-is-the-symbols-have-their-usual-meanings-16779

question:
<div class="question">The current of a conductor flowing through a conductor in terms of the drift speed of electrons is (the symbols have their usual meanings) </div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><div><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>I</mi><mo>=</mo><mi></mi><msqrt> <mrow> <mi>n</mi><mi>Ae</mi> </mrow> </msqrt> <msub> <mi>v</mi> <mi>d</mi> </msub> </mrow> </math> </span></p> <li class=""> <span class="option-label">B</span> <span class="option-data"><div><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>I</mi><mo>=</mo><mi>A</mi><msqrt> <mrow> <mi>n</mi><mi>e</mi> </mrow> </msqrt> <msub> <mi>v</mi> <mi>d</mi> </msub> </mrow> </math> </span></p><p><span></span></p><p><span></span></p><p><span></span></p><p><span></span></p><p><span></span></p><p><span></span></p></div></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><div><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>I</mi><mo>=</mo><mfrac> <mrow> <mi>n</mi><mi>e</mi> </mrow> <mrow> <mi>A</mi><msub> <mi>v</mi> <mi>d</mi> </msub> </mrow> </mfrac> </mrow> </math> </span></p><p><span></span></p><p><span></span></p><p><span></span></p><p><span></span></p><p><span></span></p><p><span></span></p></div></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><div><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>I</mi><mo>=</mo><mi>n</mi><mi>e</mi><mi>A</mi><msub> <mi>v</mi> <mi>d</mi> </msub> </mrow> </math> </span></p><p> </p><p> </p><p> </p><p> </p><p> </p><p> </p></div></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> <!-- /Question --> <!-- Solution --> <section class="solution-container" id="accepted-answer"> <div class="solution-header"> <span class="label">Solution:</span> <div class="badges-container" data-pagefind-ignore=""> <span class="badge upvotes-count"> <svg fill="none" height="16" viewbox="0 0 16 16" width="16" xmlns="http://www.w3.org/2000/svg"> <path d="M14.625 5.0075C14.4842 4.84795 14.3111 4.72019 14.1171 4.63269C13.9231 4.54519 13.7128 4.49996 13.5 4.5H10V3.5C10 2.83696 9.73661 2.20107 9.26777 1.73223C8.79893 1.26339 8.16304 1 7.5 1C7.40711 0.999934 7.31604 1.02574 7.237 1.07454C7.15795 1.12333 7.09407 1.19318 7.0525 1.27625L4.69125 6H2C1.73478 6 1.48043 6.10536 1.29289 6.29289C1.10536 6.48043 1 6.73478 1 7V12.5C1 12.7652 1.10536 13.0196 1.29289 13.2071C1.48043 13.3946 1.73478 13.5 2 13.5H12.75C13.1154 13.5001 13.4684 13.3668 13.7425 13.1252C14.0166 12.8835 14.1931 12.5501 14.2388 12.1875L14.9888 6.1875C15.0153 5.97626 14.9966 5.76179 14.9339 5.55833C14.8712 5.35488 14.7659 5.16711 14.625 5.0075ZM2 7H4.5V12.5H2V7Z" fill="#014A82"></path> </svg> 2385 Upvotes
</span> <span class="badge expert-verification-badge" data-pagefind-ignore=""> <svg fill="none" height="16" viewbox="0 0 16 16" width="16" xmlns="http://www.w3.org/2000/svg"> <path d="M14.1163 6.42625C13.8806 6.18 13.6369 5.92625 13.545 5.70312C13.46 5.49875 13.455 5.16 13.45 4.83187C13.4406 4.22187 13.4306 3.53062 12.95 3.05C12.4694 2.56937 11.7781 2.55937 11.1681 2.55C10.84 2.545 10.5012 2.54 10.2969 2.455C10.0744 2.36312 9.82 2.11937 9.57375 1.88375C9.1425 1.46937 8.6525 1 8 1C7.3475 1 6.85812 1.46937 6.42625 1.88375C6.18 2.11937 5.92625 2.36312 5.70312 2.455C5.5 2.54 5.16 2.545 4.83187 2.55C4.22187 2.55937 3.53062 2.56937 3.05 3.05C2.56937 3.53062 2.5625 4.22187 2.55 4.83187C2.545 5.16 2.54 5.49875 2.455 5.70312C2.36312 5.92562 2.11937 6.18 1.88375 6.42625C1.46937 6.8575 1 7.3475 1 8C1 8.6525 1.46937 9.14187 1.88375 9.57375C2.11937 9.82 2.36312 10.0738 2.455 10.2969C2.54 10.5012 2.545 10.84 2.55 11.1681C2.55937 11.7781 2.56937 12.4694 3.05 12.95C3.53062 13.4306 4.22187 13.4406 4.83187 13.45C5.16 13.455 5.49875 13.46 5.70312 13.545C5.92562 13.6369 6.18 13.8806 6.42625 14.1163C6.8575 14.5306 7.3475 15 8 15C8.6525 15 9.14187 14.5306 9.57375 14.1163C9.82 13.8806 10.0738 13.6369 10.2969 13.545C10.5012 13.46 10.84 13.455 11.1681 13.45C11.7781 13.4406 12.4694 13.4306 12.95 12.95C13.4306 12.4694 13.4406 11.7781 13.45 11.1681C13.455 10.84 13.46 10.5012 13.545 10.2969C13.6369 10.0744 13.8806 9.82 14.1163 9.57375C14.5306 9.1425 15 8.6525 15 8C15 7.3475 14.5306 6.85812 14.1163 6.42625ZM10.8538 6.85375L7.35375 10.3538C7.30731 10.4002 7.25217 10.4371 7.19147 10.4623C7.13077 10.4874 7.06571 10.5004 7 10.5004C6.93429 10.5004 6.86923 10.4874 6.80853 10.4623C6.74783 10.4371 6.69269 10.4002 6.64625 10.3538L5.14625 8.85375C5.05243 8.75993 4.99972 8.63268 4.99972 8.5C4.99972 8.36732 5.05243 8.24007 5.14625 8.14625C5.24007 8.05243 5.36732 7.99972 5.5 7.99972C5.63268 7.99972 5.75993 8.05243 5.85375 8.14625L7 9.29313L10.1462 6.14625C10.1927 6.09979 10.2479 6.06294 10.3086 6.0378C10.3692 6.01266 10.4343 5.99972 10.5 5.99972C10.5657 5.99972 10.6308 6.01266 10.6914 6.0378C10.7521 6.06294 10.8073 6.09979 10.8538 6.14625C10.9002 6.1927 10.9371 6.24786 10.9622 6.30855C10.9873 6.36925 11.0003 6.4343 11.0003 6.5C11.0003 6.5657 10.9873 6.63075 10.9622 6.69145C10.9371 6.75214 10.9002 6.8073 10.8538 6.85375Z" fill="#00672E"></path> </svg>
Verified Answer
</span> </div> </div> <div class="correct-answer">
The correct answer is:
<span class="option-value"><div><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>I</mi><mo>=</mo><mi>n</mi><mi>e</mi><mi>A</mi><msub> <mi>v</mi> <mi>d</mi> </msub> </mrow> </math> </span></p><p> </p><p> </p><p> </p><p> </p><p> </p><p> </p></div></span> </div> <div class="solution"><div><p><span>Relation between current and drift velocity : Consider a conductor of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> and area of cross – section <i><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></i> having <i><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></i> electrons per unit length, as shown in the figure.</span></p><p><span>The volume of the conductor = <i><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>l</mi></math></i></span></p><p><span style="position:relative;top:0.0pt"> <math> <mo>∴</mo> </math> </span><span> Total number of electrons in the conductor</span></p><p><span>= Volume  <math> <mo>×</mo> </math>  electron density = <i><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>l</mi><mi>n</mi></math></i></span></p><p><span>If <i><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></i> is the charge of an electron, then</span></p><p><span>total charge contained in the conductor,</span></p><p><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>Q</mi><mo>=</mo><mi>e</mi><mi>n</mi><mi>A</mi><mi>l</mi> </mrow> </math> </span></p><p><span><img alt="" height="148" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/IL0003535_AnsExp1_1.png" width="344"/></span></p><p><span>Let a potential difference <i>V</i> is applied across the conductor. The resulting electric field in the conductor is given by</span></p><p align="center" style="text-align:center;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>E</mi><mo>=</mo><mfrac> <mi>V</mi> <mi>l</mi> </mfrac> </mrow> </math> </span></p><p><span>Under the influence of this field <i>E</i>, free electrons begin to drift in a direction opposite to that of the field. Time taken by electrons to cross – over the conductor is</span></p><p align="center" style="text-align:center;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>t</mi><mo>=</mo><mfrac> <mi>l</mi> <mrow> <msub> <mi>v</mi> <mi>d</mi> </msub> </mrow> </mfrac> </mrow> </math> </span></p><p><span>where,  <math> <mrow> <msub> <mi>v</mi> <mi>d</mi> </msub> </mrow> </math>  is the drift velocity of electrons.</span></p><p><span>Therefore, the current through the conductor is given by</span></p><p align="center" style="text-align:center;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>I</mi><mo>=</mo><mfrac> <mi>Q</mi> <mi>t</mi> </mfrac> <mo>=</mo><mfrac> <mrow> <mi>e</mi><mi>n</mi><mi>A</mi><mi>l</mi> </mrow> <mrow> <mi>I</mi><mo>/</mo><msub> <mi>v</mi> <mi>d</mi> </msub> </mrow> </mfrac> </mrow> </math> </span></p><p><span>or  <math> <mrow> <mi>I</mi><mo>=</mo><mi>n</mi><mi>e</mi><mi>A</mi><msub> <mi>v</mi> <mi>d</mi> </msub> </mrow> </math> </span></p><p><span style="position:relative;top:0.0pt"> <math> <mrow> <mo>⇒</mo><mi>I</mi><mi>α</mi><msub> <mi>v</mi> <mi>d</mi> </msub> </mrow> </math> </span><span>                                                       <math> <mrow> <mrow> <mo>[</mo> <mrow> <mo>∵</mo><mi>n</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>A</mi> </mrow> </mrow> </mrow> </math>  are all constant]</span></p><p align="left" style="text-align:left;"><span>Hence, Current density is proportional to drift velocity.</span></p><p> </p></div><p> </p></div> </section> <!-- /Solution --> <!-- Call to Action --> <section class="call-to-action" data-pagefind-ignore=""> <div class="call-to-action-header"> <svg fill="none" height="24" viewbox="0 0 25 24" width="25" xmlns="http://www.w3.org/2000/svg"> <path d="M19.9999 13.5C20.0018 13.8058 19.9089 14.1047 19.734 14.3555C19.559 14.6063 19.3107 14.7968 19.023 14.9006L14.1874 16.6875L12.4062 21.5269C12.3007 21.8134 12.1098 22.0608 11.8594 22.2355C11.6089 22.4101 11.3109 22.5038 11.0055 22.5038C10.7002 22.5038 10.4022 22.4101 10.1517 22.2355C9.90124 22.0608 9.71039 21.8134 9.60491 21.5269L7.8124 16.6875L2.97303 14.9062C2.68646 14.8008 2.43915 14.6099 2.26445 14.3595C2.08976 14.109 1.99609 13.811 1.99609 13.5056C1.99609 13.2003 2.08976 12.9022 2.26445 12.6518C2.43915 12.4013 2.68646 12.2105 2.97303 12.105L7.8124 10.3125L9.59366 5.47313C9.69914 5.18656 9.88998 4.93924 10.1404 4.76455C10.3909 4.58985 10.6889 4.49619 10.9943 4.49619C11.2996 4.49619 11.5977 4.58985 11.8481 4.76455C12.0986 4.93924 12.2894 5.18656 12.3949 5.47313L14.1874 10.3125L19.0268 12.0938C19.3146 12.1986 19.5628 12.3901 19.7371 12.642C19.9114 12.8939 20.0033 13.1937 19.9999 13.5ZM14.7499 4.5H16.2499V6C16.2499 6.19891 16.3289 6.38968 16.4696 6.53033C16.6102 6.67098 16.801 6.75 16.9999 6.75C17.1988 6.75 17.3896 6.67098 17.5302 6.53033C17.6709 6.38968 17.7499 6.19891 17.7499 6V4.5H19.2499C19.4488 4.5 19.6396 4.42098 19.7802 4.28033C19.9209 4.13968 19.9999 3.94891 19.9999 3.75C19.9999 3.55109 19.9209 3.36032 19.7802 3.21967C19.6396 3.07902 19.4488 3 19.2499 3H17.7499V1.5C17.7499 1.30109 17.6709 1.11032 17.5302 0.96967C17.3896 0.829018 17.1988 0.75 16.9999 0.75C16.801 0.75 16.6102 0.829018 16.4696 0.96967C16.3289 1.11032 16.2499 1.30109 16.2499 1.5V3H14.7499C14.551 3 14.3602 3.07902 14.2196 3.21967C14.0789 3.36032 13.9999 3.55109 13.9999 3.75C13.9999 3.94891 14.0789 4.13968 14.2196 4.28033C14.3602 4.42098 14.551 4.5 14.7499 4.5ZM22.9999 7.5H22.2499V6.75C22.2499 6.55109 22.1709 6.36032 22.0302 6.21967C21.8896 6.07902 21.6988 6 21.4999 6C21.301 6 21.1102 6.07902 20.9696 6.21967C20.8289 6.36032 20.7499 6.55109 20.7499 6.75V7.5H19.9999C19.801 7.5 19.6102 7.57902 19.4696 7.71967C19.3289 7.86032 19.2499 8.05109 19.2499 8.25C19.2499 8.44891 19.3289 8.63968 19.4696 8.78033C19.6102 8.92098 19.801 9 19.9999 9H20.7499V9.75C20.7499 9.94891 20.8289 10.1397 20.9696 10.2803C21.1102 10.421 21.301 10.5 21.4999 10.5C21.6988 10.5 21.8896 10.421 22.0302 10.2803C22.1709 10.1397 22.2499 9.94891 22.2499 9.75V9H22.9999C23.1988 9 23.3896 8.92098 23.5302 8.78033C23.6709 8.63968 23.7499 8.44891 23.7499 8.25C23.7499 8.05109 23.6709 7.86032 23.5302 7.71967C23.3896 7.57902 23.1988 7.5 22.9999 7.5Z" fill="#1589EE"></path> </svg> <h3>Looking for more such questions to practice?</h3> </div> <p>
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correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><div><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>I</mi><mo>=</mo><mi>n</mi><mi>e</mi><mi>A</mi><msub> <mi>v</mi> <mi>d</mi> </msub> </mrow> </math> </span></p><p> </p><p> </p><p> </p><p> </p><p> </p><p> </p></div></span> </div>

answer:
<div class="solution"><div><p><span>Relation between current and drift velocity : Consider a conductor of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> and area of cross – section <i><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></i> having <i><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></i> electrons per unit length, as shown in the figure.</span></p><p><span>The volume of the conductor = <i><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>l</mi></math></i></span></p><p><span style="position:relative;top:0.0pt"> <math> <mo>∴</mo> </math> </span><span> Total number of electrons in the conductor</span></p><p><span>= Volume  <math> <mo>×</mo> </math>  electron density = <i><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>l</mi><mi>n</mi></math></i></span></p><p><span>If <i><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></i> is the charge of an electron, then</span></p><p><span>total charge contained in the conductor,</span></p><p><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>Q</mi><mo>=</mo><mi>e</mi><mi>n</mi><mi>A</mi><mi>l</mi> </mrow> </math> </span></p><p><span><img alt="" height="148" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/IL0003535_AnsExp1_1.png" width="344"/></span></p><p><span>Let a potential difference <i>V</i> is applied across the conductor. The resulting electric field in the conductor is given by</span></p><p align="center" style="text-align:center;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>E</mi><mo>=</mo><mfrac> <mi>V</mi> <mi>l</mi> </mfrac> </mrow> </math> </span></p><p><span>Under the influence of this field <i>E</i>, free electrons begin to drift in a direction opposite to that of the field. Time taken by electrons to cross – over the conductor is</span></p><p align="center" style="text-align:center;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>t</mi><mo>=</mo><mfrac> <mi>l</mi> <mrow> <msub> <mi>v</mi> <mi>d</mi> </msub> </mrow> </mfrac> </mrow> </math> </span></p><p><span>where,  <math> <mrow> <msub> <mi>v</mi> <mi>d</mi> </msub> </mrow> </math>  is the drift velocity of electrons.</span></p><p><span>Therefore, the current through the conductor is given by</span></p><p align="center" style="text-align:center;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>I</mi><mo>=</mo><mfrac> <mi>Q</mi> <mi>t</mi> </mfrac> <mo>=</mo><mfrac> <mrow> <mi>e</mi><mi>n</mi><mi>A</mi><mi>l</mi> </mrow> <mrow> <mi>I</mi><mo>/</mo><msub> <mi>v</mi> <mi>d</mi> </msub> </mrow> </mfrac> </mrow> </math> </span></p><p><span>or  <math> <mrow> <mi>I</mi><mo>=</mo><mi>n</mi><mi>e</mi><mi>A</mi><msub> <mi>v</mi> <mi>d</mi> </msub> </mrow> </math> </span></p><p><span style="position:relative;top:0.0pt"> <math> <mrow> <mo>⇒</mo><mi>I</mi><mi>α</mi><msub> <mi>v</mi> <mi>d</mi> </msub> </mrow> </math> </span><span>                                                       <math> <mrow> <mrow> <mo>[</mo> <mrow> <mo>∵</mo><mi>n</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>A</mi> </mrow> </mrow> </mrow> </math>  are all constant]</span></p><p align="left" style="text-align:left;"><span>Hence, Current density is proportional to drift velocity.</span></p><p> </p></div><p> </p></div>


title: the-curve-y-2-4-a-x-a-0-lies-in
slug: the-curve-y-2-4-a-x-a-0-lies-in-40368
question: <div class="question">The curve $y^{2}=-4 a x(a&gt;0)$ lies in</div>
tags: ['Mathematics', 'Parabola', 'NDA', 'NDA 2009 (Phase 2)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">First and fourth quadrants</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">First and second quadrants</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Second and third quadrants</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Third and fourth quadrants</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Second and third quadrants</span> </div>

answer:
<div class="solution">Given curve $y^{2}=-4 a x$ which is one of the form of parabola<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/CE2EKE1PIj1GuNqIDCy20wSLr_u3qKwBXgsjVfHJkog.original.fullsize.png"/><br/><br/>It is clear from the figure that curve lies in the second and third quadrants.</div>


title: the-curve-y-xe-x-has-minimum-value-equal-to
slug: the-curve-y-xe-x-has-minimum-value-equal-to-19190
tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The curve $\mathrm{y}=\mathrm{xe}^{\mathrm{x}}$ has minimum value equal to</div>

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

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

answer:
<div class="solution">Let $\mathrm{y}=\mathrm{xe}^{\mathrm{x}}$. Differentiate both side w.r.t. ' $\mathrm{x}$ '.<br/>$\Rightarrow \frac{d y}{d x}=e^{x}+x e^{x}=e^{x}(1+x)$<br/>Put $\frac{d y}{d x}=0$<br/>$\Rightarrow e^{x}(1+x)=0 \quad \Rightarrow x=-1$<br/>Now, $\frac{d^{2} y}{d x^{2}}=e^{x}+e^{x}(1+x)=e^{x}(x+2)$<br/>$\left(\frac{d^{2} y}{d x^{2}}\right)_{(x=-1)}=\frac{1}{e}+0&gt;0$<br/>Hence, $\mathrm{y}=\mathrm{xe}^{\mathrm{x}}$ is minimum function and<br/>$\mathrm{y}_{\min }=-\frac{1}{\mathrm{e}}$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2007 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">108</span> </div>
source_db: MarksBatch2_P2.db
title:
the-data-below-record-the-itemwise-quarterly-expenditure-of-a-private-organization-item-of-expenditure-amount-in-lakh-rupees-1-salaries-60-2-ta-da-49-

slug:
the-data-below-record-the-itemwise-quarterly-expenditure-of-a-private-organization-item-of-expenditure-amount-in-lakh-rupees-1-salaries-60-2-ta-da-49-88908

question:
<div class="question">The data below record the itemwise quarterly expenditure of a private organization $\begin{array}{ll}\text { Item of expenditure } &amp; \text { Amount (in lakh rupees) }\end{array}$<br/> 1 Salaries $6.0$<br/>$\begin{array}{lll}\text { 2. } &amp; \text { TA \&amp; DA } &amp; \text { 4.9 }\end{array}$<br/> 3 . House rent and postage $3.6$<br/> 4 . All other expenses<br/>Total The data is represented by a pie diagram. What is the sectorial angle of the sector with largest area?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$120^{4}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">108</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$100^{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$90^{\circ}$</span> </li> </ul>

answer:
<div class="solution">In a pie chart largest amount occupies largest area. So, the salaries occupies largest area<br/>$\Rightarrow$ Sectorial angle $=\frac{6}{20} \times 360^{\circ}=108^{\circ}$</div>


title: the-decimal-number-12725-10-when-converted-to-binary-nunber-takes-the-form
slug: the-decimal-number-12725-10-when-converted-to-binary-nunber-takes-the-form-15754
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The decimal number ( $127.25)_{10}$, when converted to binary nunber, takes the form</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(1111111.11)_{3}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(1111110.01)$.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(1110111.11)_{2}^{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$(1111111.01)_{2}^{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(1111111.01)_{2}^{2}$</span> </div>

answer:
<div class="solution">$127=(1111111)_{2}$<br/>Now,<br/>\begin{array}{l|l}<br/>2 &amp; 127 \\<br/>\hline 2 &amp; 63-1 \\<br/>\hline 2 &amp; 31-1 \\<br/>\hline 2 &amp; 15-1 \\<br/>\hline 2 &amp; 7-1 \\<br/>\hline 2 &amp; 3-1 \\<br/>\hline &amp; 1-1<br/>\end{array}<br/>$127=(1111111)_{2}$<br/>Now,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/NCpaJFWAoquEHliegaOzPif1V7kNwVUMzgumXesws9w.original.fullsize.png"/><br/><br/>$\therefore$ Option (d)</div>


title: the-decimal-number-57375-10-when-converted-to-binary-number-takes-the-form
slug: the-decimal-number-57375-10-when-converted-to-binary-number-takes-the-form-96387
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The decimal number $(57.375)_{10}$ when converted to binary number takes the form:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$(111001.011)_{2}$</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">$(100111.110)_{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(110011.101)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$(111011.011)$.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(111001.011)_{2}$</span> </div>

answer:
<div class="solution">$(111001.011)_{2}=\left[2^{5} \times 1+2^{4} \times 1+2^{3} \times 1+2^{2} \times 0+2^{1} \times 0\right.$<br/>$\left.+2^{0} \times 1\right] \cdot\left[2^{-1} \times 0+2^{-2} \times 1+2^{-3} \times 1\right]=(57.375)_{10}$</div>


title: the-decimal-representation-of-the-number-1011-in-binary-system-is
slug: the-decimal-representation-of-the-number-1011-in-binary-system-is-48231
question: <div class="question">The decimal representation of the number ( 1011 ), in binary system is:</div>
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2012 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">11</span> </div>
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">5</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">7</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">9</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">11</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$(1011)_{2}=2^{3} \times 1+2^{2} \times 0+2^{1} \times 1+2^{0} \times 1$<br/>$=8+0+2+1=(11)_{10}$</div>


title: the-definition-of-mode-fails-if
slug: the-definition-of-mode-fails-if-69075
question: <div class="question">The definition of Mode fails if:</div>
tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2006 (Phase 2)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">the maximum frequency is repeated</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">the maximum frequency is not repeated</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">the maximum frequency occurs in the middle</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">the curve drawn with the help of given data is $\begin{array}{ll}\text { symmetrical } &amp; {[2006-I I]}\end{array}$</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">the curve drawn with the help of given data is $\begin{array}{ll}\text { symmetrical } &amp; {[2006-I I]}\end{array}$</span> </div>

answer:
<div class="solution">The definition of Mode fails if the curve drawn with the help of given data is symmetrical.</div>


title: the-degree-and-order-respectively-of-the-differential-equation-dx-dy-x-y-1-1-are
slug: the-degree-and-order-respectively-of-the-differential-equation-dx-dy-x-y-1-1-are-68681
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2013 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1,1</span> </div>
source_db: MarksBatch2_P2.db
question:
<div class="question">The degree and order respectively of the differential<br/>equation $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{\mathrm{x}+\mathrm{y}+1}$ are $\quad$</div>

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

answer:
<div class="solution">Since order of the highest derivative in the given diff. equation is 1 and exponent of the derivative is also 1 therefore degree and order is $(1,1)$.</div>


title: the-degree-of-the-differential-equation-d-x-d-y-x-y-x-d-x-d-y-4-is
slug: the-degree-of-the-differential-equation-d-x-d-y-x-y-x-d-x-d-y-4-is-73228
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2015 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch2_P2.db
question:
<div class="question">The degree of the differential equation $\quad$ $\frac{d y}{d x}-x=\left(y-x \frac{d y}{d x}\right)^{-4}$ is</div>

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

answer:
<div class="solution">$\begin{aligned} &amp; \because \frac{d y}{d x}-x=\left(y-x \frac{d y}{d x}\right)^{-4} \\ &amp; \Rightarrow\left(\frac{d y}{d x}-x\right)\left(y-x \cdot \frac{d y}{d x}\right)^{4}=1 \end{aligned}$<br/>$\therefore$ Order of the above differential equation $=1$ $\&amp;$ degree $=5$</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'NEET', 'NEET 2003']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">none</span> </div>
source_db: MarksBatch2_P2.db
title:
the-densities-of-graphite-and-diamond-at-298-k-are-225-and-331-gcm-3-respectively-if-the-standard-free-energy-difference-g-is-equal-to-1895-j-mol-1-th

slug:
the-densities-of-graphite-and-diamond-at-298-k-are-225-and-331-gcm-3-respectively-if-the-standard-free-energy-difference-g-is-equal-to-1895-j-mol-1-th-92156

question:
<div class="question">The densities of graphite and diamond at $298 \mathrm{~K}$ are 2.25 and $3.31 \mathrm{gcm}^{-3}$, respectively. If the standard free energy difference $\left(\Delta \mathrm{G}^{\circ}\right)$ is equal to $1895 \mathrm{~J} \mathrm{~mol}^{-1}$, the pressure at which graphite will be transformed into diamond at $298 \mathrm{~K}$ is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$9.92 \times 10^8 \mathrm{~Pa}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$9.92 \times 10^7 \mathrm{~Pa}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$9.92 \times 10^6 \mathrm{~Pa}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">none</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$\Delta \mathrm{G}=-\mathrm{P} \Delta \mathrm{V}$<br/>$$<br/>\begin{aligned}<br/>&amp; 1895=P\left[\left(\frac{12}{2.25}-\frac{12}{3.31}\right) \times 10^{-6} \mathrm{~m}^3\right] \\<br/>&amp; P=\frac{1895 \times 10^6}{1.71}=1108.187 \times 10^6 \mathrm{Bar} \\<br/>&amp; =1108.1871 \times 10^{11} \mathrm{~Pa}<br/>\end{aligned}<br/>$$</div>


title: the-derivative-of-ln-x-sin-x-with-respect-to-x-cos-x-is
slug: the-derivative-of-ln-x-sin-x-with-respect-to-x-cos-x-is-19797
question: <div class="question">The derivative of $\ln (x+\sin x)$ with respect to $(x+\cos x)$ is</div>
tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{1+\cos x}{(x+\sin x)(1-\sin x)}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1-\cos x}{(x+\sin x)(1+\sin x)}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1-\cos x}{(x-\sin x)(1+\cos x)}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1+\cos x}{(x-\sin x)(1-\cos x)}$</span> </li> </ul>

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

answer:
<div class="solution">$\ln (x+\sin x)=y$ (say)<br/>$\frac{d y}{d x}=\frac{1}{(x+\sin x)}(1+\cos x)$<br/>$=\frac{(1+\cos x)}{(x+\sin x)}$<br/>$x+\cos x=z$ (say)<br/>$\quad \frac{d z}{d x}=(1-\sin x)$<br/>derivative of $\ln (x+\sin x)$ w.r.t $(x+\cos x)$ is<br/>$\frac{\mathrm{dy}}{\mathrm{dz}}=\frac{(1+\cos \mathrm{x})}{(\mathrm{x}+\sin \mathrm{x})(1-\sin \mathrm{x})}$</div>


title: the-derivative-of-sec-2-x-with-respect-to-tan-2-x-is
slug: the-derivative-of-sec-2-x-with-respect-to-tan-2-x-is-27073
question: <div class="question">The derivative of $\sec ^{2} x$ with respect to $\tan ^{2} x$ is</div>
tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2013 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2 \sec x \tan x$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 \sec ^{2} x \tan x$</span> </li> </ul>

answer:
<div class="solution">Let $u=\sec ^{2} x, v=\tan ^{2} x$<br/>To find : $\frac{\mathrm{du}}{\mathrm{dv}}$.<br/>Now, $\frac{\mathrm{du}}{\mathrm{dx}}=2 \sec \mathrm{x} \cdot \sec \mathrm{x} \cdot \tan \mathrm{x}$<br/>and $\frac{d v}{d x}=2 \tan x \cdot \sec ^{2} x$<br/>Thus, $\frac{\mathrm{du}}{\mathrm{dv}}=\frac{\mathrm{du}}{\mathrm{dx}} \times \frac{\mathrm{dx}}{\mathrm{dv}}=\frac{2 \sec \mathrm{x} \cdot \sec \mathrm{x} \cdot \tan \mathrm{x}}{2 \tan \mathrm{x} \mathrm{sec}^{2} \mathrm{x}}=1$</div>


title: the-derivative-of-x-at-x-0
slug: the-derivative-of-x-at-x-0-78543
question: <div class="question">The derivative of $|x|$ at $x=0$</div>
tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">is 1</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">is $-1$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">is 0</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">does not exist</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">does not exist</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/4vDgUxcEP6xiRYhPFm96FnuH3LIRz7YCo50L2jxxXRI.original.fullsize.png"/><br/><br/>Since $|\mathrm{x}|=\left\{\begin{array}{l}\mathrm{x} \text { if } \mathrm{x} \geq 0 \\ -\mathrm{x} \text { if } \mathrm{x} &lt; 0\end{array}\right.$<br/>$\therefore \mathrm{R} . \mathrm{H} \cdot \mathrm{D}$ of $|\mathrm{x}|=1$ at $\mathrm{x}=0$<br/>and $\mathrm{L} . \mathrm{H} .$ Dof $|\mathrm{x}|=-1$ at $\mathrm{x}=0$<br/>Now, R. H. $\mathrm{D} \neq \mathrm{L} . \mathrm{H} . \mathrm{D}$ at $\mathrm{x}=0$<br/>Hence, the derivative of $|\mathrm{x}|$ at $\mathrm{x}=0$ does not exist.</div>


tags: ['Mathematics', 'Determinants', 'NDA', 'NDA 2007 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-determinant-a-b-c-4-a-3-b-2-c-10-a-6-b-3-c-a-b-3-a-2-b-6-a-3-b-a-2-a-3-a-is-independent-of-which-one-of-the-following

slug:
the-determinant-a-b-c-4-a-3-b-2-c-10-a-6-b-3-c-a-b-3-a-2-b-6-a-3-b-a-2-a-3-a-is-independent-of-which-one-of-the-following-98725

question:
<div class="question">The determinant<br/>$\left|\begin{array}{lll}a+b+c &amp; a+b &amp; a \\ 4 a+3 b+2 c &amp; 3 a+2 b &amp; 2 a \\ 10 a+6 b+3 c &amp; 6 a+3 b &amp; 3 a\end{array}\right|$<br/>is independent of which one of the following?</div>

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

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

answer:
<div class="solution">Let $\mathrm{D}=\left|\begin{array}{ccc}\mathrm{a}+\mathrm{b}+\mathrm{c} &amp; \mathrm{a}+\mathrm{b} &amp; \mathrm{a} \\ 4 \mathrm{a}+3 \mathrm{~b}+2 \mathrm{c} &amp; 3 \mathrm{a}+2 \mathrm{~b} &amp; 2 \mathrm{a} \\ 10 \mathrm{a}+6 \mathrm{~b}+3 \mathrm{c} &amp; 6 \mathrm{a}+3 \mathrm{~b} &amp; 3 \mathrm{a}\end{array}\right|$<br/>$\mathrm{By} \mathrm{R}_{2} \rightarrow \mathrm{R}_{2}-2 \mathrm{R}_{1}$ and $\mathrm{R}_{3} \rightarrow \mathrm{R}_{3}-3 \mathrm{R}_{1}$, we get<br/>$\Rightarrow\left|\begin{array}{ccc}a+b+c &amp; a+b &amp; a \\ 2 a+b &amp; a &amp; 0 \\ 7 a+3 b &amp; 3 a &amp; 0\end{array}\right|$<br/>$\mathrm{By} \mathrm{C}_{1} \rightarrow \mathrm{C}_{1}-\mathrm{C}_{2}$ gives:<br/>$\Rightarrow\left|\begin{array}{ccc}\mathrm{c} &amp; \mathrm{a}+\mathrm{b} &amp; \mathrm{a} \\ \mathrm{a}+\mathrm{b} &amp; \mathrm{a} &amp; 0 \\ 4 \mathrm{a}+3 \mathrm{~b} &amp; 3 \mathrm{a} &amp; 0\end{array}\right|$<br/>Again by $\mathrm{R}_{3} \rightarrow \mathrm{R}_{3}-3 \mathrm{R}_{2}$, we get :<br/>$D=\left|\begin{array}{ccc}c &amp; a+b &amp; a \\ a+b &amp; a &amp; 0 \\ a &amp; 0 &amp; 0\end{array}\right|$<br/>$=\mathrm{a}\{0 .(\mathrm{a}+\mathrm{b})-\mathrm{a} \cdot \mathrm{a}\}$<br/>$=-\mathrm{a}^{3}$ which is independent of $\mathrm{b}$ and $\mathrm{c}$.</div>


tags: ['Mathematics', 'Determinants', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
the-determinant-leftbeginarraylllcos-thetaphi-sin-thetaphi-cos-2-phi-sin-theta-cos-theta-sin-phi-cos-theta-sin-theta-cos-phiendarrayright-is

slug:
the-determinant-leftbeginarraylllcos-thetaphi-sin-thetaphi-cos-2-phi-sin-theta-cos-theta-sin-phi-cos-theta-sin-theta-cos-phiendarrayright-is-41749

question:
<div class="question">The determinant \( \left|\begin{array}{lll}\cos (\theta+\phi) &amp; -\sin (\theta+\phi) &amp; \cos 2 \phi \\ \sin \theta &amp; \cos \theta &amp; \sin \phi \\ -\cos \theta &amp; \sin \theta &amp; \cos \phi\end{array}\right| \) is -</div>

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

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

answer:
<div class="solution"><math><mi mathvariant="normal">Î</mi><mi mathvariant="normal">Â </mi><mo>=</mo><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">Î¸</mi><mo>+</mo><mi mathvariant="normal">Ï</mi></mrow></mfenced></mrow></mrow><mo>.</mo><mi mathvariant="normal">Â </mi><mfenced close="]" open="[" separators="|"><mrow><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>â¡</mo><mrow><mi mathvariant="normal">Î¸</mi></mrow></mrow><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>â¡</mo><mrow><mi mathvariant="normal">Ï</mi></mrow></mrow><mo>-</mo><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>â¡</mo><mrow><mi mathvariant="normal">Î¸</mi></mrow></mrow><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>â¡</mo><mrow><mi mathvariant="normal">Ï</mi></mrow></mrow></mrow></mfenced></math> <br/> <math><mo>+</mo><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">Î¸</mi><mo>+</mo><mi mathvariant="normal">Ï</mi></mrow></mfenced></mrow></mrow><mo>.</mo><mi mathvariant="normal">Â </mi><mfenced close="]" open="[" separators="|"><mrow><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>â¡</mo><mrow><mi mathvariant="normal">Î¸</mi></mrow></mrow><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>â¡</mo><mrow><mi mathvariant="normal">Ï</mi></mrow></mrow><mo>+</mo><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>â¡</mo><mrow><mi mathvariant="normal">Î¸</mi></mrow></mrow><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>â¡</mo><mrow><mi mathvariant="normal">Ï</mi></mrow></mrow></mrow></mfenced></math> <br/> <math><mo>+</mo><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>â¡</mo><mrow><mn>2</mn><mi mathvariant="normal">Ï</mi></mrow></mrow><mo>.</mo><mi mathvariant="normal">Â </mi><mfenced close="]" open="[" separators="|"><mrow><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mi mathvariant="normal">Î¸</mi></mrow></mrow><mi mathvariant="normal">Â </mi><mo>+</mo><mrow><mrow><msup><mrow><mi mathvariant="normal">cos</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mi mathvariant="normal">Î¸</mi></mrow></mrow></mrow></mfenced></math> <br/> <math><mi mathvariant="normal">Î</mi><mo>=</mo><mfenced close="]" open="[" separators="|"><mrow><mrow><mrow><msup><mrow><mi mathvariant="normal">cos</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">Î¸</mi><mo>+</mo><mi mathvariant="normal">Ï</mi></mrow></mfenced><mo>+</mo><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">Î¸</mi><mo>+</mo><mi mathvariant="normal">Ï</mi></mrow></mfenced></mrow></mrow></mrow></mrow></mrow></mfenced><mo>+</mo><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mn>2</mn><mi mathvariant="normal">Ï</mi></mrow></mfenced></mrow></mrow></math> <br/> <math><mi mathvariant="normal">Î</mi><mo>=</mo><mn>1</mn><mi mathvariant="normal">Â </mi><mo>+</mo><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mn>2</mn><mi mathvariant="normal">Ï</mi></mrow></mfenced></mrow></mrow></math> <br/> <math><mo>â´</mo><mi mathvariant="normal">Î</mi></math>  is independent of  <math><mi mathvariant="normal">Î¸</mi></math></div>


title: the-determinant-of-a-orthogonal-matrix-is
slug: the-determinant-of-a-orthogonal-matrix-is-57390
question: <div class="question">The determinant of a orthogonal matrix is:</div>
tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\pm 1$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\pm 2$</span> </li> </ul>

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

answer:
<div class="solution">Let A be orthogonal matrix, therefore $\mathrm{AA}^{\mathrm{T}}=1$ $\Rightarrow\left|\mathrm{AA}^{\mathrm{T}}\right|=1 \Rightarrow|\mathrm{A}| \cdot\left|\mathrm{A}^{\mathrm{T}}\right|=1$<br/>$\Rightarrow|\mathrm{A}|^{2}=1$<br/>$\Rightarrow|\mathrm{A}|=\pm 1$</div>


title: the-determinant-of-an-odd-order-skew-symmetric-matrix-is-always
slug: the-determinant-of-an-odd-order-skew-symmetric-matrix-is-always-41479
question: <div class="question">The determinant of an odd order skew symmetric matrix is always:</div>
tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2014 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Zero</span> </div>
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">One</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Negative</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Depends on the matrix</span> </li> </ul>

answer:
<div class="solution">We know that, elements of principal diagonals of a skew-symmetric matrix are all zero.<br/>$A=\left|\begin{array}{ccc}0 &amp; a &amp; b \\ -a &amp; 0 &amp; -c \\ -b &amp; c &amp; 0\end{array}\right|_{3 \times 3} \Rightarrow|A|\left|\begin{array}{ccc}0 &amp; a &amp; b \\ -a &amp; 0 &amp; -c \\ -b &amp; c &amp; 0\end{array}\right|$<br/>$=a b c-a b c=0$</div>


title: the-diagram-given-here-is-the-standard-ecg-of-a-normal-person-the-pwave-represents-the
slug: the-diagram-given-here-is-the-standard-ecg-of-a-normal-person-the-pwave-represents-the-17791
tags: ['Biology', 'Body Fluids and Circulation', 'NEET', 'NEET 2013 (All India)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The diagram given here is the standard ECG of a normal person. The P-wave represents the<br/><img src="https://cdn-question-pool.getmarks.app/pyq/neet/dUs2Y_AIpBcYw5jANBE_VtQPtf7lgyjz0BQb1uGT-Ok.original.fullsize.png"/><br/></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">contraction of both the atria</span> </div>

answer:
<div class="solution">In ECG, P-wave represents the depolarisation of atria, which leads to the contraction of both atria. T-wave represents the return of ventricles from excited to normal state. The QRS complex represents the depolarisation of the ventricles, which initiates ventricular contraction. The contraction starts shortly after $Q$ and marks the beginning of systole.</div>


tags: ['Biology', 'Breathing and Exchange of Gases', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-diagram-shows-three-features-found-in-the-tissues-of-the-human-respiratory-system-which-tubes-of-the-gas-exchange-system-could-be-represented-at-p

slug:
the-diagram-shows-three-features-found-in-the-tissues-of-the-human-respiratory-system-which-tubes-of-the-gas-exchange-system-could-be-represented-at-p-67890

question:
<div class="question">The diagram shows three features found in the tissues of the human respiratory system. Which tubes of the gas exchange system could be represented at position P in the diagram?<br/> <br/> <img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/oxdlwufokbuerbkmshdbofpdwqecyothvvcgytnoozgnahiukv.jpeg"/></div>

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

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

answer:
<div class="solution">The mucosal surface of the trachea is lined by ciliated, pseudostratified columnar epithelium (i.e., respiratory epithelium) interspersed with goblet cells. The trachea divides into the left and right bronchi and they are histologically similar to the trachea. Bronchi are lined by ciliated, pseudostratified columnar epithelium (respiratory epithelium) and interspersed with goblet cells. Bronchi give way to smaller conducting airways, bronchioles which are thin-walled airways lined by variably ciliated or non-ciliated columnar epithelium but lack glandular cells. The tracheae, primary, secondary and tertiary bronchi and initial bronchioles are supported by incomplete cartilaginous rings.</div>


tags: ['Mathematics', 'Statistics']
options: None
correct_option: None
source_db: MarksBatch2_P2.db
title:
the-diameter-of-circles-in-mm-drawn-in-a-design-are-given-below-calculate-the-standard-deviation-and-mean-diameter-of-the-circles-hint-first-make-the-

slug:
the-diameter-of-circles-in-mm-drawn-in-a-design-are-given-below-calculate-the-standard-deviation-and-mean-diameter-of-the-circles-hint-first-make-the-48780

question:
<div class="question">The diameter of circles (in mm) drawn in a design are given below :<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/BoQtkGq51aUoRgfVV3Z2GCnMX88zDpbbmjELxNqVVmo.original.fullsize.png"/><br/><br/>Calculate the standard deviation and mean diameter of the circles.<br/>[Hint : First make the data continuous by making the classes as $32.5-36.5,36.5-40.5,40.5-44.5,44.5$ $-48.5,48.5-52.5$ and then proceed]</div>

answer:
<div class="solution">Making the distribution overlapping type, we get<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/P7-M2qTTGBDoucnFd6VgLbNGpVJykVcnlCjs519Ub9s.original.fullsize.png"/><br/><br/>$\begin{aligned}<br/>&amp;\text { Mean }=A+\frac{\Sigma f_i d_i}{N} \times h \\<br/>&amp;=42.5+\frac{25 \times 4}{100}=42.5+1=43.5<br/>\end{aligned}$<br/>Standard Deviation $=h \sqrt{\frac{\Sigma f_i d_i^2}{N}-\left(\frac{\Sigma f_i d_i}{N}\right)^2}$<br/>$\begin{aligned}<br/>&amp;=4 \sqrt{\frac{199}{100}-\left(\frac{25}{100}\right)^2} \\<br/>&amp;=4 \sqrt{1.99-0.0625}=4 \sqrt{1.9275}=4 \times 1.388 \\<br/>&amp;=5.552=5.55<br/>\end{aligned}$<br/>Hence $\bar{x}=43.5$ and S.D. $=5.55$.</div>


title: the-difference-between-lectin-and-lecithin-is
slug: the-difference-between-lectin-and-lecithin-is-62960
question: <div class="question">The difference between lectin and lecithin is:</div>
tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Lectin is a secondary metabolite while lecithin is a phospholipid.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Lectin is a fat binding protein while lecithin is a phospholipid.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Lectin is a phospholipid with choline while lecithin is a carbohydrate-binding protein.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Lectin is a phospholipid while lecithin is a secondary metabolite.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Lectin is a secondary metabolite while lecithin is a phospholipid.</span> </div>

answer:
<div class="solution">The main differentiating factor between lectin and lecithin is that lectin is a secondary metabolite. Concanavalin A is a plant protein which binds with carbohydrate whereas lecithin is a fatty substance which is found in plant and animal tissues. Lectin, due to its ability to bind with carbohydrate reduces nutrient absorption. Lecithin itself is an essential fatty nutrient, a major component of phosphatidylcholine with the ability to lower the bad cholesterol in the body.</div>


title: the-difference-between-oogenesis-and-spermatogenesis-is
slug: the-difference-between-oogenesis-and-spermatogenesis-is-12735
question: <div class="question">The difference between oogenesis and spermatogenesis is</div>
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">oogenesis begins at puberty and spermatogenesis during embryonic development.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">oogenesis results in formation of four haploid ova from a primary oocyte, while during spermatogenesis only one sperm is formed from a primary spermatocyte.</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">the cytoplasmic division is unequal in oogenesis and equal in spermatogenesis.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">spermatogenesis is not completed until after fertilization occurs, but oogenesis is completed at the time of birth.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">the cytoplasmic division is unequal in oogenesis and equal in spermatogenesis.</span> </div>

answer:
<div class="solution">Oogenesis is formation of female gametes while spermatogenesis is formation of male gametes. Both begins with primary mother cells in the gonads. Primary oocyte undergoes meiosis 1 and forms secondary oocyte and first polar body while Primary spermatocyte undergoes meiosis1 and forms two secondary spermatocyte. The process is the same in both but the daughter cells formed are different. In oogenesis, the daughter cells are of unequal size i.e. secondary oocyte is larger than the first polar body because secondary oocyte has maximum amount of cytoplasm retained in it. This unequal division is important because incase sperms approach these gametes, there is a chance of fertilization and zygote formation. Hence cytoplasm can act as stored food for the zygote. While in spermatogenesis the daughter cells formed are of same size as seen in Meiosis of other cells. This is the main difference.</div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2008 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">AP</span> </div>
source_db: MarksBatch2_P2.db
title:
the-difference-between-the-nth-term-and-n-1-th-term-of-a-sequence-is-independent-of-n-then-the-sequence-follows-which-one-of-the-following

slug:
the-difference-between-the-nth-term-and-n-1-th-term-of-a-sequence-is-independent-of-n-then-the-sequence-follows-which-one-of-the-following-36750

question:
<div class="question">The difference between the nth term and $(\mathrm{n}-1)$ th term of a sequence is independent of $\mathrm{n}$. Then the sequence follows which one of the following?</div>

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

answer:
<div class="solution">If the sequence is in AP with first term, a and common difference, $\mathrm{d}$. $\Rightarrow \mathrm{T}_{\mathrm{n}}=\mathrm{a}+(\mathrm{n}-1) \mathrm{d}$<br/>Also $T_{n-1}=a+(n-2) d$<br/>So, the sequence is in AP for which difference between the nth term and $(\mathrm{n}-1)$ th term is independent of $\mathrm{n}$.</div>


title: the-difference-between-the-red-list-and-red-data-book-is-1
slug: the-difference-between-the-red-list-and-red-data-book-is-1-18013
question: <div class="question">The difference between the Red List and Red Data Book is</div>
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET', 'NEET 2014']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The Red Data Book contains three colored pages - Red, pink and green and The Red List has the names typed with brown, blue and orange.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">The Red List contains names of endangered species and Red Data Book contains information of 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><li class=""> <span class="option-label">C</span> <span class="option-data">Both (a) and (b).</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The Red List contains names of endangered species and Red Data Book contains information of endangered species.</span> </div>

answer:
<div class="solution">IUCN is the International Union of Conservation of Nature and Natural Resources which is now called the World Conservation Union (WCU). The (IUCN) Red List also known as the Red List or Red Data List was founded in 1964. This book gives the global conservation status of biological species. It uses a set of criteria to evaluate the Threatened species and subspecies under the extinction risk.</div>


title: the-difference-between-the-red-list-and-red-data-book-is
slug: the-difference-between-the-red-list-and-red-data-book-is-79507
question: <div class="question">The difference between the Red List and Red Data Book is</div>
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The Red Data Book contains three colored pages - Red, pink and green and The Red List has the animals typed with brown, blue and orange.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">The Red List contains names of endangered species and Red Data Book contains information of 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><li class=""> <span class="option-label">C</span> <span class="option-data">Both (a) and (b).</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The Red List contains names of endangered species and Red Data Book contains information of endangered species.</span> </div>

answer:
<div class="solution">IUCN is the International Union of Conservation of Nature and Natural Resources which is now called the World Conservation Union (WCU). The (IUCN) Red List also known as the Red List or Red Data List was founded in 1964. This book gives the global conservation status of biological species. It uses a set of criteria to evaluate the Threatened species and subspecies under the extinction risk.</div>


title: the-difference-of-focal-distances-of-any-point-on-a-hyperbola-is-equal-to
slug: the-difference-of-focal-distances-of-any-point-on-a-hyperbola-is-equal-to-71641
tags: ['Mathematics', 'Hyperbola', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The difference of focal distances of any point on a hyperbola is equal to</div>

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

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

answer:
<div class="solution">Transverse axis Proof: The focal distance of any point $(x, y)$ on<br/>hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ is<br/>$e|x|-a$ from the nearer focus<br/>$e|x|+a$ from the farther focus Difference $=(e|x|+a)-(e|x|-a)=2 a$<br/>$=$ length of transverse axes.</div>


tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-difference-of-two-angles-is-1-the-circular-measure-of-their-sum-is-1-what-is-the-smaller-angle-in-circular-measure

slug:
the-difference-of-two-angles-is-1-the-circular-measure-of-their-sum-is-1-what-is-the-smaller-angle-in-circular-measure-59734

question:
<div class="question">The difference of two angles is $1^{\circ}$; the circular measure of their sum is $1 .$ What is the smaller angle in circular measure?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left[\frac{180}{\pi}-1\right]$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left[1-\frac{\pi}{180}\right]$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{1}{2}\left[1-\frac{\pi}{180}\right]$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{2}\left[\frac{180}{\pi}-1\right]</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{2}\left[1-\frac{\pi}{180}\right]$</span> </div>

answer:
<div class="solution">Let the angles are $\alpha$ and $\beta$, then $\alpha-\beta=1^{\circ}$<br/>$\Rightarrow \alpha-\beta=\frac{\pi}{180^{\circ}}$ is circular measure<br/>As given, $\quad \alpha+\beta=1$<br/>On solving Eqs. (i) and (ii), we get, $\alpha=\frac{1}{2}\left[1+\frac{\pi}{180^{\circ}}\right]$ and $\beta=\frac{1}{2}\left[1-\frac{\pi}{180^{\circ}}\right]$<br/>$\beta$ is the smaller angle. Hence, smaller angle $=\frac{1}{2}\left[1-\frac{\pi}{180^{\circ}}\right]$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2008 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">31</span> </div>
source_db: MarksBatch2_P2.db
title:
the-difference-of-two-numbers-10001100-and-1101101-in-binary-system-is-expressed-in-decimal-system-by-which-one-of-the-following

slug:
the-difference-of-two-numbers-10001100-and-1101101-in-binary-system-is-expressed-in-decimal-system-by-which-one-of-the-following-13362

question:
<div class="question">The difference of two numbers 10001100 and 1101101 in binary system is expressed in decimal system by which one of the following?</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">29</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">31</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">33</span> </li> </ul>

answer:
<div class="solution">The given binary number $10001100=1 \times 2^{7}+1 \times 2^{3}+1$ $\times 2^{2}$<br/>$=128+8+4=140$ (decimal numbers)<br/>and $1101101=1 \times 2^{6}+1 \times 2^{5}+1 \times 2^{3}+1 \times 2^{2}+1 \times 2^{0}$<br/>$=64+32+8+4+1=109$<br/>their difference $=140-109=31$</div>


title: the-differential-equation-3-x-4-y-1-d-x-4-x-5-y-1-d-y-0-represents-a-family-of
slug: the-differential-equation-3-x-4-y-1-d-x-4-x-5-y-1-d-y-0-represents-a-family-of-13962
tags: ['Mathematics', 'Differential Equations', 'VITEEE', 'VITEEE 2015']
source_db: MarksBatch2_P2.db
question:
<div class="question">The differential equation $(3 x+4 y+1) d x+(4 x+5 y+1) d y=0$ represents a family of</div>

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

answer:
<div class="solution">The given differential equation is
<br/>$(3 x+4 y+1) d x+(4 x+5 y+1) d y=0$
<br/>Comparing eq. (i) with $\mathrm{Mdx}+\mathrm{Ndy}=0$, we get
<br/>$M=3 x+4 y+1$
<br/>and $\mathrm{N}=4 \mathrm{x}+5 \mathrm{y}+1$
<br/>Here, $\frac{\partial \mathrm{M}}{\partial \mathrm{y}}=\frac{\partial \mathrm{N}}{\partial \mathrm{x}}=4$
<br/>Hence, eq. (i) is exact and solution is given by
<br/>$\begin{aligned}
<br/>&amp; \int(3 x+4 y+1) d x+\int(5 y+1) d y=C \\
<br/>\Rightarrow &amp; \frac{3 x^{2}}{2}+4 x y+x+\frac{5 y^{2}}{2}+y-C=0 \\
<br/>\Rightarrow &amp; 3 x^{2}+8 x y+2 x+5 y^{2}+2 y-2 C=0 \\
<br/>\Rightarrow &amp; 3 x^{2}+2.4 x y+2 x+5 y^{2}+2 y+C^{\prime}=0 \\
<br/>&amp; \text { where, } C^{\prime}=-2 C
<br/>\end{aligned}$
<br/>On comparing eq. (ii) with standard form of conic section
<br/>$a x^{2}+2 h x y+b y^{2}+2 g x+2 f y+C=0$
<br/>We get,
<br/>$\mathrm{a}=3, \mathrm{~h}=4, \mathrm{~b}=5$
<br/>Here, $h^{2}-a b=16-15=1&gt;0$
<br/>Hence, the solution of differential equation represents family of hyperbolas.</div>


title: the-differential-equation-of-all-circles-whose-centres-are-at-the-origin-is
slug: the-differential-equation-of-all-circles-whose-centres-are-at-the-origin-is-48396
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2013 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The differential equation of all circles whose centres are at the origin is $\quad$</div>

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

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

answer:
<div class="solution">$\mathrm{x}^{2}+\mathrm{y}^{2}=\mathrm{r}^{2} \quad$ [equation of circle]<br/>Differentiating both sides w.r.t. $\mathrm{x}$.<br/>$2 x+2 y \frac{d y}{d x}=0$<br/>$\frac{d y}{d x}=-\frac{x}{y}$</div>


tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-differential-equation-of-minimum-order-by-eliminating-the-arbitrat-constants-a-and-c-in-the-equatic-y-a-sin-x-c-cos-x-c-is

slug:
the-differential-equation-of-minimum-order-by-eliminating-the-arbitrat-constants-a-and-c-in-the-equatic-y-a-sin-x-c-cos-x-c-is-47015

question:
<div class="question">The differential equation of minimum order by eliminating the arbitrat constants $A$ and $C$ in the equatic $\mathrm{y}=\mathrm{A}[\sin (\mathrm{x}+\mathrm{C})+\cos (\mathrm{x}+\mathrm{C})]$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{y}^{n}+(\sin \mathrm{x}+\cos \mathrm{x}) \mathrm{y}^{\prime}=1$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$y^{\prime \prime}=(\sin x+\cos x) y^{\prime}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$y^{n}=\left(y^{\prime}\right)^{2}+\sin x \cos x$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{y}^{\prime \prime}+\mathrm{y}=0$</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> </ul>

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

answer:
<div class="solution">$\mathrm{y}=\mathrm{A}[\sin (\mathrm{x}+\mathrm{c})+\cos (\mathrm{x}+\mathrm{c})]$<br/>$\mathrm{y}^{\prime}=\mathrm{A}[\cos (\mathrm{x}+\mathrm{c})-\sin (\mathrm{x}+\mathrm{c})]$<br/>$\mathrm{y}^{\prime \prime}=-\mathrm{A}[\sin (\mathrm{x}+\mathrm{c})+\cos (\mathrm{x}+\mathrm{c})]$<br/>$=-\mathrm{y}$<br/>$\therefore \mathrm{y}^{\prime \prime}+\mathrm{y}=0$</div>


title: the-differential-equation-of-the-curve-y-sin-x-is
slug: the-differential-equation-of-the-curve-y-sin-x-is-27285
question: <div class="question">The differential equation of the curve $\mathrm{y}=\sin \mathrm{x}$ is</div>
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{d^{2} y}{d x^{2}}+y \frac{d y}{d x}+x=0$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}+\mathrm{y}=0$</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">C</span> <span class="option-data">$\frac{d^{2} y}{d x^{2}}-y=0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{d^{2} y}{d x^{2}}+x=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}+\mathrm{y}=0$</span> </div>

answer:
<div class="solution">Given curve is $\mathrm{y}=\sin \mathrm{x}$<br/>Differentiate both the sides w.r.t 'x'.<br/>$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\cos \mathrm{x} \Rightarrow \frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{d} \mathrm{x}^{2}}=-\sin \mathrm{x}$<br/>$\Rightarrow \frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}=-\mathrm{y}$<br/>$\therefore \quad \mathrm{y}+\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}=0$</div>


tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-differential-equation-of-the-family-of-circles-passing-through-the-origin-and-having-centres-on-the-x-axis-is

slug:
the-differential-equation-of-the-family-of-circles-passing-through-the-origin-and-having-centres-on-the-x-axis-is-78005

question:
<div class="question">The differential equation of the family of circles passing through the origin and having centres on the $\mathrm{x}$ -axis is</div>

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

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

answer:
<div class="solution">Eq. of family of circles passing through the origin \&amp; having centres on the $\mathrm{x}$ -axis is:<br/>$\mathrm{x}^{2}+\mathrm{y}^{2}+2 \mathrm{gx}=0$<br/>$2 \mathrm{x}+2 \mathrm{y} \cdot \frac{\mathrm{dy}}{\mathrm{dx}}+2 \mathrm{~g}=0 \quad$ [on differentiating]<br/>$\Rightarrow g=-\left[x+y \frac{d y}{d x}\right]$<br/>Putting the value of $(\mathrm{g})$ in eq. $(1)$ we get;<br/>$2 x y \frac{d y}{d x}=y^{2}-x^{2}$</div>


tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-differential-equation-of-the-family-of-curves-y-p-cos-ax-q-sin-ax-where-p-q-are-arbitrary-constants-is

slug:
the-differential-equation-of-the-family-of-curves-y-p-cos-ax-q-sin-ax-where-p-q-are-arbitrary-constants-is-77000

question:
<div class="question">The differential equation of the family of curves $\mathrm{y}=\mathrm{p} \cos$ $(\mathrm{ax})+\mathrm{q} \sin (\mathrm{ax})$, where $\mathrm{p}, \mathrm{q}$ are arbitrary constants, is</div>

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

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

answer:
<div class="solution">$y=p \cos a x+q \sin a x$<br/>$\Rightarrow \quad \frac{d y}{d x}=-p a \sin a x+q a \cos a x$<br/>$\Rightarrow \quad \frac{d^{2} y}{d x^{2}}=-p a^{2} \cos a x-q a^{2} \sin a x=-a^{2} y$<br/>$\Rightarrow \quad \frac{d^{2} y}{d x^{2}}+a^{2} y=0$</div>


title: the-differential-equation-of-the-system-of-circles-touching-the-yaxis-at-the-origin-is
slug: the-differential-equation-of-the-system-of-circles-touching-the-yaxis-at-the-origin-is-90440
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The differential equation of the system of circles touching the y-axis at the origin is</div>

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

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

answer:
<div class="solution">The equation of circle touching $\mathrm{y}$ -axis at origin is $(\mathrm{x}-\alpha)^{2}+(\mathrm{y}-0)^{2}=\alpha^{2}$<br/>$\Rightarrow x^{2}+\alpha^{2}-2 \alpha x+y^{2}=\alpha^{2}$<br/>$\Rightarrow x^{2}+y^{2}-2 \alpha x=0$<br/>$\Rightarrow x+\frac{y^{2}}{x}-2 \alpha=0$<br/>Differentiating, $1+\frac{x \cdot 2 y \cdot \frac{d y}{d x}-y^{2}}{x^{2}}=0$<br/>$\Rightarrow x^{2}+2 x y \cdot \frac{d y}{d x}-y^{2}=0$</div>


title: the-differential-equation-representing-the-family-of-curves-y-a-sin-x-is
slug: the-differential-equation-representing-the-family-of-curves-y-a-sin-x-is-44102
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The differential equation representing the family of curves $\mathrm{y}=\mathrm{a} \sin (\lambda \mathrm{x}+\alpha)$ is: $\quad$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{d^{2} y}{d x^{2}}+\lambda^{2} y=0$</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">$\frac{d^{2} y}{d x^{2}}-\lambda^{2} y=0$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{d^{2} y}{d x^{2}}+\lambda y=0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above</span> </li> </ul>

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

answer:
<div class="solution">Let $\mathrm{y}=\mathrm{a} \sin (\lambda \mathrm{x}+\alpha)$<br/>$\Rightarrow \quad \frac{d y}{d x}=\lambda a \cos (\lambda x+\alpha)$<br/>Again differentiating on both side we get<br/>$$<br/>\begin{aligned}<br/>&amp; \frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}=-\lambda^{2} \text { a } \sin (\mathrm{x}+\alpha) \\<br/>\Rightarrow &amp; \frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}+\lambda^{2} \mathrm{y}=0 \text { Required equation. }<br/>\end{aligned}<br/>$$</div>


title: the-differential-equation-y-dx-dy-x-a-where-a-is-any-constant-represents
slug: the-differential-equation-y-dx-dy-x-a-where-a-is-any-constant-represents-92542
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The differential equation $\mathrm{y} \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{x}=\mathrm{a}$ where 'a' is any<br/>constant represents : $\quad$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A set of circles</span> </div>

answer:
<div class="solution">Given diff. equation is<br/>$$<br/>y \frac{d y}{d x}+x=a<br/>$$<br/>$\begin{aligned} \Rightarrow &amp; y \frac{d y}{d x}=a-x \\ \Rightarrow &amp; y d y=(a-x) d x \\ &amp; \int y d y=\int(a-x) d x \\ \Rightarrow &amp; \frac{y^{2}}{2}=a x-\frac{x^{2}}{2}+k \\ \Rightarrow &amp; x^{2}+y^{2}-2 a x=2 k \end{aligned}$<br/>Which represents a set of circles.</div>


tags: ['Physics', 'Wave Optics', 'JEE Main', 'JEE Main 2024 (30 Jan Shift 1)']
source_db: MarksBatch2_P2.db
title:
the-diffraction-pattern-of-a-light-of-wavelength-400-nm-diffracting-from-a-slit-of-width-0-2-mm-is-focused-on-the-focal-plane-of-a-convex-lens-of-foca

slug:
the-diffraction-pattern-of-a-light-of-wavelength-400-nm-diffracting-from-a-slit-of-width-0-2-mm-is-focused-on-the-focal-plane-of-a-convex-lens-of-foca-15027

question:
<div class="question">The diffraction pattern of a light of wavelength <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>400</mn><mo>Â </mo><mi>nm</mi></math> diffracting from a slit of width <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>2</mn><mo>Â </mo><mi>mm</mi></math> is focused on the focal plane of a convex lens of focal length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>Â </mo><mi>cm</mi></math>. The width of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>1</mn><mtext>stÂ </mtext></msup></math> secondary maxima 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>2</mn><mo>Â </mo><mi>mm</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>2</mn><mo>Â </mo><mi>cm</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>0</mn><mo>.</mo><mn>02</mn><mo>Â </mo><mi>mm</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>0</mn><mo>.</mo><mn>2</mn><mo>Â </mo><mi>mm</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>2</mn><mo>Â </mo><mi>mm</mi></math></span> </div>

answer:
<div class="solution"><p>Width of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>1</mn><mi>st</mi></msup></math> secondary maximaÂ <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mi>Î»</mi><mi>a</mi></mfrac><mo>Â·</mo><mi>D</mi></math></p><p>Here</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><mo>Ã</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>Â </mo><mi mathvariant="normal">m</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Î»</mi><mo>=</mo><mn>400</mn><mo>Ã</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>9</mn></mrow></msup><mo>Â </mo><mi mathvariant="normal">m</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mn>100</mn><mo>Ã</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>=</mo><mn>1</mn><mo>Â </mo><mi mathvariant="normal">m</mi></math></p><p>Therefore, width of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>1</mn><mi>st</mi></msup></math> secondary maxima</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>400</mn><mo>Ã</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>9</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><mn>2</mn><mo>Ã</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfrac><mo>Ã</mo><mn>1</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mo>Ã</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>Â </mo><mi mathvariant="normal">m</mi><mspace linebreak="newline"></mspace><mo>=</mo><mn>2</mn><mo>Â </mo><mi>mm</mi></math></p></div>


tags: ['Physics', 'Wave Optics', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-diffraction-pattern-of-a-single-slit-is-shown-in-the-figure-the-point-at-which-the-path-difference-of-the-extreme-rays-is-two-times-the-wavelength-1

slug:
the-diffraction-pattern-of-a-single-slit-is-shown-in-the-figure-the-point-at-which-the-path-difference-of-the-extreme-rays-is-two-times-the-wavelength-1-58693

question:
<div class="question">The diffraction pattern of a single slit is shown in the figure. The point at which the path difference of the extreme rays is two times the wavelength is<br/> <br/> <img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/ikbcjrtnpmykknwrnxjbxagztqysawrqorhqywyfrqorpvkkdt.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">point <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">point <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">point <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">point <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">point <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></span> </div>

answer:
<div class="solution">In diffraction of light at a single slit, the pattern obtained consists of a central bright band having alternate dark and bright bands of decreasing intensity on both sides.<br/><br/>For n<sup>th </sup>minima (secondary),<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo>â¡</mo><msub><mi mathvariant="normal">Î¸</mi><mi mathvariant="normal">n</mi></msub><mo>=</mo><mfrac><mi>nÎ»</mi><mi mathvariant="normal">a</mi></mfrac><mi mathvariant="normal"> </mi></math><br/><br/>For n<sup>th</sup> maxima (secondary),<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo>â¡</mo><msub><mi mathvariant="normal">Î¸</mi><mi mathvariant="normal">n</mi></msub><mo>=</mo><mfenced separators="|"><mrow><mn>2</mn><mi mathvariant="normal">n</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfrac><mi mathvariant="normal">Î»</mi><mrow><mn>2</mn><mi mathvariant="normal">a</mi></mrow></mfrac></math><br/><br/>Thus, point <math><mn>5</mn></math> corresponds to the path difference of extreme rays equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi mathvariant="normal">Î»</mi></math>.<br/><br/><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/jksxbechrvzrluifslhiexhyrjnetfjdgfoslatrhwgkaobzoe.png"/></div>


tags: ['Physics', 'Wave Optics', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-diffraction-pattern-of-a-single-slit-is-shown-in-the-figure-the-point-at-which-the-path-difference-of-the-extreme-rays-is-two-times-the-wavelength

slug:
the-diffraction-pattern-of-a-single-slit-is-shown-in-the-figure-the-point-at-which-the-path-difference-of-the-extreme-rays-is-two-times-the-wavelength-52782

question:
<div class="question">The diffraction pattern of a single slit is shown in the figure. The point at which the path difference of the extreme rays is two times the wavelength is<br/> <br/> <img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/ikbcjrtnpmykknwrnxjbxagztqysawrqorhqywyfrqorpvkkdt.png" style="max-width:100%; object-fit:contain"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">point <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">point <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">point <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">point <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">point <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></span> </div>

answer:
<div class="solution">In diffraction of light at a single slit, the pattern obtained consists of a central bright band having alternate dark and bright bands of decreasing intensity on both sides.<br/><br/>For n<sup>th </sup>minima (secondary),<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo>â¡</mo><msub><mi mathvariant="normal">Î¸</mi><mi mathvariant="normal">n</mi></msub><mo>=</mo><mfrac><mi>nÎ»</mi><mi mathvariant="normal">a</mi></mfrac><mi mathvariant="normal"> </mi></math><br/><br/>For n<sup>th</sup> maxima (secondary),<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo>â¡</mo><msub><mi mathvariant="normal">Î¸</mi><mi mathvariant="normal">n</mi></msub><mo>=</mo><mfenced separators="|"><mrow><mn>2</mn><mi mathvariant="normal">n</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfrac><mi mathvariant="normal">Î»</mi><mrow><mn>2</mn><mi mathvariant="normal">a</mi></mrow></mfrac></math><br/><br/>Thus, point <math><mn>5</mn></math> corresponds to the path difference of extreme rays equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi mathvariant="normal">Î»</mi></math>.<br/><br/><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/jksxbechrvzrluifslhiexhyrjnetfjdgfoslatrhwgkaobzoe.png" style="max-width:100%; object-fit:contain"/></div>


title: the-digital-signals-are-used-for-transmission-in-communication-system-they-are
slug: the-digital-signals-are-used-for-transmission-in-communication-system-they-are-25516
tags: ['Physics', 'Communication System', 'MHT CET', 'MHT CET 2020 (13 Oct Shift 2)']
answer: <div class="solution">Only for discrete stepwise values.</div>
source_db: MarksBatch2_P2.db
question:
<div class="question">The digital signals are used for transmission in communication system. They are</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">only of discrete stepwise values.</span> </div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-dircction-ratios-of-the-linc-perpendicular-to-the-lincs-with-direction-ratios-1-2-2-and-0-2-1-are

slug:
the-dircction-ratios-of-the-linc-perpendicular-to-the-lincs-with-direction-ratios-1-2-2-and-0-2-1-are-22333

question:
<div class="question">The dircction ratios of the linc perpendicular to the lincs with direction ratios $   &lt; 1,-2,-2&gt;$ and $ &lt; 0,2,1&gt;$ are</div>

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

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

answer:
<div class="solution">Let the direction ratio be $   &lt; a, b, c\rangle$ $\cos 90^{\circ}=\frac{(\mathrm{a})(1)+(\mathrm{b})(-2)+(\mathrm{c})(-2)}{\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}+\mathrm{c}^{2}} \sqrt{(1)^{2}+(-2)^{2}+(-2)^{2}}}$<br/>$a-2 b-2 c=0$<br/>$\cos 90^{\circ}=\frac{(\mathrm{a})(0)+\mathrm{b}(2)+(\mathrm{c})(1)}{\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}+\mathrm{c}^{2}} \sqrt{(0)^{2}+(-2)^{2}+(1)^{2}}}$<br/>$2 b+c=0$<br/>From eq. $(1) \&amp;(2)$ $a=-2 b ; c=-2 b$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2009 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P2.db
title:
the-direction-cosines-of-a-line-are-proportional-to-2-1-2-and-the-line-intersects-a-plane-perpendicularly-at-the-point-1-2-4-what-is-the-distance-of-t

slug:
the-direction-cosines-of-a-line-are-proportional-to-2-1-2-and-the-line-intersects-a-plane-perpendicularly-at-the-point-1-2-4-what-is-the-distance-of-t-32675

question:
<div class="question">The direction cosines of a line are proportional to $(2,1,2)$ and the line intersects a plane perpendicularly at the point $(1,-2,4)$. What is the distance of the plane from the point $(3,$, $2,3) ? \quad$</div>

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

answer:
<div class="solution">Equation of plane passing through $(1,-2,4)$ and whose normal $(2,1,2)$ is $2(x-1)+1(y+2)+2(z-4)=0$<br/>$\Rightarrow 2 x-2+y+2+2 z-8=0$<br/>$\Rightarrow 2 x+y+2 z-8=0$<br/>So, distance of the plane $2 x+y+2 z-8=0$ from the point $(3,2,3)$ is<br/>$=\frac{2(3)+1(2)+(2)(3)-8}{\sqrt{4+1+4}}=\frac{6}{3}=2$</div>


title: the-direction-cosines-of-the-line-3-3-x-1-6-3-y-2-1-z-are
slug: the-direction-cosines-of-the-line-3-3-x-1-6-3-y-2-1-z-are-47201
tags: ['Mathematics', 'Three Dimensional Geometry', 'JEE Main']
source_db: MarksBatch2_P2.db
question:
<div class="question">The direction cosines of the line $\frac{3 x+1}{-3}=\frac{3 y+2}{6}=\frac{z}{-1}$ are</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(-\frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}},-\frac{1}{\sqrt{6}}\right)$</span> </div>

answer:
<div class="solution">Change the given equation in standard form, we get,<br/>$\frac{x+\frac{1}{3}}{-1}=\frac{y+\frac{2}{3}}{2}=\frac{z}{-1}$<br/><br/>So direction cosine are, $\left(\frac{-1}{\sqrt{6}}, \frac{2}{\sqrt{6}}, \frac{-1}{\sqrt{6}}\right)$.</div>


tags: ['Physics', 'Oscillations', 'TS EAMCET', 'TS EAMCET 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0.4 J</span> </div>
source_db: MarksBatch2_P2.db
title:
the-displacement-of-a-particle-executing-shm-is-given-by-y-5-sin-4-t-3-if-t-is-the-time-period-and-the-mass-of-the-particle-is-2-g-the-kinetic-energy--1

slug:
the-displacement-of-a-particle-executing-shm-is-given-by-y-5-sin-4-t-3-if-t-is-the-time-period-and-the-mass-of-the-particle-is-2-g-the-kinetic-energy-1-73742

question:
<div class="question">The displacement of a particle executing SHM is given by<br/>$y=5 \sin \left(4 t+\frac{\pi}{3}\right) .$<br/>If $T$ is the time period and the mass of the particle is $2 \mathrm{~g}$, the kinetic energy of the particle when $t=\frac{T}{4}$ is given by</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">0.4 J</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">0.5 J</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">3 J</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">0.3 J</span> </li> </ul>

answer:
<div class="solution">The displacement of particle, executing SHM<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/O0rq52vMCV9u-reb69yYjnL-3Ng4RQXeaQFafHKCDxY.original.fullsize.png"/><br/><br/>Velocity of particle<br/>$\begin{aligned}<br/>\left(\frac{d y}{d t}\right) &amp; =\frac{5 d}{d t} \sin \left(4 t+\frac{\pi}{3}\right) \\<br/>&amp; =5 \cos \left(4 t+\frac{\pi}{3}\right) \cdot 4 \\<br/>&amp; =20 \cos \left(4 t+\frac{\pi}{3}\right)<br/>\end{aligned}$<br/>Velocity at $t=\left(\frac{T}{4}\right)$<br/>$\left(\frac{d y}{d t}\right)_{t=\frac{T}{4}}=20 \cos \left(4 \times \frac{T}{4}+\frac{\pi}{3}\right)$<img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/pRsHc2P0lSEiu-1e1zDWG-p3gw_TX-lYnMWeTNqKxc0.original.fullsize.png"/><br/><br/>Comparing the given equation with standard equation of SHM, given by<br/>We get<br/>$\begin{aligned}<br/>&amp; y=a \sin (\omega t+\phi) \\<br/>&amp; \omega=4<br/>\end{aligned}$<br/>As<br/>$\omega=\frac{2 \pi}{T}$<br/>$\begin{aligned} &amp; \Rightarrow \quad T=\frac{2 \pi}{\omega} \\ &amp; \text { or } &amp; T=\frac{2 \pi}{4} \\ &amp; \text { or } &amp; T=\left(\frac{\pi}{2}\right) \\ &amp; \end{aligned}$<br/>Now, putting value of $T$ in Eq. (ii), we get<br/>$\begin{aligned}<br/>u &amp; =20 \cos \left(\frac{\pi}{2}+\frac{\pi}{3}\right) \\<br/>&amp; =-20 \sin \frac{\pi}{3} \\<br/>&amp; =-20 \times \frac{\sqrt{3}}{2} \\<br/>&amp; =-10 \times \sqrt{3}<br/>\end{aligned}$<br/>The kinetic energy of particle,<br/>$\begin{aligned}<br/>&amp; \mathrm{KE}=\frac{1}{2} m u^2 \\<br/>&amp; \because \quad m=2 \mathrm{~g}=2 \times 10^{-3} \mathrm{~kg} \\<br/>&amp; =\frac{1}{2} \times 2 \times 10^{-3} \times(-10 \sqrt{3})^2 \\<br/>&amp; =10^{-3} \times 100 \times 3 \\<br/>&amp; =3 \times 10^{-1} \\<br/>&amp; \mathrm{KE}=0.3 \mathrm{~J} \\<br/>&amp;<br/>\end{aligned}$</div>


tags: ['Physics', 'Oscillations', 'AP EAMCET', 'AP EAMCET 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0.4 J</span> </div>
source_db: MarksBatch2_P2.db
title:
the-displacement-of-a-particle-executing-shm-is-given-by-y-5-sin-4-t-3-if-t-is-the-time-period-and-the-mass-of-the-particle-is-2-g-the-kinetic-energy--2

slug:
the-displacement-of-a-particle-executing-shm-is-given-by-y-5-sin-4-t-3-if-t-is-the-time-period-and-the-mass-of-the-particle-is-2-g-the-kinetic-energy-2-50577

question:
<div class="question">The displacement of a particle executing SHM is given by<br/>$y=5 \sin \left(4 t+\frac{\pi}{3}\right) .$<br/>If $T$ is the time period and the mass of the particle is $2 \mathrm{~g}$, the kinetic energy of the particle when $t=\frac{T}{4}$ is given by</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">0.4 J</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">0.5 J</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">3 J</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">0.3 J</span> </li> </ul>

answer:
<div class="solution">The displacement of particle, executing SHM<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/O0rq52vMCV9u-reb69yYjnL-3Ng4RQXeaQFafHKCDxY.original.fullsize.png"/><br/><br/>Velocity of particle<br/>$\begin{aligned}<br/>\left(\frac{d y}{d t}\right) &amp; =\frac{5 d}{d t} \sin \left(4 t+\frac{\pi}{3}\right) \\<br/>&amp; =5 \cos \left(4 t+\frac{\pi}{3}\right) \cdot 4 \\<br/>&amp; =20 \cos \left(4 t+\frac{\pi}{3}\right)<br/>\end{aligned}$<br/>Velocity at $t=\left(\frac{T}{4}\right)$<br/>$\left(\frac{d y}{d t}\right)_{t=\frac{T}{4}}=20 \cos \left(4 \times \frac{T}{4}+\frac{\pi}{3}\right)$<img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/pRsHc2P0lSEiu-1e1zDWG-p3gw_TX-lYnMWeTNqKxc0.original.fullsize.png"/><br/><br/>Comparing the given equation with standard equation of SHM, given by<br/>We get<br/>$\begin{aligned}<br/>&amp; y=a \sin (\omega t+\phi) \\<br/>&amp; \omega=4<br/>\end{aligned}$<br/>As<br/>$\omega=\frac{2 \pi}{T}$<br/>$\begin{aligned} &amp; \Rightarrow \quad T=\frac{2 \pi}{\omega} \\ &amp; \text { or } &amp; T=\frac{2 \pi}{4} \\ &amp; \text { or } &amp; T=\left(\frac{\pi}{2}\right) \\ &amp; \end{aligned}$<br/>Now, putting value of $T$ in Eq. (ii), we get<br/>$\begin{aligned}<br/>u &amp; =20 \cos \left(\frac{\pi}{2}+\frac{\pi}{3}\right) \\<br/>&amp; =-20 \sin \frac{\pi}{3} \\<br/>&amp; =-20 \times \frac{\sqrt{3}}{2} \\<br/>&amp; =-10 \times \sqrt{3}<br/>\end{aligned}$<br/>The kinetic energy of particle,<br/>$\begin{aligned}<br/>&amp; \mathrm{KE}=\frac{1}{2} m u^2 \\<br/>&amp; \because \quad m=2 \mathrm{~g}=2 \times 10^{-3} \mathrm{~kg} \\<br/>&amp; =\frac{1}{2} \times 2 \times 10^{-3} \times(-10 \sqrt{3})^2 \\<br/>&amp; =10^{-3} \times 100 \times 3 \\<br/>&amp; =3 \times 10^{-1} \\<br/>&amp; \mathrm{KE}=0.3 \mathrm{~J} \\<br/>&amp;<br/>\end{aligned}$</div>


tags: ['Physics', 'Oscillations', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0.4 J</span> </div>
source_db: MarksBatch2_P2.db
title:
the-displacement-of-a-particle-executing-shm-is-given-by-y-5-sin-4-t-3-if-t-is-the-time-period-and-the-mass-of-the-particle-is-2-g-the-kinetic-energy--3

slug:
the-displacement-of-a-particle-executing-shm-is-given-by-y-5-sin-4-t-3-if-t-is-the-time-period-and-the-mass-of-the-particle-is-2-g-the-kinetic-energy-3-64547

question:
<div class="question">The displacement of a particle executing SHM is given by<br/>$y=5 \sin \left(4 t+\frac{\pi}{3}\right) .$<br/>If $T$ is the time period and the mass of the particle is $2 \mathrm{~g}$, the kinetic energy of the particle when $t=\frac{T}{4}$ is given by</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">0.4 J</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">0.5 J</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">3 J</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">0.3 J</span> </li> </ul>

answer:
<div class="solution">The displacement of particle, executing SHM<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/O0rq52vMCV9u-reb69yYjnL-3Ng4RQXeaQFafHKCDxY.original.fullsize.png"/><br/><br/>Velocity of particle<br/>$\begin{aligned}<br/>\left(\frac{d y}{d t}\right) &amp; =\frac{5 d}{d t} \sin \left(4 t+\frac{\pi}{3}\right) \\<br/>&amp; =5 \cos \left(4 t+\frac{\pi}{3}\right) \cdot 4 \\<br/>&amp; =20 \cos \left(4 t+\frac{\pi}{3}\right)<br/>\end{aligned}$<br/>Velocity at $t=\left(\frac{T}{4}\right)$<br/>$\left(\frac{d y}{d t}\right)_{t=\frac{T}{4}}=20 \cos \left(4 \times \frac{T}{4}+\frac{\pi}{3}\right)$<img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/pRsHc2P0lSEiu-1e1zDWG-p3gw_TX-lYnMWeTNqKxc0.original.fullsize.png"/><br/><br/>Comparing the given equation with standard equation of SHM, given by<br/>We get<br/>$\begin{aligned}<br/>&amp; y=a \sin (\omega t+\phi) \\<br/>&amp; \omega=4<br/>\end{aligned}$<br/>As<br/>$\omega=\frac{2 \pi}{T}$<br/>$\begin{aligned} &amp; \Rightarrow \quad T=\frac{2 \pi}{\omega} \\ &amp; \text { or } &amp; T=\frac{2 \pi}{4} \\ &amp; \text { or } &amp; T=\left(\frac{\pi}{2}\right) \\ &amp; \end{aligned}$<br/>Now, putting value of $T$ in Eq. (ii), we get<br/>$\begin{aligned}<br/>u &amp; =20 \cos \left(\frac{\pi}{2}+\frac{\pi}{3}\right) \\<br/>&amp; =-20 \sin \frac{\pi}{3} \\<br/>&amp; =-20 \times \frac{\sqrt{3}}{2} \\<br/>&amp; =-10 \times \sqrt{3}<br/>\end{aligned}$<br/>The kinetic energy of particle,<br/>$\begin{aligned}<br/>&amp; \mathrm{KE}=\frac{1}{2} m u^2 \\<br/>&amp; \because \quad m=2 \mathrm{~g}=2 \times 10^{-3} \mathrm{~kg} \\<br/>&amp; =\frac{1}{2} \times 2 \times 10^{-3} \times(-10 \sqrt{3})^2 \\<br/>&amp; =10^{-3} \times 100 \times 3 \\<br/>&amp; =3 \times 10^{-1} \\<br/>&amp; \mathrm{KE}=0.3 \mathrm{~J} \\<br/>&amp;<br/>\end{aligned}$</div>


tags: ['Physics', 'Oscillations', 'VITEEE', 'VITEEE 2009']
source_db: MarksBatch2_P2.db
title:
the-displacement-of-a-particle-executing-shm-is-given-by-y-5-sin-4-t-3-if-t-is-the-time-period-and-the-mass-of-the-particle-is-2-g-the-kinetic-energy-

slug:
the-displacement-of-a-particle-executing-shm-is-given-by-y-5-sin-4-t-3-if-t-is-the-time-period-and-the-mass-of-the-particle-is-2-g-the-kinetic-energy-74347

question:
<div class="question">The displacement of a particle executing SHM is given by<br/>$y=5 \sin \left(4 t+\frac{\pi}{3}\right)$<br/>If $T$ is the time period and the mass of the particle is $2 \mathrm{~g}$, the kinetic energy of the particle when $\mathrm{t}=\mathrm{T} / 4$ is given by</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.4 \mathrm{~J}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.5 \mathrm{~J}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3 \mathrm{~J}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$0.3 \mathrm{~J}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.3 \mathrm{~J}$</span> </div>

answer:
<div class="solution">Particle executing SHM.<br/>Displacement $y=5 \sin \left(4 t+\frac{\pi}{3}\right)...(i)$<br/>Velocity of particle<br/>$$<br/>\begin{array}{l}<br/>\left(\frac{d y}{d t}\right)=\frac{5 d}{d t} \sin \left(4 t+\frac{\pi}{3}\right) \\<br/>=5 \cos \left(4 t+\frac{\pi}{3}\right) \cdot 4=20 \cos \left(4 t+\frac{\pi}{3}\right)<br/>\end{array}<br/>$$<br/>Velocity at $t=\left(\frac{T}{4}\right)$<br/>$$<br/>\left(\frac{d y}{d t}\right)_{t=\frac{T}{4}}=20 \cos \left(4 \times \frac{T}{4}+\frac{\pi}{3}\right)<br/>$$<br/>or $\quad u=20 \cos \left(T+\frac{\pi}{3}\right)...(ii)$<br/>Comparing the given equation with standard equation of SHM.<br/>$y=a \sin (\omega t+\phi)$<br/>We get, $\omega=4$<br/>As $\omega=\frac{2 \pi}{T} \Rightarrow T=\frac{2 \pi}{\omega}$<br/>or $T=\frac{2 \pi}{4}=\left(\frac{\pi}{2}\right)$<br/>Now, putting value of $T$ in Eq. (ii), we get<br/>$$<br/>\begin{aligned}<br/>u &amp;=20 \cos \left(\frac{\pi}{2}+\frac{\pi}{3}\right)=-20 \sin \frac{\pi}{3} \\<br/>&amp;=-10 \times \sqrt{3}<br/>\end{aligned}<br/>$$<br/>The kinetic energy of particle,<br/>$$<br/>\begin{aligned}<br/>\mathrm{KE} &amp;=\frac{1}{2} m u^{2}=\frac{1}{2} \times 2 \times 10^{-3} \times(-10 \sqrt{3})^{2} \\<br/>&amp;=10^{-3} \times 100 \times 3=0.3 \mathrm{~J}<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Oscillations']
source_db: MarksBatch2_P2.db
title:
the-displacement-of-a-particle-is-represented-by-the-equation-y-3-cos-4-2-t-the-motion-of-the-particle-is

slug:
the-displacement-of-a-particle-is-represented-by-the-equation-y-3-cos-4-2-t-the-motion-of-the-particle-is-23358

question:
<div class="question">The displacement of a particle is represented by the equation $y=3 \cos \left(\frac{\pi}{4}-2 \omega t\right)$. The motion of the particle is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>simple harmonic with period $2 \pi / \omega$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>simple harmonic with period $\pi / \omega$<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/>periodic but not simple harmonic<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>non-periodic</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>simple harmonic with period $\pi / \omega$<br/></span> </div>

answer:
<div class="solution">As given that, $y=3 \cos \left(\frac{\pi}{4}-2 \omega t\right)$<br/>Velocity of the particle<br/>$$<br/>\begin{aligned}<br/>v &amp;=\frac{d y}{d t}=\frac{d}{d t}\left[3 \cos \left(\frac{\pi}{4}-2 \omega t\right)\right] \\<br/>&amp;=3(-2 \omega)\left[-\sin \left(\frac{\pi}{4}-2 \omega t\right)\right] \\<br/>&amp;=6 \omega \sin \left(\frac{\pi}{4}-2 \omega t\right)<br/>\end{aligned}<br/>$$<br/>So, acceleration,<br/>$$<br/>\begin{aligned}<br/>a &amp;=\frac{d v}{d t}=\frac{d}{d t}\left[6 \omega \sin \left(\frac{\pi}{4}-2 \omega t\right)\right] \\<br/>&amp;=(6 \omega) \times(-2 \omega) \cos \left(\frac{\pi}{4}-2 \omega t\right) \\<br/>&amp;=-4 \omega^2\left[3 \cos \left(\frac{\pi}{4}-2 \omega t\right)\right] \\<br/>\Rightarrow a=-4 \omega^2 y<br/>\end{aligned}<br/>$$<br/>In simple harmonic motion acceleration (or force) is directly proportional to the negative of displacement of particle<br/>$\Rightarrow$ as acceleration, $a \propto-y$<br/>Hence, due to negative sign motion is simple harmonic motion (SHM.)<br/>A simple harmonic motion is always periodic. So motion is periodic simple harmonic.<br/>From the given equation,<br/>$$<br/>y=3 \cos \left(\frac{\pi}{4}-2 \omega t\right)<br/>$$<br/>Compare it by standard equation<br/>$$<br/>y=a \cos (\omega t+\phi)<br/>$$<br/>So, $\omega^{\prime}=2 \omega$<br/>$$<br/>\frac{2 \pi}{T^{\prime}}=2 \omega \Rightarrow T^{\prime}=\frac{2 \pi}{2 \omega}=\frac{\pi}{\omega}<br/>$$<br/>Hence, the motion is SHM with period $\frac{\pi}{\omega}$.</div>


tags: ['Physics', 'Oscillations', 'MHT CET', 'MHT CET 2021 (24 Sep Shift 2)']
source_db: MarksBatch2_P2.db
title:
the-displacement-of-a-particle-performing-shm-is-given-by-x-5-sin-3-t-3-where-x-is-in-cm-and-t-is-in-second-the-maximum-acceleration-of-the-particle-w

slug:
the-displacement-of-a-particle-performing-shm-is-given-by-x-5-sin-3-t-3-where-x-is-in-cm-and-t-is-in-second-the-maximum-acceleration-of-the-particle-w-21963

question:
<div class="question">The displacement of a particle performing S.H.M is given by $x=5 \sin (3 t+3)$, where $x$ is in $\mathrm{cm}$ and $t$ is in second. The maximum acceleration of the particle will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$15 \mathrm{~cm} \mathrm{~s}^{-2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$30 \mathrm{~cm} \mathrm{~s}^{-2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$45 \mathrm{~cm} \mathrm{~s}^{-2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$90 \mathrm{~cm} \mathrm{~s}^{-2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$45 \mathrm{~cm} \mathrm{~s}^{-2}$</span> </div>

answer:
<div class="solution">$x=5 \sin (3 t+3)$<br/>Standard equation of S.H.M. is $x=A \sin (\omega t+\alpha)$<br/>$\therefore \mathrm{A}=5 \mathrm{~cm}, \omega=3 \mathrm{rad} / \mathrm{s}$<br/>Maximum acceleration $\mathrm{a}_{\mathrm{m}}=\mathrm{A} \omega^2=5 \times(3)^2$<br/>$=5 \times 9=45 \mathrm{~cm} \mathrm{~s}^{-2}$</div>


tags: ['Physics', 'Oscillations', 'JEE Main', 'JEE Main 2003']
source_db: MarksBatch2_P2.db
title:
the-displacement-of-a-particle-varies-according-to-the-relation-x-4-cos-t-sin-t-the-amplitude-of-the-particle-is

slug:
the-displacement-of-a-particle-varies-according-to-the-relation-x-4-cos-t-sin-t-the-amplitude-of-the-particle-is-60693

question:
<div class="question">The displacement of a particle varies according to the relation $x=4(\cos \pi t+\sin \pi t)$. The amplitude of the particle is</div>

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

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

answer:
<div class="solution">$\left.x=4(\cos \pi t+\sin \pi t)=4\left[\sin \left(\frac{\pi}{2}-\pi t\right)\right]+\sin \pi t\right]=4\left[2 \times \sin \left(\frac{\pi t-\frac{\pi}{2}-\pi t}{2}\right) \cos \left(\frac{\pi \mathrm{t}-\frac{\pi}{2}+\pi \mathrm{t}}{2}\right)\right]$<br/>$=8\left[\sin \frac{\pi}{4} \cdot \cos \left(-\frac{\pi}{4}+\pi t\right)\right]$<br/>$=\frac{8}{\sqrt{2}} \cdot \cos \left[\pi t-\frac{\pi}{4}\right]=4 \sqrt{2} \cos \left[\pi t-\frac{\pi}{4}\right]$<br/>Comparing it with standard equation<br/>$X=A \cos (w t-K x) \quad \Rightarrow A=4 \sqrt{2}$</div>


tags: ['Physics', 'Waves and Sound']
source_db: MarksBatch2_P2.db
title:
the-displacement-of-a-string-is-given-by-y-x-t-006-sin-3-2-x-cos-120-t-where-x-and-y-are-in-metre-and-t-in-second-the-length-of-the-string-is-15-m-and

slug:
the-displacement-of-a-string-is-given-by-y-x-t-006-sin-3-2-x-cos-120-t-where-x-and-y-are-in-metre-and-t-in-second-the-length-of-the-string-is-15-m-and-38770

question:
<div class="question">The displacement of a string is given by $y(x, t)=0.06 \sin \left(\frac{2 \pi x}{3}\right) \cos (120 \pi t)$<br/>where $x$ and $y$ are in metre and $t$ in second. The length of the string is $1.5 \mathrm{~m}$ and its mass is $3.0 \times 10^{-2} \mathrm{~kg}$.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>It represents a progressive wave of frequency $60 \mathrm{~Hz}$.<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>It represents a stationary wave of frequency $60 \mathrm{~Hz}$<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="correct"> <span class="option-label">C</span> <span class="option-data"><br/>It is the result superposition of two waves of wavelength $3 \mathrm{~m}$, frequency $60 \mathrm{~Hz}$ each travelling with a speed of $180 \mathrm{~m} / \mathrm{s}$ in opposite direction<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/>Amplitude of this wave is constant.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>It represents a stationary wave of frequency $60 \mathrm{~Hz}$<br/>, <br/>It is the result superposition of two waves of wavelength $3 \mathrm{~m}$, frequency $60 \mathrm{~Hz}$ each travelling with a speed of $180 \mathrm{~m} / \mathrm{s}$ in opposite direction<br/></span> </div>

answer:
<div class="solution">As we know that, standard equation of stationary wave<br/>$$<br/>y(x, t)=a \sin (k x) \cos (\omega t)<br/>$$<br/>As given that the equation is<br/>$$<br/>y(x, t)=0.06 \sin \left(\frac{2 \pi x}{3}\right) \cos (120 \pi t)<br/>$$<br/>Comparing with a standard equation of stationary wave with given equation. So, $a=0.06, k=\frac{2 \pi}{3}$, $\omega=120 \pi$<br/>(a) Clearly, the given equation belongs to stationary wave. Hence, option (a) is not verifies.<br/>(b) Given, $\omega=120 \pi$<br/>$$<br/>2 \pi v=120 \pi \Rightarrow v=60 \mathrm{~Hz}<br/>$$<br/>(c) $k=\frac{2 \pi}{3}=\frac{2 \pi}{\lambda} \quad\left(\because k=\frac{2 \pi}{\lambda}\right)$<br/>So, $\lambda$ (wavelength) $=3 \mathrm{~m}$<br/>Frequency $(v)=60 \mathrm{~Hz}$<br/>Speed $(v)=v \lambda=(60 \mathrm{~Hz}) \times(3 \mathrm{~m})=180 \mathrm{~m} / \mathrm{s}$<br/>(d) As waves are stationary so the amplitude of particles varies from 0 to $0.06 \mathrm{~m}$ from nodes to antinodes i.e. amplitude is not constant always.<br/>Since in stationary wave, all particles of the medium execute SHM with varying amplitude nodes. So option<br/>(d) is not verifies.</div>


tags: ['Physics', 'Oscillations', 'MHT CET', 'MHT CET 2020 (14 Oct Shift 1)']
source_db: MarksBatch2_P2.db
title:
the-displacement-of-the-particle-executing-linear-shm-is-x-025-sin-11-t-05-m-the-period-of-shm-is-7-22

slug:
the-displacement-of-the-particle-executing-linear-shm-is-x-025-sin-11-t-05-m-the-period-of-shm-is-7-22-70874

question:
<div class="question">The displacement of the particle executing linear S.H.M. is $\mathrm{x}=0.25 \mathrm{sin}(11 \mathrm{t}+0.5) \mathrm{m}$. The period of S.H.M. is $\left(\pi=\frac{22}{7}\right)$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{2}{7} \mathbf{S}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{4}{7} \mathrm{~S}$</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">C</span> <span class="option-data">$\frac{3}{7} \mathrm{~S}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{7}$ S</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{4}{7} \mathrm{~S}$</span> </div>

answer:
<div class="solution">Comparing with standard equation of S.H.M.<br/>$x=A \sin (\omega t+\phi)$<br/>we get $\omega=11$<br/>$\therefore  T=\frac{2 \pi}{\omega}=\frac{2 \times 22}{11 \times 7}=\frac{4}{7} \kappa$</div>


tags: ['Physics', 'Oscillations', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2.0 Hz</span> </div>
source_db: MarksBatch2_P2.db
title:
the-displacement-x-in-meter-of-a-particle-performing-simple-harmonic-motion-is-related-to-time-t-in-second-as-x-005-c-o-s-4-t-4-the-frequency-of-the-m

slug:
the-displacement-x-in-meter-of-a-particle-performing-simple-harmonic-motion-is-related-to-time-t-in-second-as-x-005-c-o-s-4-t-4-the-frequency-of-the-m-36864

question:
<div class="question">The displacement <math><mi>x </mi></math>(in meter) of a particle performing simple harmonic motion is related to time t (in second) as <math><mi>x</mi><mo>=</mo><mn>0.05</mn><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mfenced separators="|"><mrow><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></math>.The frequency of the motion will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0.5 Hz</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1.0 Hz</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1.5 Hz</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">2.0 Hz</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">Compare the given equation with the standard form<br/><br/><math><mi>y</mi><mo>=</mo><mi>r</mi><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>â¡</mo><mrow><mfenced close="]" open="[" separators="|"><mrow><mfrac><mrow><mn>2</mn><mi>Ï</mi><mi>t</mi></mrow><mrow><mi>T</mi></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>2</mn><mi>Ï</mi><mi>x</mi></mrow><mrow><mi>Î»</mi></mrow></mfrac></mrow></mfenced></mrow></mrow></math><br/><br/>Coefficient of <math><mi>t</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>Ï</mi></mrow><mrow><mi>T</mi></mrow></mfrac><mo>=</mo><mn>2</mn><mi>Ï</mi><mi>n</mi><mo>=</mo><mn>4</mn><mi>Ï</mi><mo>,</mo><mi>n</mi><mo>=</mo><mn>2</mn><mi>Â </mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math></div>


tags: ['Physics', 'Oscillations', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-displacement-x-in-metre-of-a-particle-in-simple-harmonic-motion-is-related-to-time-t-in-second-as-x-001-cos-t-4-the-frequency-of-the-motion-will-b

slug:
the-displacement-x-in-metre-of-a-particle-in-simple-harmonic-motion-is-related-to-time-t-in-second-as-x-001-cos-t-4-the-frequency-of-the-motion-will-b-14876

question:
<div class="question">The displacement <math><mi>x</mi></math>(in metre) of a particle in simple harmonic motion is related to time <math><mi>t</mi></math> (in second) as<br/> <br/> <math><mi>x</mi><mo>=</mo><mn>0.01</mn><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mi>Ï</mi><mi>t</mi><mo>+</mo><mfrac><mrow><mi>Ï</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math><br/> <br/>
The frequency of the motion 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>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>Hz</mi></math><div id="gtx-trans" style="position: absolute; left: 107px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div><div id="gtx-trans" style="position: absolute; left: 107px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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>1</mn><mo>.</mo><mn>0</mn><mo> </mo><mi>Hz</mi></math><div id="gtx-trans" style="position: absolute; left: 103px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Hz</mi></math><div id="gtx-trans" style="position: absolute; left: 86px; top: 5.76736px;"><div class="gtx-trans-icon"> </div></div></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mi>π</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Hz</mi></math><div id="gtx-trans" style="position: absolute; left: 163px; top: -4.21528px;"><div class="gtx-trans-icon"> </div></div></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>5</mn><mo> </mo><mi>Hz</mi></math><div id="gtx-trans" style="position: absolute; left: 107px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div><div id="gtx-trans" style="position: absolute; left: 107px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> </div>

answer:
<div class="solution">The standard equation in SHM is<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>a</mi><mi>cos</mi><mo>⁡</mo><mrow><mo>(</mo><mi>ω</mi><mi>t</mi><mo>+</mo><mi>ϕ</mi><mo>)</mo></mrow></math> ...(i)<br/><br/>Where <math><mi>a</mi></math> is amplitude, <math><mi>ω</mi></math> the angular velocity and (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi></math>) the phase difference.<br/><br/>Also, <math><mi>ω</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mi>T</mi><mi> </mi></mrow></mfrac><mi> </mi><mi mathvariant="normal">w</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi> </mi><mi>T</mi></math> is periodic time.<br/><br/>So, Eq. (i) becomes<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>a</mi><mi>cos</mi><mo>⁡</mo><mfenced separators="|"><mrow><mfrac><mrow><mn>2</mn><mi>π</mi><mi>t</mi></mrow><mi>T</mi></mfrac><mo>+</mo><mi>ϕ</mi></mrow></mfenced></math> ...(ii)<br/><br/>Given, the equation is<br/><br/><math><mi>x</mi><mo>=</mo><mn>0.01</mn><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>⁡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>2</mn><mi>π</mi><mi>t</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math> ...(iii)<br/><br/>Comparing Eq. (ii) with Eq. (iii), we get<br/><br/><math><mfrac><mrow><mn>2</mn><mi>π</mi><mi>t</mi></mrow><mrow><mi>T</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi><mi>t</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi> </mi><mi>T</mi><mo>=</mo><mn>2</mn><mo> </mo><mi mathvariant="normal">s</mi></math><br/><br/>So, frequency <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mfrac><mn>1</mn><mi>T</mi></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mn>0.5</mn><mo> </mo><mi>Hz</mi></math> </div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
the-displacement-y-of-a-particle-in-a-medium-can-be-expressed-as-y-10-6-sin-100-t-20x-4-m-where-t-is-in-seconds-and-x-in-meters-the-speed-of-the-wave-

slug:
the-displacement-y-of-a-particle-in-a-medium-can-be-expressed-as-y-10-6-sin-100-t-20x-4-m-where-t-is-in-seconds-and-x-in-meters-the-speed-of-the-wave-87918

question:
<div class="question">The displacement <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>y</mtext></math> of a particle in a medium can be expressed as <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>y</mtext><mo>=</mo><msup><mtext>10</mtext><mrow><mo>-</mo><mn>6</mn></mrow></msup><mtext>sin</mtext><mfenced><mrow><mtext>100</mtext><mi mathvariant="normal">t</mi><mo>-</mo><mtext>20x</mtext><mo>+</mo><mi mathvariant="normal">Ï</mi><mo>/</mo><mn>4</mn></mrow></mfenced><mo> </mo><mi mathvariant="normal">m</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>t</mtext></math> is in seconds and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>x</mtext></math> in meters. The speed of the wave 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>2000</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> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</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">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</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> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</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> </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>5</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"><p>Given wave equation :<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>y</mtext><mo>=</mo><msup><mtext>10</mtext><mrow><mo>-</mo><mn>6</mn></mrow></msup><mtext>sin</mtext><mfenced><mrow><mtext>100</mtext><mi mathvariant="normal">t</mi><mo>+</mo><mtext>20x</mtext><mo>+</mo><mfrac><mi mathvariant="normal">π</mi><mn>4</mn></mfrac></mrow></mfenced><mo> </mo><mi mathvariant="normal">m</mi></math><br/><br/>Standard equation : <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>y</mtext><mo>=</mo><mtext>a sin </mtext><mfenced><mrow><mi>ωt</mi><mo>+</mo><mi mathvariant="normal">k</mi><mtext>x</mtext><mo>+</mo><mi mathvariant="normal">ϕ</mi></mrow></mfenced></math><br/><br/>Comparing the two, we obtain<br/><br/><math> <mrow> <mo>∴  </mo> </mrow> </math><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">ω</mi><mo>=</mo><mn>100</mn></math> and  <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">k</mi><mo>=</mo><mn>20</mn></math><br/><br/><math> <mrow> <mo>∴</mo> </mrow> </math>   <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi mathvariant="normal">ω</mi><mi mathvariant="normal">k</mi></mfrac><mo>=</mo><mfrac><mtext>100</mtext><mtext>20</mtext></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mrow><mn>2</mn><mi>πn</mi></mrow><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mo>/</mo><mi mathvariant="normal">λ</mi></mrow></mfrac><mo>=</mo><mi>nλ</mi><mo>=</mo><mi mathvariant="normal">v</mi><mo>=</mo><mn>5</mn></math><br/><br/><math> <mrow> <mo>∴</mo> </mrow> </math>  <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">v</mi><mo>=</mo><mn>5</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></div>


tags: ['Physics', 'Waves and Sound', 'JEE Main', 'JEE Main 2003']
source_db: MarksBatch2_P2.db
title:
the-displacement-y-of-a-wave-travelling-in-the-x-direction-is-given-by-y-1-0-4-sin-600-t-2-x-3-metres-where-x-is-expressed-in-metres-and-t-in-seconds-

slug:
the-displacement-y-of-a-wave-travelling-in-the-x-direction-is-given-by-y-1-0-4-sin-600-t-2-x-3-metres-where-x-is-expressed-in-metres-and-t-in-seconds-99744

question:
<div class="question">The displacement $y$ of a wave travelling in the $x$-direction is given by $y=10^{-4} \sin \left(600 t-2 x+\frac{\pi}{3}\right)$ metres where $\mathrm{x}$ is expressed in metres and $\mathrm{t}$ in seconds. The speed of the wave-motion, in $\mathrm{ms}^{-1}$, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$300$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$600$<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/>$1200$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$200$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$600$<br/></span> </div>

answer:
<div class="solution">$y=10^{-4} \sin \left(600 t-2 x+\frac{\pi}{3}\right)$. Comparing it with standard equation<br/>$y=A \sin (v t-k x) ; \quad v=600 m / s$</div>


tags: ['Mathematics', 'Straight Lines', 'AP EAMCET', 'AP EAMCET 2021 (24 Aug Shift 1)']
source_db: MarksBatch2_P2.db
title:
the-distance-between-pair-of-parallel-lines-represented-by-x-2-2-x-y-y-2-8-a-x-8-a-y-9-a-2-0-is-units

slug:
the-distance-between-pair-of-parallel-lines-represented-by-x-2-2-x-y-y-2-8-a-x-8-a-y-9-a-2-0-is-units-58637

question:
<div class="question">The distance between pair of parallel lines represented by<br/>$$<br/>x^2+2 x y+y^2-8 a x-8 a y-9 a^2=0<br/>$$<br/>is. units</div>

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

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

answer:
<div class="solution">Given, $\because x^2+2 x y+y^2-8 a x-8 a y-9 a^2=0$ represents a pair of parallel lines.<br/>Compare with standard form<br/>$$<br/>\begin{aligned}<br/>&amp; a x^2+b y^2+2 h x y+2 g x+2 f y+c=0 \\<br/>&amp; a=1, b=1, h=1, g=-4 a, f=-4 a, c=-9 a^2<br/>\end{aligned}<br/>$$<br/>$\because$ We know that distance between the parallel lines.<br/>$$<br/>\begin{aligned}<br/>D &amp; =2 \sqrt{\frac{g^2-a c}{a(a+b)}} \\<br/>&amp; =2 \sqrt{\frac{(-4 a)^2-(1)\left(-9 a^2\right)}{1(1+1)}} \\<br/>&amp; =2 \sqrt{\frac{16 a^2+9 a^2}{2}}=2 \sqrt{\frac{25 a^2}{2}}=2 \times \frac{5 a}{\sqrt{2}}=5 \sqrt{2} a<br/>\end{aligned}<br/>$$</div>


title: the-distance-between-the-parallel-planes-4-x-2-y-4-z-9-0-and-8-x-4-y-8-z-21-0-is
slug: the-distance-between-the-parallel-planes-4-x-2-y-4-z-9-0-and-8-x-4-y-8-z-21-0-is-98278
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The distance between the parallel planes $4 x-2 y+4 z+9=0$ and $8 x-4 y+8 z+21=0$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{1}{4}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{3}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{7}{4}$</span> </li> </ul>

answer:
<div class="solution">Given planes $: 4 x-2 y+4 z+9=0$ $\Rightarrow 8 x-4 y+8 z+18=0$<br/>$8 x-4 y+8 z+21=0$<br/>Distance $=\frac{\left|d_{1}-d_{2}\right|}{\sqrt{a^{2}+b^{2}+c^{2}}}=\frac{|18-21|}{\sqrt{64+16+64}}$<br/>$=\frac{3}{\sqrt{144}}=\frac{3}{12}=\frac{1}{4}$</div>


title: the-distance-of-the-point-1-3-from-the-line-2-x-3-y-6-measured-parallel-to-the-line-4-x-y-4-is
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P2.db
slug:
the-distance-of-the-point-1-3-from-the-line-2-x-3-y-6-measured-parallel-to-the-line-4-x-y-4-is-51071

question:
<div class="question">The distance of the point $(1,3)$ from the line $2 \mathrm{x}+3 \mathrm{y}=6$, measured parallel to the line $4 \mathrm{x}+\mathrm{y}=4$, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{5}{\sqrt{13}}$ units</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{3}{\sqrt{17}}$ unit</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\sqrt{17}$ units</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{\sqrt{17}}{2}$ units</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\sqrt{17}}{2}$ units</span> </div>

answer:
<div class="solution">The line $4 \mathrm{x}+\mathrm{y}=4$ can be written as $\mathrm{y}=-4 \mathrm{x}+4$. So, slope is $-4$. The line parallel to $4 \mathrm{x}+\mathrm{y}=4$ will have slope $-4$ only. Given point $=(1,3)$ Equation of line passing through $(1,3)$ and slope $-4$ is $\mathrm{y}-3=-4(\mathrm{x}-1)$<br/>$\Rightarrow \mathrm{y}-3=-4 \mathrm{x}+4 \Rightarrow 4 \mathrm{x}+\mathrm{y}=7$<br/>Solving the two equations, we get<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/0-ejDGQmhw_A1p5U78D_sgZLxax06OcT_kTY3O2U2Y8.original.fullsize.png"/><br/><br/>$2 x+3 y=6 \Rightarrow 2 x+3(1)=6$<br/>$\Rightarrow 2 \mathrm{x}=3 \Rightarrow \mathrm{x}=\frac{3}{2}$<br/>Distance between the points $(1,3)$ and $\left(\frac{3}{2}, 1\right)$ is<br/>$\sqrt{\left(\frac{3}{2}-1\right)^{2}+(1-3)^{2}}=\sqrt{\left(\frac{1}{2}\right)^{2}+(-2)^{2}}=\sqrt{\frac{1}{4}+4}=\sqrt{\frac{17}{4}}=\frac{\sqrt{17}}{2}$</div>


tags: ['Mathematics', 'Statistics', 'TS EAMCET', 'TS EAMCET 2018 (04 May Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch2_P2.db
title:
the-distribution-of-a-random-variable-x-is-given-below-beginarraylllll-hlinexx-1-2-3-4-hlinepxx-20-40-60-80-hline-endarray-then-the-standard-deviation

slug:
the-distribution-of-a-random-variable-x-is-given-below-beginarraylllll-hlinexx-1-2-3-4-hlinepxx-20-40-60-80-hline-endarray-then-the-standard-deviation-45694

question:
<div class="question">The distribution of a random variable $X$ is given below<br/>\begin{array}{lllll}<br/>\hlineX=x &amp; 1 &amp; 2 &amp; 3 &amp; 4 \\<br/>\hlineP(X=x) &amp; 20 &amp; 40 &amp; 60 &amp; 80 \\<br/>\hline<br/>\end{array}<br/>Then, the standard deviation of $X$ is</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">$\frac{3}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">\begin{array}{ccccc}<br/>\hlinex &amp; 1 &amp; 2 &amp; 3 &amp; 4 \\<br/>\hlineP_x=x &amp; 2 c &amp; 4 c &amp; 6 c &amp; 8 c \\<br/>\hline<br/>\end{array}<br/>So, standard deviation of $X$ is<br/>Now, $2 c+4 c+6 c+8 c=1 \Rightarrow c=\frac{1}{20}$ for standard deviation<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/yW-yEG2T871OsMeb_YK590DqP6UWbH_h3kcg6CDnQ9s.original.fullsize.png"/><br/><br/><br/>$$<br/>\begin{aligned}<br/>&amp; \sigma=\sqrt{\Sigma x^2 \cdot P x-(\Sigma x \cdot P x)^2} \\<br/>&amp; \Rightarrow \quad \sigma=\sqrt{10-(3)^2} \Rightarrow 1 \\<br/>&amp;<br/>\end{aligned}<br/>$$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2010 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">336</span> </div>
source_db: MarksBatch2_P2.db
title:
the-distributiong-x-and-y-with-total-number-of-combined-what-is-the-mean-of-the-resulting-distribution-x-y

slug:
the-distributiong-x-and-y-with-total-number-of-combined-what-is-the-mean-of-the-resulting-distribution-x-y-64358

question:
<div class="question">The distributiong $X$ and $Y$ with total number of<br/>combined. What is the mean of the resulting distribution $x+Y ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$3.26$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3.32$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">336</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$3.42$</span> </li> </ul>

answer:
<div class="solution">Required mean $=\frac{36 \times 4+64 \times 3}{36+64}=\frac{144+192}{100}=\frac{336}{100}$<br/>$=3.36$</div>


title: the-domain-of-the-function-f-defined-by-f-x-lo-g-x-10-is
slug: the-domain-of-the-function-f-defined-by-f-x-lo-g-x-10-is-74974
tags: ['Mathematics', 'Functions', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The domain of the function $\mathrm{f}$ defined by $\mathrm{f}(\mathrm{x})=\log _{\mathrm{x}} 10$ is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$x&gt;0$ excluding $x=1$</span> </div>

answer:
<div class="solution">$\mathrm{f}(\mathrm{x})=\log _{\mathrm{x}} 10$<br/>Domain of logarithmic function is $\mathrm{x}&gt;0$ excluding $\mathrm{x}=1$.</div>


title: the-domain-of-the-function-f-x-2-x-x-3-is
slug: the-domain-of-the-function-f-x-2-x-x-3-is-71829
tags: ['Mathematics', 'Functions', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The domain of the function $\mathrm{f}(\mathrm{x})=\sqrt{(2-x)(x-3)}$ is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$[2,3]$</span> </div>

answer:
<div class="solution">$\begin{aligned} &amp; f(x)=\sqrt{(2-x)(x-3)} \\ &amp; \text { Here }(2-\mathrm{x})(\mathrm{x}-3) \geq 0 \\ &amp; \Rightarrow-(\mathrm{x}-2)(\mathrm{x}-3) \geq 0 \\ &amp; \Rightarrow(\mathrm{x}-2)(\mathrm{x}-3) \leq 0 \\ &amp; \Rightarrow \mathrm{x} \in[2,3] \end{aligned}$</div>


title: the-domain-of-the-function-f-x-x-x-1-is
slug: the-domain-of-the-function-f-x-x-x-1-is-66633
tags: ['Mathematics', 'Functions', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The domain of the function $\mathrm{f}(\mathrm{x})=\frac{1}{\sqrt{|\mathrm{x}|-\mathrm{x}}}$ is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(-\infty, 0)$</span> </div>

answer:
<div class="solution">$\mathrm{f}(\mathrm{x})=\frac{1}{\sqrt{|\mathrm{x}|-\mathrm{x}}}$<br/>$|x|-x \neq 0$<br/>So $\mathrm{x}   &lt; 0$<br/>$\mathrm{x}=(-\infty, 0)$<br/>again $|x|-x&gt;0$ $|x|&gt;x$<br/>it is possible only when $\mathrm{x}$ is negative.<br/>$\mathrm{x}=(-\infty, 0)$<br/>So from eq. (1) \&amp; eq. (2)<br/>domain $\mathrm{x}=(-\infty, 0)$</div>


title: the-domestic-sewage-in-large-cities
slug: the-domestic-sewage-in-large-cities-46674
question: <div class="question">The domestic sewage in large cities</div>
tags: ['Biology', 'Microbes in Human Welfare', 'NEET', 'NEET 2012 (Mains)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">has a high BOD as it contains both aerobic and anaerobic bacteria</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">is processed by aerobic and then anaerobic bacteria in the secondary treatment in Sewage Treatment Plants (STPs)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">when treated in STPs does not really require the aeration step as the sewage contains adequate oxygen</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">has very high amounts of suspended solids and dissolved salts</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">is processed by aerobic and then anaerobic bacteria in the secondary treatment in Sewage Treatment Plants (STPs)</span> </div>

answer:
<div class="solution">Sewage is waste water having food residue, animal and human excreta, detergents, discharges from commercial and industrial establishments. The domestic sewage is processed first by aerobic and then by anaerobic bacteria in secondary treatment in Sewage Treatment Plant (STPs).</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Main', 'JEE Main 2022 (26 Jun Shift 1)']
source_db: MarksBatch2_P2.db
title:
the-e-t-p-of-different-types-of-half-cells-are-as-follows-a-b-c-d-1-10-4-2-10-4-0-1-10-4-0-2-10-4-where-e-is-the-electromotive-force-which-of-the-abov

slug:
the-e-t-p-of-different-types-of-half-cells-are-as-follows-a-b-c-d-1-10-4-2-10-4-0-1-10-4-0-2-10-4-where-e-is-the-electromotive-force-which-of-the-abov-96868

question:
<div class="question"><p>The <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mfenced><mfrac><mrow><mo>∂</mo><mi mathvariant="normal">E</mi></mrow><mrow><mo>∂</mo><mi mathvariant="normal">T</mi></mrow></mfrac></mfenced><mi mathvariant="normal">P</mi></msub></math> of different types of half cells are as follows :<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi mathvariant="normal">A</mi></mtd><mtd><mi mathvariant="normal">B</mi></mtd><mtd><mi mathvariant="normal">C</mi></mtd><mtd><mi mathvariant="normal">D</mi></mtd></mtr><mtr><mtd><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup></mtd><mtd><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup></mtd><mtd><mn>0</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup></mtd><mtd><mn>0</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup></mtd></mtr></mtable></math></p><p>(Where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">E</mi></math> is the electromotive force). Which of the above half cells would be preferred to be used as reference electrode</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 mathvariant="normal">A</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"><mi mathvariant="normal">B</mi></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"><mi mathvariant="normal">C</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">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">D</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"><mi mathvariant="normal">C</mi></math></span> </div>

answer:
<div class="solution">Metal Which have lower value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mfenced><mfrac><mi>dE</mi><mi>dT</mi></mfrac></mfenced><mi mathvariant="normal">p</mi></msub></math> is best used for standard or reference half Electrode because if can be used for wider range of temperature Without much derivation from standard Value.</div>


title: the-e-values-for-mn-and-zn-are-more-negative-than-expected-because
slug: the-e-values-for-mn-and-zn-are-more-negative-than-expected-because-61872
tags: ['Chemistry', 'd and f Block Elements', 'JIPMER', 'JIPMER 2016']
source_db: MarksBatch2_P2.db
question:
<div class="question">The $E^{\circ}$ values for Mn and Zn are more negative than expected because</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">they have either half-filled and fully-filled configurations</span> </div>

answer:
<div class="solution">The values of standard electrode potentials for Mn, and Zn are more negative than expected. The reason behind this is that they have exactly half-filled and fully-filled configuration ons.<br/>$\begin{aligned} &amp; { }_{25} \mathrm{Mn}: \left[\mathrm{Ar}\right] 3 d^5 4 s^2 \\ &amp; { }_{30} \mathrm{Zn}:[\mathrm{Ar}] 3 d^{10} 4 s^2\end{aligned}$</div>


title: the-earth-summit-held-in-rio-de-janeiro-in-1992-was-called
slug: the-earth-summit-held-in-rio-de-janeiro-in-1992-was-called-26527
question: <div class="question">The Earth Summit held in Rio de Janeiro in 1992 was called:</div>
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET', 'NEET 2019 (All India)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">To reduce CO<sub>2</sub> emission and global warming</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">For conservation of biodiversity and sustainable utilization of its benefits</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">To assess threat posed to native species by invasive weed species</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">For immediate steps to discontinue use of CFCs that were damaging the ozone layer</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">For conservation of biodiversity and sustainable utilization of its benefits</span> </div>

answer:
<div class="solution">In 1992, leaders from more than 100 countries participated in the first International Earth Summit at Rio de Janeiro in Brazil. The major objective was that every country should portray its own Agenda 21 for attaining sustainable development. The other objectives of the summit are (i) To achieve global sustainable development in the 21st century (ii) To conserve biological diversity (iii) To eliminate diseases with the help of shared welfare, requirements and obligations amongst various nations (iv) To prevent poverty and environmental damage.</div>


title: the-ease-of-dehydrohalogenation-of-alkyl-halide-with-alcoholic-koh-is-1
slug: the-ease-of-dehydrohalogenation-of-alkyl-halide-with-alcoholic-koh-is-1-23346
question: <div class="question">The ease of dehydrohalogenation of alkyl halide with alcoholic KOH is</div>
tags: ['Chemistry', 'General Organic Chemistry', 'NEET']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">3<math><mo>°</mo></math> &lt; 2<math><mo>° &lt;  </mo></math>1<math><mo>°</mo></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">3<math><mo>Â°</mo></math> &gt; 2<math><mo>Â° &gt;  </mo></math>1<math><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><li class=""> <span class="option-label">C</span> <span class="option-data">3<math><mo>°</mo></math> &lt; 2<math><mo>° &gt;  </mo></math>1<math><mo>°</mo></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">3<math><mo>°</mo></math> &gt; 2<math><mo>° &lt;  </mo></math>1<math><mo>°</mo></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">3<math><mo>Â°</mo></math> &gt; 2<math><mo>Â° &gt;  </mo></math>1<math><mo>Â°</mo></math></span> </div>

answer:
<div class="solution">Such dehydrohalogenation follow <math><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><mn>2</mn></mrow></msub></math> mechanism. The driving force of such reaction is the stability of alkene produced. Since, tertiary alkyl halide can give more substituted alkene, it reacts fastest followed by secondary and primary <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">i</mi><mo>.</mo><mi mathvariant="normal">e</mi><mo>.</mo><mo>,</mo><mi mathvariant="normal"> </mi><mn>3</mn><mo>Â°</mo><mo>&gt;</mo><mn>2</mn><mo>Â°</mo><mo>&gt;</mo><mn>1</mn><mo>Â°</mo><mo>.</mo></math></div>


title: the-ease-of-dehydrohalogenation-of-alkyl-halide-with-alcoholic-mathrmkoh-is-1
slug: the-ease-of-dehydrohalogenation-of-alkyl-halide-with-alcoholic-mathrmkoh-is-1-60496
tags: ['Chemistry', 'Hydrocarbons', 'JEE Main']
source_db: MarksBatch2_P2.db
question:
<div class="question">The ease of dehydrohalogenation of alkyl halide with alcoholic \(\mathrm{KOH}\) is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(3^{\circ} &gt; 2^{\circ} &gt; 1^{\circ}\)</span> </div>

answer:
<div class="solution">Hints : Such dehydrohalogenation follows \(\mathrm{E}_2\) mechanism. The driving force of such reactions is the stability of alkene produced. Since tetriary alkyl halide can give more substituted alkene, it reacts fastest followed by secondary and primary i.e. \(3^{\circ} &gt; 2^{\circ} &gt; 1^{\circ}\).</div>


title: the-eccentricity-e-of-an-ellipse-satisfies-the-condition
slug: the-eccentricity-e-of-an-ellipse-satisfies-the-condition-35624
question: <div class="question">The eccentricity e of an ellipse satisfies the condition</div>
tags: ['Mathematics', 'Ellipse', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">e   &lt; 0</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$0   &lt; \mathrm{e} &lt; 1$</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">e=1</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">e&gt;1</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0   &lt; \mathrm{e} &lt; 1$</span> </div>

answer:
<div class="solution">The eccentricity e of an ellipse satisties the condition $0   &lt; \mathrm{e} &lt; 1$</div>


title: the-eccentricity-of-the-conjugate-hyperbola-of-the-hyperbola-x-2-3-y-2-1-is
slug: the-eccentricity-of-the-conjugate-hyperbola-of-the-hyperbola-x-2-3-y-2-1-is-15504
tags: ['Mathematics', 'Hyperbola', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$2$</span> </div>
source_db: MarksBatch2_P2.db
question:
<div class="question">The eccentricity of the conjugate hyperbola of the hyperbola $x^2-3 y^2=1$, is</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">$\frac{2}{\sqrt{3}}$</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">$\frac{4}{3}$</span> </li> </ul>

answer:
<div class="solution">Eccentricity of $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is $e=\sqrt{\frac{a^2+b^2}{a^2}}$<br/>Eccentricity of conjugate hyperbola,<br/>$e^{\prime}=\sqrt{\frac{a^2+b^2}{b^2}}$<br/>Write the given equation in standard form,<br/>$\begin{aligned}<br/>&amp; \frac{x^2}{1}-\frac{y^2}{1 / 3}=1 \Rightarrow a^2=1, b^2=\frac{1}{3} \\<br/>&amp; \quad e^{\prime}=\sqrt{\frac{1+1 / 3}{1 / 3}}=\sqrt{4}=2 .<br/>\end{aligned}$</div>


title: the-eccentricity-of-the-hyperbola-16-x-2-9-y-2-1-is
slug: the-eccentricity-of-the-hyperbola-16-x-2-9-y-2-1-is-74230
question: <div class="question">The eccentricity of the hyperbola $16 x^{2}-9 y^{2}=1$ is</div>
tags: ['Mathematics', 'Hyperbola', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{3}{5}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{5}{3}$</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">$\frac{4}{5}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{5}{4}$</span> </li> </ul>

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

answer:
<div class="solution">$\mathrm{r}+\mathrm{s}=\frac{13}{5}+\frac{37}{5}=\frac{50}{5}=10$ unit<br/>$\because 16 \mathrm{x}^{2}-9 \mathrm{y}^{2}=1$<br/>or $\frac{x^{2}}{\left(\frac{1}{4}\right)^{2}}-\frac{y^{2}}{\left(\frac{1}{3}\right)^{2}}=1$<br/>Comparing with $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$<br/>$\therefore \mathrm{a}^{2}=\frac{1}{16}$<br/>$\&amp; b^{2}=\frac{1}{9}$<br/>$\because \mathrm{e}=\sqrt{1+\frac{\mathrm{b}^{2}}{\mathrm{a}^{2}}}$<br/>$\therefore \mathrm{e}=\sqrt{1+\frac{1 / 9}{1 / 16}}$<br/>$\Rightarrow \mathrm{e}=\frac{5}{3}$</div>


tags: ['Mathematics', 'Hyperbola', 'JEE Main', 'JEE Main 2016 (03 Apr)']
source_db: MarksBatch2_P2.db
title:
the-eccentricity-of-the-hyperbola-whose-length-of-its-conjugate-axis-is-equal-to-half-of-the-distance-between-its-foci-is

slug:
the-eccentricity-of-the-hyperbola-whose-length-of-its-conjugate-axis-is-equal-to-half-of-the-distance-between-its-foci-is-18953

question:
<div class="question">The eccentricity of the hyperbola whose length of its conjugate axis is equal to half of the distance between its foci, is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math><mfrac><mrow><mn>2</mn></mrow><mrow><msqrt><mn>3</mn></msqrt></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">B</span> <span class="option-data"><math><msqrt><mn>3</mn></msqrt></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mfrac><mrow><mn>4</mn></mrow><mrow><msqrt><mn>3</mn></msqrt></mrow></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mfrac><mrow><mn>2</mn></mrow><mrow><msqrt><mn>3</mn></msqrt></mrow></mfrac></math></span> </div>

answer:
<div class="solution"><p>For any standard hyperbola we know that</p><p>eccentricity, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><msqrt><mn>1</mn><mo>+</mo><mfrac><msup><mi>b</mi><mn>2</mn></msup><msup><mi>a</mi><mn>2</mn></msup></mfrac></msqrt></math>, conjugate axis <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mi>b</mi></math> and distance between the foci <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mi>a</mi><mi>e</mi></math>.</p><p>Given,  <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>b</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced><mrow><mn>2</mn><mi>a</mi><mi>e</mi></mrow></mfenced></math>. </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>b</mi><mi>a</mi></mfrac><mo>=</mo><mfrac><mi>e</mi><mn>2</mn></mfrac></math></p><p>Now, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi> </mi><msqrt><mn>1</mn><mo>+</mo><mfrac><msup><mi>b</mi><mn>2</mn></msup><msup><mi>a</mi><mn>2</mn></msup></mfrac></msqrt><mo>=</mo><mi> </mi><msqrt><mn>1</mn><mo>+</mo><mfrac><msup><mi>e</mi><mn>2</mn></msup><mn>4</mn></mfrac></msqrt></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mo> </mo><msup><mi>e</mi><mn>2</mn></msup><mo>=</mo><mn>1</mn><mo>+</mo><mfrac><msup><mi>e</mi><mn>2</mn></msup><mn>4</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mo> </mo><mfrac><mn>3</mn><mn>4</mn></mfrac><msup><mi>e</mi><mn>2</mn></msup><mo>=</mo><mn>1</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mo> </mo><msup><mi>e</mi><mn>2</mn></msup><mo>=</mo><mfrac><mn>4</mn><mn>3</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mo> </mo><mi>e</mi><mo>=</mo><mfrac><mn>2</mn><msqrt><mn>3</mn></msqrt></mfrac></math></p></div>


tags: ['Biology', 'Microbes in Human Welfare', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-effluent-from-the-treatment-plant-is-generally-released-into-natural-water-bodies-like-rivers-and-streams

slug:
the-effluent-from-the-treatment-plant-is-generally-released-into-natural-water-bodies-like-rivers-and-streams-99693

question:
<div class="question">The effluent from the ______ treatment plant is generally released into natural water bodies like rivers and streams.</div>

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

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

answer:
<div class="solution">The primary effluent is passed to the aeration tanks in the secondary treatment where the aerobic microbes grow and form flocs. These microbes help in consuming the organic matter and in doing so reduce the BOD of the effluent significantly. <br/><br/>After reducing the BOD, the effluent is passed in to settling tanks where the settled flocs formed the activated sludge. Some part of it is used as inoculum and remaining is passed into large tanks called anaerobic sludge digesters. In the digestor, produce a mixture of gases which can be used as source of energy. <br/><br/>The effluent from the secondary treatment plant is generally released into natural water bodies like rivers and streams.</div>


tags: ['Physics', 'Electromagnetic Waves', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
the-electric-field-part-of-an-electromagnetic-wave-in-a-medium-is-represented-by-beginaligned-ex0-ey25-mathrmnc1-cos-leftleft2-pi-times-106-mathrmrad--1

slug:
the-electric-field-part-of-an-electromagnetic-wave-in-a-medium-is-represented-by-beginaligned-ex0-ey25-mathrmnc1-cos-leftleft2-pi-times-106-mathrmrad-1-95993

question:
<div class="question">The electric field part of an electromagnetic wave in a medium is represented by<br/>\(\begin{aligned} &amp; E_x=0 \\ &amp; E_y=2.5 \mathrm{NC}^{-1} \cos \left[\left(2 \pi \times 10^6 \mathrm{rad} \mathrm{s}^{-1}\right) \mathrm{t}-\left(\pi \times 10^{-2} \mathrm{rad} \mathrm{m}^{-1}\right) \mathrm{x}\right] \\ &amp; E_z=0\end{aligned}\)
<br/>The wave is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">moving along $y$ direction with frequency $2 \pi \times 10^6 \mathrm{~Hz}$ and wavelength $200 \mathrm{~m}$.</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">B</span> <span class="option-data">moving along $x$ direction with frequency $10^6 \mathrm{~Hz}$ and wavelength $100 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">moving along $x$ direction with frequency $10^6 \mathrm{~Hz}$ and wavelength $200 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">moving along $-x$ direction with frequency $10^6 \mathrm{~Hz}$ and wavelength $200 \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">moving along $y$ direction with frequency $2 \pi \times 10^6 \mathrm{~Hz}$ and wavelength $200 \mathrm{~m}$.</span> </div>

answer:
<div class="solution">Comparing the given equation<br/>$$<br/>\begin{aligned}<br/>&amp; \mathrm{E}_{\mathrm{y}}=2.5 \frac{\mathrm{N}}{\mathrm{C}} \cos \left[\left(2 \pi \times 10^6 \frac{\mathrm{rad}}{\mathrm{m}}\right) \mathrm{t}\right. \\<br/>&amp;\left.-\left(\pi \times 10^{-2} \frac{\mathrm{rad}}{\mathrm{sec}}\right) \mathrm{x}\right]<br/>\end{aligned}<br/>$$<br/>With the standard equation<br/>$$<br/>\mathrm{E}_{\mathrm{y}}=\mathrm{E}_0 \cos (\omega \mathrm{t}-\mathrm{kx})<br/>$$<br/>we get<br/>$$<br/>\begin{array}{ll} <br/>&amp; \omega=2 \pi \mathrm{f}=2 \pi \times 10^6 \\<br/>\therefore &amp; \mathrm{f}=10^6 \mathrm{~Hz}<br/>\end{array}<br/>$$<br/>Moreover, we know that<br/>$$<br/>\Rightarrow \quad \begin{aligned}<br/>\frac{2 \pi}{\lambda} &amp; =\mathrm{k}=\pi \times 10^{-2} \mathrm{~m}^{-1} \\<br/>\Rightarrow \quad \lambda &amp; =200 \mathrm{~m}<br/>\end{aligned}<br/>$$<br/>Hence, the wave is moving along positive $x$-direction with frequency $10^6 \mathrm{~Hz}$ and wavelength $200 \mathrm{~m}$.</div>


