# questions

title: what-is-the-number-of-odd-integers-between-1000-and-9999-with-no-digit-repeated
slug: what-is-the-number-of-odd-integers-between-1000-and-9999-with-no-digit-repeated-61140
tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2016 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2240</span> </div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the number of odd integers between 1000 and 9999 with no digit repeated?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2100</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2120</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">2240</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">3331</span> </li> </ul>

answer:
<div class="solution">Case I When unit digit can be $1,3,5$ or 7 \&amp; digit at thousand's place can be $1,2,3,4,5,6,7$ or 8 . No. of ways digits can be filled are:<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/c5qkKC9PPSj-SsOCpV_GmJdltYiiGT97eUOI0BlHIaI.original.fullsize.png"/><br/><br/>Total no's $=7 \times 8 \times 7 \times 4=1568$.<br/>Case II When unit digit can be 9 \&amp; digit at thousand's place can be $1,2,3,4,5,6,7$ or 8 . No. of ways digits can be filled are:<img src="https://cdn-question-pool.getmarks.app/pyq/nda/G3VPf2O93RyFXtxGVDo1nTp26H0-ftaFu6grXKkYum0.original.fullsize.png"/><br/><br/>Total no's $=8 \times 8 \times 7 \times 1=448$.<br/>Case III When unit digit can be $1,3,5$ or 7 \&amp; digit at thousand's place can be $9 .$ No. of ways digits can be filled are:<img src="https://cdn-question-pool.getmarks.app/pyq/nda/HMjcnX0_cbRhSt0NPdLcuretL8EpXefisKkqCsscZD4.original.fullsize.png"/><br/><br/>Total no's $=1 \times 8 \times 7 \times 4=224$.<br/>$\therefore \quad$ Number of odd digits between 1000 \&amp; 9999 with no digit repeated $=1568+448+224$ $=2240 .$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2013 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: MarksBatch2_P4.db
title:
what-is-the-number-of-outcomes-when-a-coin-is-tossed-and-then-a-die-is-rolled-only-in-case-a-head-is-shown-on-the-coin

slug:
what-is-the-number-of-outcomes-when-a-coin-is-tossed-and-then-a-die-is-rolled-only-in-case-a-head-is-shown-on-the-coin-31940

question:
<div class="question">What is the number of outcomes when a coin is tossed and then a die is rolled only in case a head is shown on the coin?</div>

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

answer:
<div class="solution">Possible outcomes are (Head, 1), (Head, 2), (Head, 3), $($ Head, 4$),($ Head, 5$),($ Head, 6$)$, Tail</div>


tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2016 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">One</span> </div>
answer: <div class="solution">Local maxima is $[\mathrm{x}=1$ ]</div>
source_db: MarksBatch2_P4.db
title:
what-is-the-number-of-points-of-local-maxima-of-the-function-f-x-consider-the-function-f-x-x-1-2-x-1-x-2-3

slug:
what-is-the-number-of-points-of-local-maxima-of-the-function-f-x-consider-the-function-f-x-x-1-2-x-1-x-2-3-23573

question:
<div class="question">What is the number of points of local maxima of the function $\mathrm{f}(\mathrm{x}) ?$<br/>Consider the function $\mathrm{f}(\mathrm{x})=(\mathrm{x}-1)^{2}(\mathrm{x}+1)(\mathrm{x}-2)^{3}$</div>

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


tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2016 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Two</span> </div>
source_db: MarksBatch2_P4.db
title:
what-is-the-number-of-points-of-local-minima-of-the-function-f-x-consider-the-function-f-x-x-1-2-x-1-x-2-3

slug:
what-is-the-number-of-points-of-local-minima-of-the-function-f-x-consider-the-function-f-x-x-1-2-x-1-x-2-3-14693

question:
<div class="question">What is the number of points of local minima of the function $\mathrm{f}(\mathrm{x}) ?$<br/>Consider the function $\mathrm{f}(\mathrm{x})=(\mathrm{x}-1)^{2}(\mathrm{x}+1)(\mathrm{x}-2)^{3}$</div>

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

answer:
<div class="solution">$f(x)=(x-1)^{2}(x+1)(x-2)^{3}$<br/>$f^{\prime}(x)=2(x-1)(x+1)(x-2)^{3}+(x-1)^{2}(x-2)^{3}$<br/>$+(x-1)^{2}(x+1) 3(x-2)^{2}$<br/>$$<br/>\begin{aligned}(x-1)(x-2)^{2}[2(x+1)(x-2)+(x-1)(x-2)\\+3(x-1)(x+1)] \end{aligned}<br/>$$<br/>$f^{\prime}(x)=(x-1)(x-2)^{2}\left[2 x^{2}-2 x-4+x^{2}-3 x+2\right.$<br/>$\left.+3 x^{2}-3\right]$<br/>$=(x-1)(x-2)^{2}\left[6 x^{2}-5 x-5\right]$<br/>For maxima and minima $f^{\prime}(x)=0$<br/>$(x-1)(x-2)^{2}\left[6 x^{2}-5 x-5\right]=0$<br/>$x=1,2,2, \frac{5 \pm \sqrt{145}}{12}$ The change in signs of $\mathrm{f}^{\prime}(\mathrm{x})$ for<br/>diffrent values of $x$ is shown:<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/JRxsQ0D4KSNBmHICpz5GiHW7JstNSI6cUJTg_md8p5o.original.fullsize.png"/><br/><br/>$\therefore$ Local Minima are<br/>$x=\frac{5-\sqrt{145}}{12} \&amp; x=\frac{5+\sqrt{145}}{12}$</div>


title: what-is-the-number-of-primary-amine-molecules-among-the-following-compounds
slug: what-is-the-number-of-primary-amine-molecules-among-the-following-compounds-12108
tags: ['Chemistry', 'General Organic Chemistry', 'MHT CET', 'MHT CET 2022 (07 Aug Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the number of primary amine molecules among the following compounds?<br/><img src="https://cdn-question-pool.getmarks.app/pyq/mht_cet/B6KKORLFvUY4sf9NIp6TGxrBXlNkRsj4Cljx08uzgtY.original.fullsize.png"/></div>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/mht_cet/lgfurQ8AGoZCtYc26k_PFrcic9lOOBqGOlbjjcoEnys.original.fullsize.png"/><br/>primary alcohol group $=1$<br/>secondary alcohol group $=4$<br/>Ans. 1, 4</div>


title: what-is-the-number-of-primary-and-secondary-alcoholic-groups-respectively-present-in-glucose
slug: what-is-the-number-of-primary-and-secondary-alcoholic-groups-respectively-present-in-glucose-65568
tags: ['Chemistry', 'Biomolecules', 'MHT CET', 'MHT CET 2022 (07 Aug Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1,4</span> </div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the number of primary and secondary alcoholic groups respectively present in glucose?</div>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/mht_cet/2a3MoM_Zze9nansfZX1OPDVm6lwiRzeb8okOQ0AZdjE.original.fullsize.png"/></div>


title: what-is-the-number-of-proper-subsets-of-a-given-finite-set-with-n-elements
slug: what-is-the-number-of-proper-subsets-of-a-given-finite-set-with-n-elements-84280
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the number of proper subsets of a given finite set with $n$ elements?</div>

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

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

answer:
<div class="solution">We know that Total number of proper subsets of finite set with $n$ elements is $2^{n}-1$</div>


title: what-is-the-number-of-real-solutions-of-x-2-x-6-x-2
slug: what-is-the-number-of-real-solutions-of-x-2-x-6-x-2-73910
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2006 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the number of real solutions of <br/>$\left|x^{2}-x-6\right|=x+2 ?$</div>

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

answer:
<div class="solution">Theequation is $\left|x^{2}-x-6\right|=x+2$ for $x \geq 0$<br/>$x^{2}-x-6=x+2$<br/>$\Rightarrow x^{2}-2 x-8=0$<br/>$\Rightarrow(x-4)(x+2)=0$<br/>$\Rightarrow \mathrm{x}=4,-2$<br/>and for $x   &lt; 0$ $-x^{2}+x+6=x+2$<br/>$\Rightarrow x^{2}=4 \Rightarrow x=\pm 2$<br/>Thus, the number of real solutionsare, $-2,2$ and $4 .$<br/>So, numbers of real solution of the equation $\left|x^{2}-x-6\right|=x+2$ are 3</div>


tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2010 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">63</span> </div>
source_db: MarksBatch2_P4.db
title:
what-is-the-number-of-signals-that-can-be-sent-by-6-flags-of-different-colours-taking-one-or-more-at-a-time

slug:
what-is-the-number-of-signals-that-can-be-sent-by-6-flags-of-different-colours-taking-one-or-more-at-a-time-30061

question:
<div class="question">What is the number of signals that can be sent by 6 flags of different colours taking one or more at a time?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">21</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">63</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">720</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1956</span> </li> </ul>

answer:
<div class="solution">Required number of ways<br/>${ }^{6} C_{0}+6_{C_{1}}+6_{C_{2}}+\ldots . .+{ }^{6} C_{6}-1=2^{6}-1=64-1=63$</div>


title: what-is-the-number-of-terms-in-the-expansion-of-2-x-3-y-2-2-x-3-y-2-2
slug: what-is-the-number-of-terms-in-the-expansion-of-2-x-3-y-2-2-x-3-y-2-2-85006
tags: ['Mathematics', 'Binomial Theorem', 'NDA', 'NDA 2019 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the number of terms in the expansion of $\left[(2 \mathrm{x}-3 \mathrm{y})^{2}\right.$ $\left.(2 \mathrm{x}+3 \mathrm{y})^{2}\right]^{2} ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">4</span> </li><li class="correct"> <span class="option-label">B</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><li class=""> <span class="option-label">C</span> <span class="option-data">8</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">16</span> </li> </ul>

answer:
<div class="solution">$\left[(2 x-3 y)^{2}(2 x+3 y)^{2}\right]^{2}$<br/>$=\left[\left(4 x^{2}-9 y^{2}\right)^{2}\right]^{2}=\left(4 x^{2}-9 y^{2}\right)^{4}$<br/>$\therefore$ Number of terms $=4+1=5$</div>


title: what-is-the-number-of-terms-in-the-expansion-of-a-b-c-n-n-n
slug: what-is-the-number-of-terms-in-the-expansion-of-a-b-c-n-n-n-54006
tags: ['Mathematics', 'Binomial Theorem', 'NDA', 'NDA 2010 (Phase 2)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the number of terms in the expansion of $(a+b+c)^{n}$, $n \in N$?</div>

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

answer:
<div class="solution">Required number of terms in $(a+b+c)^{\mathrm{n}}$<br/>$={ }^{n+2} \mathrm{C}_{2} \frac{(n+2) !}{2 ! n !}=\frac{(n+1)(n+2)}{2}$</div>


tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2010 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">108</span> </div>
source_db: MarksBatch2_P4.db
title:
what-is-the-number-of-threedigit-odd-numbers-formed-by-using-the-digits-1-2-3-4-5-6-if-repetition-of-digits-is-allowed

slug:
what-is-the-number-of-threedigit-odd-numbers-formed-by-using-the-digits-1-2-3-4-5-6-if-repetition-of-digits-is-allowed-27706

question:
<div class="question">What is the number of three-digit odd numbers formed by using the digits $1,2,3,4,5,6$ if repetition of digits is allowed?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">60</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">120</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">216</span> </li> </ul>

answer:
<div class="solution">Total no. of digits $=6$ To form a odd numbers we have only 3 choice for the unit digits. Now, Extreme left place can be filled in 6 ways the middle place can be filled in 6 ways. $\therefore$ Required number of numbers $=6 \times 6 \times 3=108$</div>


tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2018 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">185</span> </div>
source_db: MarksBatch2_P4.db
title:
what-is-the-number-of-triangles-that-can-be-formed-by-choosing-the-vertices-from-a-set-of-12-points-in-a-plane-seven-of-which-lie-on-the-same-straight

slug:
what-is-the-number-of-triangles-that-can-be-formed-by-choosing-the-vertices-from-a-set-of-12-points-in-a-plane-seven-of-which-lie-on-the-same-straight-65565

question:
<div class="question">What is the number of triangles that can be formed by choosing the vertices from a set of 12 points in a plane, seven of which lie on the same straight line?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">185</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">175</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">115</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">105</span> </li> </ul>

answer:
<div class="solution">To form a triangle, we need 3 points. 12 points are given.<br/>So, ${ }^{12} \mathrm{C}_{3}$ triangles can be formed. But, given that 7 points are on a straight line. selecting 3 points from this set will not form a triangle.<br/>So, number of triangles formed ${ }^{12} \mathrm{C}_{3}-{ }^{7} \mathrm{C}_{3}$<br/>$=\frac{12 !}{3 ! 9 !}-\frac{7 !}{3 ! 4 !}$<br/>$=\frac{12 \times 11 \times 10}{3 \times 2 \times 1}-\frac{7 \times 6 \times 5}{3 \times 2 \times 1}=220-35=185$</div>


title: what-is-the-number-of-vectors-of-length-5-unit-perpendicular-to-the-vectors-a-1-1-0-and-b-0-1-1
tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2008 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P4.db
slug:
what-is-the-number-of-vectors-of-length-5-unit-perpendicular-to-the-vectors-a-1-1-0-and-b-0-1-1-13426

question:
<div class="question">What is the number of vectors of length 5 unit perpendicular<br/>to the vectors $\vec{a}=(1,1,0)$ and $\vec{b}=(0,1,1) ?$</div>

answer:
<div class="solution">As given, vectors are: $\overrightarrow{\mathrm{a}}=\widehat{\mathrm{i}}+\overline{\mathrm{j}}$ and $\widehat{\mathrm{b}}=\widehat{\mathrm{j}}+\widehat{\mathrm{k}}$<br/>So, $\vec{a} \times \vec{b}$ is perpendicular to $\vec{a}$ and $\vec{b}$<br/>$\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}=\left|\begin{array}{ccc}\mathrm{i} &amp; \hat{\mathrm{j}} &amp; \hat{\mathrm{k}} \\ 1 &amp; 1 &amp; 0 \\ 0 &amp; 1 &amp; 1\end{array}\right|$<br/>$=\widehat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}$<br/>and $|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|=\sqrt{1+1+1}=\sqrt{3}$<br/>Unit vector perpendicular to $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$<br/>$=\pm \frac{(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}})}{|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|}=\pm \frac{\widehat{\mathrm{i}}-\widehat{\mathrm{j}}+\widehat{\mathrm{k}}}{\sqrt{3}}$<br/>Thus, the number of vectors perpendicular to the<br/>vectors a and $\overrightarrow{\mathrm{b}}$ is 2 . This is true for vectors of any length. So, it is true for vector of length 5 unit.</div>


tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2016 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1000</span> </div>
source_db: MarksBatch2_P4.db
title:
what-is-the-number-of-ways-in-which-3-holiday-travel-tickets-are-to-be-given-to-10-employees-of-an-organization-if-each-employee-is-eligible-for-any-o

slug:
what-is-the-number-of-ways-in-which-3-holiday-travel-tickets-are-to-be-given-to-10-employees-of-an-organization-if-each-employee-is-eligible-for-any-o-19309

question:
<div class="question">What is the number of ways in which 3 holiday travel tickets are to be given to 10 employees of an organization, if each employee is eligible for any one or more of the tickets?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">60</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">120</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">500</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">1000</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">No. of ways in which 3 holiday travel tickets are to be given to 10 employees $=10^{3}=1000$</div>


title: what-is-the-number-of-ways-in-which-one-can-post-5-letters-in-7-letters-boxes
slug: what-is-the-number-of-ways-in-which-one-can-post-5-letters-in-7-letters-boxes-99609
tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the number of ways in which one can post 5 letters in 7 letters boxes?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$7^{5}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3^{5}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$5^{7}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">2520</span> </li> </ul>

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

answer:
<div class="solution">First letter can be put any 7 letters boxes $=7$ ways Similarly, 2nd, $3 \mathrm{rd}, 4$ th and 5 th letters be put in 7 ways each, respectively $\therefore 7 \times 7 \times 7 \times 7 \times 7=7^{5}$</div>


tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2010 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">40</span> </div>
source_db: MarksBatch2_P4.db
title:
what-is-the-number-of-ways-of-arranging-the-letters-of-the-word-banana-so-that-no-two-ns-appear-together

slug:
what-is-the-number-of-ways-of-arranging-the-letters-of-the-word-banana-so-that-no-two-ns-appear-together-82301

question:
<div class="question">What is the number of ways of arranging the letters of the word 'BANANA' so that no two N's appear together?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">40</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">60</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">80</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">100</span> </li> </ul>

answer:
<div class="solution">Total no. of letters in BANANA=6 No. of repeated letter $\mathrm{N}=2$ No. of repeated letter $\mathrm{A}=2$ Therefore Number of ways that can be formed by using the words<br/>'BANANA' $=\frac{6 !}{3 ! 2 !}=\frac{6 \times 5 \times 4 \times 3 !}{3 ! \times 2 !}=60$<br/>Number of ways in which two $\mathrm{N}$ comes together<br/>$=\frac{5 !}{3 !}=20$<br/>$\therefore$ Required number of ways $=60-20=40$</div>


title: what-is-the-number-of-ways-that-4-boys-and-3-girls-can-be-seated-so-that-boys-and-girls-alternate
tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2012 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">144</span> </div>
answer: <div class="solution">BG BG B G B Required no. of ways $=4 ! \times 3 !=144$</div>
source_db: MarksBatch2_P4.db
slug:
what-is-the-number-of-ways-that-4-boys-and-3-girls-can-be-seated-so-that-boys-and-girls-alternate-32941

question:
<div class="question">What is the number of ways that 4 boys and 3 girls can be seated so that boys and girls alternate?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">12</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">72</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">120</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">144</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>


title: what-is-the-number-of-ways-that-a-cricket-team-of-11-players-can-be-made-out-of-15-players
slug: what-is-the-number-of-ways-that-a-cricket-team-of-11-players-can-be-made-out-of-15-players-52342
tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2014 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1365</span> </div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the number of ways that a cricket team of 11 players can be made out of 15 players?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">364</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1001</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">1365</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">32760</span> </li> </ul>

answer:
<div class="solution">Number of ways that a cricket team of 11 players can<br/>be made out of 15 players $={ }^{15} \mathrm{C}_{11}=\frac{15 !}{11 ! 4 !}$<br/>$=\frac{15 \times 14 \times 13 \times 12 \times 11 !}{11 ! \times 1 \times 2 \times 3 \times 4}=1365$</div>


tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2009 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch2_P4.db
title:
what-is-the-number-of-words-formed-from-the-letters-of-the-word-joke-so-that-the-vowels-and-consonants-alternate

slug:
what-is-the-number-of-words-formed-from-the-letters-of-the-word-joke-so-that-the-vowels-and-consonants-alternate-97220

question:
<div class="question">What is the number of words formed from the letters of the word 'JOKE' so that the vowels and consonants alternate?</div>

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

answer:
<div class="solution">Total number of letters $=4$ No. of vowels $=2$ No. of consonants $-2$ Possibilities of words formed from the letters of word "JOKE" are JOKE, KOJE, KEJO, JEKO, EJOK, EKOJ, OKEJ, OJEK Thus, required number of words $=8$</div>


tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2010 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">17280</span> </div>
source_db: MarksBatch2_P4.db
title:
what-is-the-number-of-words-that-can-be-formed-from-the-letters-of-the-word-universal-the-vowels-remaining-always-together

slug:
what-is-the-number-of-words-that-can-be-formed-from-the-letters-of-the-word-universal-the-vowels-remaining-always-together-60973

question:
<div class="question">What is the number of words that can be formed from the letters of the word 'UNIVERSAL', the vowels remaining always together?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">720</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1440</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">17280</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">21540</span> </li> </ul>

answer:
<div class="solution">Consider the word UNIVERSAL Total no. of vowels $=\mathrm{U}, \mathrm{I}, \mathrm{E}, \mathrm{A}=4$<br/>Let us consider these as a single letter. UIEA N VRSL Then, total no. of letters $=6$<br/>Then, number of ways to arrange them $=6 !=720$ But vowels can also arranged in $4 !$ or 24 ways. Hence, total number of ways $=720 \times 24=17280$</div>


title: what-is-the-number-ofplanespassing-through-threenoncollinear-points
slug: what-is-the-number-ofplanespassing-through-threenoncollinear-points-60988
question: <div class="question">What is the number ofplanespassing through threenon-collinear points?</div>
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2009 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">3</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">0</span> </li> </ul>

answer:
<div class="solution">We know that the number of planes passing through the non-collinear points is 1 .</div>


title: what-is-the-only-solution-of-the-initial-value-problem-y-t-1-y-y-0-0
slug: what-is-the-only-solution-of-the-initial-value-problem-y-t-1-y-y-0-0-93206
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2007 (Phase 2)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the only solution of the initial value problem $\mathrm{y}^{\prime}=\mathrm{t}(1+\mathrm{y}), \mathrm{y}(0)=0 ?$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{y}=-1+\mathrm{e}^{\mathrm{t}^{2} / 2}$</span> </div>

answer:
<div class="solution">Given, equation is: $\mathrm{y}^{\prime}=\mathrm{t}(1+\mathrm{y})$<br/>i.e., $\frac{\mathrm{dy}}{\mathrm{dt}}=\mathrm{t}(1+\mathrm{y})$<br/>$\Rightarrow \int \frac{1}{1+y} d y=\int t d t \Rightarrow \log (1+y)=\frac{t^{2}}{2}+c$<br/>As per initial conditions $\mathrm{y}(0)=0$ when $\mathrm{t}=0, \mathrm{y}=0$<br/>$\Rightarrow \log 1=\mathrm{c} \Rightarrow \mathrm{c}=0$<br/>$\therefore \log (1+\mathrm{y})=\frac{\mathrm{t}^{2}}{2} \Rightarrow 1+\mathrm{y}=\mathrm{e}^{t^{2} / 2}$<br/>$\Rightarrow \quad y=-1+e^{t^{2} / 2}$<br/>which is required solution.</div>


title: what-is-the-order-of-the-differential-equation-d-x-d-y-2-d-x-d-y-sin-2-y-0
slug: what-is-the-order-of-the-differential-equation-d-x-d-y-2-d-x-d-y-sin-2-y-0-13111
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2013 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the order of the differential equation$\left(\frac{d y}{d x}\right)^{2}+\frac{d y}{d x}-\sin ^{2} y=0 ?$</div>

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">3</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Undefined</span> </li> </ul>

answer:
<div class="solution">Highest order derivative, present in the differential<br/>equations is $\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)$, therefore its order is one.</div>


title: what-is-the-order-of-the-differential-equation-d-x-d-y-y-d-x-d-y-1
slug: what-is-the-order-of-the-differential-equation-d-x-d-y-y-d-x-d-y-1-89963
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2008 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the order of the differential equation?<br/>$\frac{d y}{d x}+y=\frac{1}{\left(\frac{d y}{d x}\right)}$</div>

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

answer:
<div class="solution">$\frac{d y}{d x}+y=\frac{1}{\left(\frac{d y}{d x}\right)} \Rightarrow\left(\frac{d y}{d x}\right)^{2}+y\left(\frac{d y}{d x}\right)=1$<br/>Hence required order of differential equation $=1$</div>


title: what-is-the-order-of-the-differential-equation-dy-dx-ydx-x-3
slug: what-is-the-order-of-the-differential-equation-dy-dx-ydx-x-3-26052
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2016 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the order of the differential equation<br/>$\frac{\mathrm{dx}}{\mathrm{dy}}+\int \mathrm{y} \mathrm{d} \mathrm{x}=\mathrm{x}^{3} ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1</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">3</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Cannot be determined</span> </li> </ul>

answer:
<div class="solution">$\frac{d x}{d y}+\int y \cdot d x=x^{3} \Rightarrow \int y \cdot d x=x^{3}-\frac{d x}{d y}$<br/>$\Rightarrow 1+\frac{d y}{d x}\left(\int y \cdot d x\right)=x^{3} \cdot \frac{d y}{d x}$<br/>Differentiate both sides w.e.t. $x$<br/>$\Rightarrow 0+\frac{d y}{d x}(y)+\left(\int y \cdot d x\right)\left(\frac{d^{2} y}{d x^{2}}\right)=x^{3} \cdot \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}\left(2 x^{2}\right)$<br/>$\Rightarrow y \cdot \frac{d y}{d x}+\frac{d^{2} y}{d x^{2}}\left[x^{3}-\frac{d x}{d y}\right]=x^{3} \cdot \frac{d^{2} y}{d x^{2}}+2 x^{2} \frac{d y}{d x}$<br/>$\Rightarrow y \frac{d y}{d x}+x^{3} \frac{d^{2} y}{d x^{2}}-\left(\frac{d x}{d y}\right)\left(\frac{d^{2} y}{d x^{2}}\right)=x^{3} \frac{d^{2} y}{d x^{2}}+2 x^{2} \frac{d y}{d x}$<br/>$\Rightarrow y \frac{d y}{d x}-\frac{d x}{d y} \cdot \frac{d^{2} y}{d x^{2}}=2 x^{2} \cdot \frac{d y}{d x}$<br/>Multiplying both side by $\frac{d y}{d x}$<br/>$y\left(\frac{d y}{d x}\right)^{2}-\frac{d^{2} y}{d x^{2}}=2 x^{2}\left(\frac{d y}{d x}\right)^{2}$<br/>$\Rightarrow \frac{d^{2} y}{d x^{2}}+\left(2 x^{2}-y\right)\left(\frac{d y}{d x}\right)^{2}=0$<br/>Order $=2$, degree $=1$</div>


tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2018 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
answer: <div class="solution">Order $=4(\because$ No. of arbitrary constants $=4$ )</div>
source_db: MarksBatch2_P4.db
title:
what-is-the-order-of-the-differential-equation-whose-solution-is-y-a-cos-x-b-sin-x-ce-x-d-where-a-b-c-and-d-are-arbitrary-constants

slug:
what-is-the-order-of-the-differential-equation-whose-solution-is-y-a-cos-x-b-sin-x-ce-x-d-where-a-b-c-and-d-are-arbitrary-constants-91626

question:
<div class="question">What is the order of the differential equation whose solution is $\mathrm{y}=\mathrm{a} \cos \mathrm{x}+\mathrm{b} \sin \mathrm{x}+\mathrm{ce}^{-\mathrm{x}}+\mathrm{d}$, where $\mathrm{a}, \mathrm{b}, \mathrm{c}$ and<br/>$\begin{array}{lc}\text { d are arbitrary constants? } &amp; {}\end{array}$</div>


title: what-is-the-order-of-the-product-x-y-z-a-h-g-h-b-f-g-f-c-x-y-z
slug: what-is-the-order-of-the-product-x-y-z-a-h-g-h-b-f-g-f-c-x-y-z-57027
tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the order of the product<br/>$\left[\begin{array}{lll}\mathrm{x} &amp; \mathrm{y} &amp; \mathrm{z}\end{array}\right]\left[\begin{array}{lll}\mathrm{a} &amp; \mathrm{h} &amp; \mathrm{g} \\ \mathrm{h} &amp; \mathrm{b} &amp; \mathrm{f} \\ \mathrm{g} &amp; \mathrm{f} &amp; \mathrm{c}\end{array}\right]\left[\begin{array}{l}\mathrm{x} \\ \mathrm{y} \\ \mathrm{z}\end{array}\right]$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$3 \times 1$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$1 \times 1$</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">$1 \times 3$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3 \times 3$</span> </li> </ul>

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

answer:
<div class="solution">Given $\left[\begin{array}{lll}\mathrm{x} &amp; \mathrm{y} &amp; \mathrm{z}\end{array}\right]\left[\begin{array}{lll}\mathrm{a} &amp; \mathrm{h} &amp; \mathrm{g} \\ \mathrm{h} &amp; \mathrm{b} &amp; \mathrm{f} \\ \mathrm{g} &amp; \mathrm{f} &amp; \mathrm{c}\end{array}\right]\left[\begin{array}{l}\mathrm{x} \\ \mathrm{y} \\ \mathrm{z}\end{array}\right]$<br/>Consider $\left[\begin{array}{lll}x &amp; y &amp; z\end{array}\right]_{1 \times 3}\left[\begin{array}{lll}a &amp; h &amp; g \\ h &amp; b &amp; f \\ g &amp; f &amp; c\end{array}\right]_{3 \times 3}$<br/>$\Rightarrow$ order of product $=1 \times 3$<br/>Now, order of product $=1 \times 3$ and order of $\left[\begin{array}{l}\mathrm{x} \\ \mathrm{y} \\ \mathrm{z}\end{array}\right]=3 \times 1$<br/>$\therefore$ Required order $=1 \times 1$</div>


title: what-is-the-order-of-xy-z-a-h-g-h-b-f-g-f-c-x-y-z
slug: what-is-the-order-of-xy-z-a-h-g-h-b-f-g-f-c-x-y-z-84974
tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2017 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the order of <br/>$\left(\begin{array}{llll}\mathrm{x} \mathrm{y} &amp; \mathrm{z}\end{array}\right)\left[\begin{array}{lll}\mathrm{a} &amp; \mathrm{h} &amp; \mathrm{g} \\ \mathrm{h} &amp; \mathrm{b} &amp; f \\ \mathrm{~g} &amp; f &amp; \mathrm{c}\end{array}\right]\left[\begin{array}{l}\mathrm{x} \\ \mathrm{y} \\ \mathrm{z}\end{array}\right] ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$3 \times 1$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$1 \times 1$</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">$1 \times 3$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3 \times 3$</span> </li> </ul>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/hCIzaK7iKrc0bRuGGXoR3rUCWSvyr6AYwxoAIp33FR8.original.fullsize.png"/></div>


title: what-is-the-outer-boundary-structure-of-a-typical-plant-cell-1
slug: what-is-the-outer-boundary-structure-of-a-typical-plant-cell-1-83618
question: <div class="question">What is the outer boundary structure of a typical plant cell?</div>
tags: ['Biology', 'Cell - The Unit of Life', 'NEET']
answer: <div class="solution">The outer boundary of a typical plant cell is a distinct cell wall.</div>
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Cell membrane</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Cell wall</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Nucleus</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Cytoplasm</span> </li> </ul>

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


title: what-is-the-overall-change-represented-by-the-standard-electrode-potential-e-o-for-reducing-power
tags: ['Chemistry', 's Block Elements', 'NEET']
source_db: MarksBatch2_P4.db
slug:
what-is-the-overall-change-represented-by-the-standard-electrode-potential-e-o-for-reducing-power-29865

question:
<div class="question">What is the overall change represented by the standard electrode potential (E<sub>o</sub>) for reducing power?</div>

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

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

answer:
<div class="solution">The standard electrode potential (E<sub>o</sub>) for reducing power represents the overall change in the process, which includes sublimation enthalpy, ionization enthalpy, and hydration enthalpy. Among these, the hydration enthalpy plays a significant role in determining the reducing power of alkali metals.</div>


title: what-is-the-overall-development-of-an-individual-with-klinefelters-syndrome
slug: what-is-the-overall-development-of-an-individual-with-klinefelters-syndrome-69471
tags: ['Biology', 'Principles of Inheritance and Variation', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the overall development of an individual with Klinefelterâs Syndrome?</div>

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

answer:
<div class="solution">An individual with Klinefelterâs Syndrome has overall masculine development, but feminine development, such as the development of breasts (Gynaecomastia), is also expressed.</div>


title: what-is-the-perimeter-of-the-triangle-with-vertices-a-4-2-b-0-1-and-c-3-3
slug: what-is-the-perimeter-of-the-triangle-with-vertices-a-4-2-b-0-1-and-c-3-3-98022
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the perimeter of the triangle with vertices $\begin{array}{ll}\mathrm{A}(-4,2), \mathrm{B}(0,-1) \text { and } \mathrm{C}(3,3) ? &amp; {}\end{array}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$7+3 \sqrt{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$10+5 \sqrt{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$11+6 \sqrt{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$5+\sqrt{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$10+5 \sqrt{2}$</span> </div>

answer:
<div class="solution">By using Distance formula,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/OxPx8BPexx1Lbu-TCXsPLOKaxvJcbJ1WrPpsAd1p60A.original.fullsize.png"/><br/><br/>We have, $A B=\sqrt{(0+4)^{2}+(-1-2)^{2}}=\sqrt{16+9}=5$<br/>$\mathrm{BC}=\sqrt{9+16}=5$<br/>$\mathrm{CA}=\sqrt{49+(1)^{2}}=\sqrt{50}=5 \sqrt{2}$<br/>Hence, Required Perimeter $=\mathrm{AB}+\mathrm{BC}+\mathrm{CA}$ $=10+5 \sqrt{2}$</div>


title: what-is-the-period-of-the-function-mathrmfmathrmxsin-mathrmx
slug: what-is-the-period-of-the-function-mathrmfmathrmxsin-mathrmx-49100
tags: ['Mathematics', 'Trigonometric Equations', 'NDA', 'NDA 2018 (Phase 1)']
answer: <div class="solution">Period of the function, $\sin x$ is $2 \pi$.</div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the period of the function $\mathrm{f}(\mathrm{x})=\sin \mathrm{x} ?</div>

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

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


title: what-is-the-perpendicular-distance-between-the-parallel-lines-3-x-4-y-9-and-9-x-12-y-28-0
slug: what-is-the-perpendicular-distance-between-the-parallel-lines-3-x-4-y-9-and-9-x-12-y-28-0-11704
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the perpendicular distance between the parallel lines $3 \mathrm{x}+4 \mathrm{y}=9$ and $9 \mathrm{x}+12 \mathrm{y}+28=0 ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{7}{3}$ units</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{8}{3}$ units</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{10}{3}$ units</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{11}{3}$ 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">$\frac{11}{3}$ units</span> </div>

answer:
<div class="solution">The given lines are:$3 x+4 y=9$<br/>$\Rightarrow \quad y=\frac{9}{4}-\frac{3}{4} x$ ...(i)<br/>and $9 x+12 y+28=0 \Rightarrow y=\frac{-7}{3}-\frac{3 x}{4}$ ...(ii)<br/>We have,<br/>$$<br/>\mathrm{m}=\frac{-3}{4} ; \mathrm{C}_{1}=\frac{9}{4} ; \mathrm{C}_{2}=\frac{-7}{3}<br/>$$<br/>$$<br/>\text { Now, Distance }=\frac{\left|C_{1}-C_{2}\right|}{\sqrt{1+m^{2}}}=\frac{\left|\frac{9}{4}-\left(-\frac{7}{3}\right)\right|}{\sqrt{1+\frac{9}{16}}}=\frac{11}{3} \text { units }<br/>$$</div>


title: what-is-the-perpendicular-distance-of-the-point-x-y-from-x-axis
slug: what-is-the-perpendicular-distance-of-the-point-x-y-from-x-axis-98120
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2012 (Phase 1)']
answer: <div class="solution">$\mathrm{p}=\frac{|\mathrm{y}|}{\sqrt{1}}=|\mathrm{y}|$</div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the perpendicular distance of the point $(\mathrm{x}, \mathrm{y})$ from $\begin{array}{ll}\mathrm{x} \text { -axis? } &amp; {}\end{array}$</div>

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

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


title: what-is-the-positive-square-root-of-7-4-3
slug: what-is-the-positive-square-root-of-7-4-3-85321
question: <div class="question">What is the positive square root of $7+4 \sqrt{3}$ ?</div>
tags: ['Mathematics', 'Basic of Mathematics', 'NDA', 'NDA 2013 (Phase 2)']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\sqrt{3}-1$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\sqrt{3}+1$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\quad \sqrt{3}-2$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\sqrt{3}+2$</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">$\sqrt{3}+2$</span> </div>

answer:
<div class="solution">$7+4 \sqrt{3}=(\sqrt{4})^{2}+(\sqrt{3})^{2}+2 \sqrt{4} \times \sqrt{3}$<br/>$=(\sqrt{4}+\sqrt{3})^{2}$<br/>$\sqrt{7+4 \sqrt{3}}=2+\sqrt{3}$</div>


title: what-is-the-potential-assigned-to-the-standard-hydrogen-electrode-at-all-temperatures
slug: what-is-the-potential-assigned-to-the-standard-hydrogen-electrode-at-all-temperatures-17453
tags: ['Chemistry', 'Electrochemistry', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the potential assigned to the standard hydrogen electrode at all temperatures?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0.34 V</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1.10 V</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Zero potential</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1 bar</span> </li> </ul>

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

answer:
<div class="solution">The standard hydrogen electrode is assigned a zero potential at all temperatures.</div>


tags: ['Chemistry', 'General Organic Chemistry', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">neo-</span> </div>
source_db: MarksBatch2_P4.db
title:
what-is-the-prefix-used-to-indicate-a-branched-chain-alkyl-group-that-is-derived-from-a-fundamental-name

slug:
what-is-the-prefix-used-to-indicate-a-branched-chain-alkyl-group-that-is-derived-from-a-fundamental-name-21645

question:
<div class="question">What is the prefix used to indicate a branched chain alkyl group that is derived from a fundamental name?</div>

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

answer:
<div class="solution">The prefixes iso- and neo- are used to indicate branched chain alkyl groups derived from fundamental names.</div>


tags: ['Chemistry', 'Thermal Properties of Matter', 'NEET']
source_db: MarksBatch2_P4.db
title:
what-is-the-primary-advantage-of-using-the-triplepoint-of-water-as-a-standard-fixed-point-in-modern-thermometry-over-using-the-melting-point-of-ice-an

slug:
what-is-the-primary-advantage-of-using-the-triplepoint-of-water-as-a-standard-fixed-point-in-modern-thermometry-over-using-the-melting-point-of-ice-an-73631

question:
<div class="question">What is the primary advantage of using the triple-point of water as a standard fixed point in modern thermometry over using the melting point of ice and the boiling point of water, as originally done in the Celsius scale?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">The triple-point is more precise and reproducible.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The Celsius scale has been updated to use the triple-point.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The triple-point is easier to measure accurately.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">The melting point and boiling point are not well-defined.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The triple-point is more precise and reproducible.</span> </div>

answer:
<div class="solution">Correct Option is : (A)<br/>The triple-point is more precise and reproducible.</div>


title: what-is-the-primary-characteristic-feature-of-ice-and-water-in-equilibrium
slug: what-is-the-primary-characteristic-feature-of-ice-and-water-in-equilibrium-95341
tags: ['Chemistry', 'Chemical Equilibrium', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the primary characteristic feature of ice and water in equilibrium?</div>

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

answer:
<div class="solution">In equilibrium, the mass of ice and water remains constant, and the temperature remains constant.</div>


title: what-is-the-primary-function-of-secondary-valences-in-coordination-compounds
slug: what-is-the-primary-function-of-secondary-valences-in-coordination-compounds-42636
tags: ['Chemistry', 'Coordination Compounds', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the primary function of secondary valences in coordination compounds?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">To bond with neutral molecules</span> </div>

answer:
<div class="solution">The primary function of secondary valences in coordination compounds is to bond with neutral molecules.</div>


title: what-is-the-primary-oocyte-surrounded-by
slug: what-is-the-primary-oocyte-surrounded-by-88062
question: <div class="question">What is the primary oocyte surrounded by?</div>
tags: ['Biology', 'Human Reproduction', 'NEET']
answer: <div class="solution">The primary oocyte is surrounded by a layer of granulosa cells.</div>
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Secondary follicles</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">A layer of granulosa cells</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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 theca</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">The zona pellucida</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A layer of granulosa cells</span> </div>


tags: ['Chemistry', 'Amines', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Amides</span> </div>
source_db: MarksBatch2_P4.db
title:
what-is-the-primary-product-obtained-when-aliphatic-or-aromatic-primary-and-secondary-amines-react-with-acid-chlorides-anhydrides-or-esters

slug:
what-is-the-primary-product-obtained-when-aliphatic-or-aromatic-primary-and-secondary-amines-react-with-acid-chlorides-anhydrides-or-esters-57836

question:
<div class="question">What is the primary product obtained when aliphatic or aromatic primary and secondary amines react with acid chlorides, anhydrides, or esters?</div>

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

answer:
<div class="solution">The reaction of amines with acid chlorides, anhydrides, or esters results in the formation of amides.</div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Alkene</span> </div>
source_db: MarksBatch2_P4.db
title:
what-is-the-primary-product-of-dehydrogenation-when-a-secondary-alcohol-is-passed-over-heated-copper

slug:
what-is-the-primary-product-of-dehydrogenation-when-a-secondary-alcohol-is-passed-over-heated-copper-18217

question:
<div class="question">What is the primary product of dehydrogenation when a secondary alcohol is passed over heated copper?</div>

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

answer:
<div class="solution">The primary product of dehydrogenation of a secondary alcohol is an alkene.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'NEET']
source_db: MarksBatch2_P4.db
title:
what-is-the-primary-purpose-of-defining-a-boundary-between-the-system-and-the-surroundings-in-thermodynamics

slug:
what-is-the-primary-purpose-of-defining-a-boundary-between-the-system-and-the-surroundings-in-thermodynamics-97438

question:
<div class="question">What is the primary purpose of defining a boundary between the system and the surroundings in thermodynamics?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">To isolate the system from the surroundings</span> </div>

answer:
<div class="solution">Defining a boundary allows for the isolation of the system from the surroundings, as mentioned in the paragraph.</div>


title: what-is-the-primary-reason-for-the-difficulty-in-separating-zr-and-hf-in-nature
slug: what-is-the-primary-reason-for-the-difficulty-in-separating-zr-and-hf-in-nature-14248
tags: ['Chemistry', 'd and f Block Elements', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the primary reason for the difficulty in separating Zr and Hf in nature?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Their almost identical radii</span> </div>

answer:
<div class="solution">The almost identical radii of Zr (160 pm) and Hf (159 pm), a consequence of the lanthanoid contraction, account for their occurrence together in nature and for the difficulty faced in their separation</div>


title: what-is-the-primary-standard-used-in-volumetric-analysis
slug: what-is-the-primary-standard-used-in-volumetric-analysis-34883
question: <div class="question">What is the primary standard used in volumetric analysis?</div>
tags: ['Chemistry', 'd and f Block Elements', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Sodium chromate</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Sodium dichromate</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Potassium dichromate</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Chromite ore</span> </li> </ul>

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

answer:
<div class="solution">Potassium dichromate is used as a primary standard in volumetric analysis.</div>


title: what-is-the-principal-argument-of-1-i-where-i-1
slug: what-is-the-principal-argument-of-1-i-where-i-1-88196
tags: ['Mathematics', 'Complex Number', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the principal argument of $(-1-\mathrm{i})$, where $\mathrm{i}=\sqrt{-1}$ ?</div>

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

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

answer:
<div class="solution">$\mathrm{z}=\mathrm{x}+\mathrm{iy}=(-1-\mathrm{i})$<br/>$\therefore \mathrm{x}=-1, \mathrm{y}=-1$<br/>This lies in $3^{\text {rd }}$ Quadrant. $\therefore \arg (\mathrm{z})=\theta-\pi$<br/>$=\tan ^{-1}\left(\frac{\mathrm{y}}{\mathrm{x}}\right)-\pi$<br/>$=\tan ^{-1}\left(\frac{-1}{-1}\right)-\pi$<br/>$=\tan ^{-1}(1)-\pi$<br/>$=\frac{\pi}{4}-\pi$<br/>$=\frac{-3 \pi}{4}$</div>


title: what-is-the-principal-value-of-sec-1-3-2
slug: what-is-the-principal-value-of-sec-1-3-2-54585
tags: ['Mathematics', 'Inverse Trigonometric Functions', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the principal value of $\sec ^{-1}\left(\frac{2}{\sqrt{3}}\right) ?$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\pi}{6}$</span> </div>

answer:
<div class="solution">Let $\sec ^{-1}\left(\frac{2}{\sqrt{3}}\right)=y$ where $0   &lt; \mathrm{y} \leq \frac{\pi}{2}$<br/>$\Rightarrow$ sec $y=\frac{2}{\sqrt{3}}$<br/>$\Rightarrow \sec y=\sec \frac{\pi}{6} \Rightarrow y=\frac{\pi}{6}$<br/>The principal value of $\sec ^{-1}\left(\frac{2}{\sqrt{3}}\right)=\frac{\pi}{6}$</div>


title: what-is-the-principal-value-of-sin-1-sin-3-2
slug: what-is-the-principal-value-of-sin-1-sin-3-2-85595
tags: ['Mathematics', 'Inverse Trigonometric Functions', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the principal value of $\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)$?</div>

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

answer:
<div class="solution">$\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)=\sin ^{-1}\left(\sin \left(\pi-\frac{\pi}{3}\right)\right)$<br/>$=\sin ^{-1}\left(\sin \frac{\pi}{3}\right)=\frac{\pi}{3}$.</div>


title: what-is-the-principle-value-of-cosec-1-2
slug: what-is-the-principle-value-of-cosec-1-2-37057
question: <div class="question">What is the principle value of $\operatorname{cosec}^{-1}(-\sqrt{2}) ?$</div>
tags: ['Mathematics', 'Inverse Trigonometric Functions', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\pi}{4}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\pi}{2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$-\frac{\pi}{4}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">0</span> </li> </ul>

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

answer:
<div class="solution">Let the principal value of $\operatorname{cosec}^{-1}(-\sqrt{2})=\theta$<br/>$\Rightarrow-\sqrt{2}=\operatorname{cosec} \theta \Rightarrow-\sqrt{2}=\frac{1}{\sin \theta}$<br/>$\Rightarrow \quad \sin \theta=-\frac{1}{\sqrt{2}} \Rightarrow \theta=-\frac{\pi}{4}$<br/>Principal value of $\operatorname{cosec}^{-1}(-\sqrt{2})=-\frac{\pi}{4}$</div>


title: what-is-the-probability-of-5-sundays-in-the-month-of-december
slug: what-is-the-probability-of-5-sundays-in-the-month-of-december-32431
question: <div class="question">What is the probability of 5 Sundays in the month of December?</div>
tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{7}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{2}{7}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{3}{7}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{3}{7}$</span> </div>

answer:
<div class="solution">In month of December 31 days i.e. $(28+3)$ days. In 28 days will get 4 Sundays. If we get any Sunday in first 3 days of December than only we can get 5 Sundays in month. $n(5$ th Sunday $)=3 \quad[4$ weeks $+3$ days $]$ $n(5)=7$<br/>Hence prob. of 5 Sundays in month of December $=\frac{3}{7}$.</div>


title: what-is-the-probability-of-getting-a-sum-of-7-with-two-dice
slug: what-is-the-probability-of-getting-a-sum-of-7-with-two-dice-47453
question: <div class="question">What is the probability of getting a sum of 7 with two dice?</div>
tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{1}{6}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{3}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{12}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{5}{36}$</span> </li> </ul>

answer:
<div class="solution">Total case $=6 \times 6=36$ Favourable $=(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)$<br/>Probability $=\frac{6}{36}=\frac{1}{6}$</div>


title: what-is-the-probability-of-getting-five-heads-and-seven-tails-in-12-flips-of-a-balanced-coin
slug: what-is-the-probability-of-getting-five-heads-and-seven-tails-in-12-flips-of-a-balanced-coin-54546
tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2007 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the probability of getting five heads and seven tails in 12 flips of a balanced coin?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{C}(12,5) /\left(2^{5}\right)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{C}(12,5) /\left(2^{7}\right)$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{C}(12,5) /\left(2^{12}\right)$</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">$\mathrm{C}(12,7) /\left(2^{6}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{C}(12,5) /\left(2^{12}\right)$</span> </div>

answer:
<div class="solution">Number of ways of selecting 5 heads cut of total 12<br/>flips = $12_{\mathrm{C}_{5}}$<br/>Probability of getting one head in a coin $=\frac{1}{2}$<br/>Also, probability of getting one tail in a coin $=\frac{1}{2}$<br/>Probability of getting 5 head $=\left(\frac{1}{2}\right)^{5}$<br/>Probability of getting 7 tails $=\left(\frac{1}{2}\right)^{7}$<br/>So, required probability<br/>$=12_{\mathrm{C}_{5}}\left(\frac{1}{2}\right)^{5}\left(\frac{1}{2}\right)^{7}=12_{\mathrm{C}_{5}}\left(\frac{1}{2}\right)^{12}=\frac{12_{\mathrm{C}_{5}}}{2^{12}}$</div>


title: what-is-the-probability-of-having-53-sundays-or-53-mondays-in-a-leap-year-1
slug: what-is-the-probability-of-having-53-sundays-or-53-mondays-in-a-leap-year-1-39727
tags: ['Mathematics', 'Probability', 'JEE Main']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the probability of having 53 Sundays or 53 Mondays in a leap year?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 / 7$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$3 / 7$</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">4/7</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$5 / 7$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3 / 7$</span> </div>

answer:
<div class="solution">A leap year has 366 days, in which 2 days may be any one of the following pairs. (Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday), (Thursday, Friday) (Friday, Saturday) (Saturday, Sunday).<br/>$\therefore \quad$ Required probability $=\frac{2}{7}+\frac{2}{7}-\frac{1}{7}=\frac{3}{7}$<br/>(By using $\mathrm{P}(\mathrm{A} \cup \mathrm{B})=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2006 (Phase 2)']
source_db: MarksBatch2_P4.db
title:
what-is-the-probability-of-having-a-knave-and-a-queen-when-two-cards-are-drawn-from-a-pack-of-52-cards

slug:
what-is-the-probability-of-having-a-knave-and-a-queen-when-two-cards-are-drawn-from-a-pack-of-52-cards-96606

question:
<div class="question">What is the probability of having a knave and a queen when two cards are drawn from a pack of 52 cards?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{16}{663}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{2}{663}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{4}{663}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$\frac{8}{663}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{4}{663}$</span> </div>

answer:
<div class="solution">Required probability $=\frac{4}{52} \times \frac{4}{51}$<br/>[Since, card is not replaced after first draw]<br/>$=\frac{4}{13 \times 51}=\frac{4}{663}$</div>


title: what-is-the-probability-of-two-persons-being-born-on-the-same-day-ignoring-date
slug: what-is-the-probability-of-two-persons-being-born-on-the-same-day-ignoring-date-73008
tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the probability of two persons being born on the same day (ignoring date)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 / 49$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$1 / 365$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$1 / 7$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 / 7$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1 / 365$</span> </div>

answer:
<div class="solution">Required probability $=\frac{365}{365} \times \frac{1}{365}=\frac{1}{365}$</div>


title: what-is-the-probability-that-a-leap-year-selected-at-random-contains-53-mondays
slug: what-is-the-probability-that-a-leap-year-selected-at-random-contains-53-mondays-92851
tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the probability that a leap year selected at random contains 53 Mondays?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{7}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{2}{7}$</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">$\frac{7}{366}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{26}{183}$</span> </li> </ul>

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

answer:
<div class="solution">No. of days in leap year $=366$ No. of complete week $=52$<br/>$(\because 366 \div 7$ gives 2 as remainder $)$<br/>$\therefore \quad$ No. of days left $=2$<br/>Required probability $=\frac{2}{7}$</div>


title: what-is-the-probability-that-a-leap-year-selected-at-random-will-contain-53-mondays
slug: what-is-the-probability-that-a-leap-year-selected-at-random-will-contain-53-mondays-34703
tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the probability that a leap year selected at random will contain 53 Mondays?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 / 5$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$2 / 7$</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">$1 / 7$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$5 / 7$</span> </li> </ul>

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

answer:
<div class="solution">Total no. of days in leap year $=366$ Favourable cases $=2$<br/>Required prob $=\frac{2}{7}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P4.db
title:
what-is-the-probability-that-an-interior-point-in-a-circle-is-closer-to-the-centre-than-to-the-circumference

slug:
what-is-the-probability-that-an-interior-point-in-a-circle-is-closer-to-the-centre-than-to-the-circumference-78328

question:
<div class="question">What is the probability that an interior point in a circle is closer to the centre than to the circumference?</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">$\frac{3}{4}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">It cannot be determined</span> </li> </ul>

answer:
<div class="solution">Ifr is the radius of circle, $A=\pi r^{2}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/ov9etlzOYGeWrL56uQQ9x281vu0bRIJdoRG6UkQbK-o.original.fullsize.png"/><br/><br/>Probability $=\frac{\pi\left(\frac{r}{2}\right)^{2}}{\pi r^{2}}=\frac{\pi r^{2}}{4} \times \frac{1}{\pi r^{2}}=\frac{1}{4}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P4.db
title:
what-is-the-probability-that-at-least-two-persons-out-of-a-group-of-three-persons-were-born-in-the-same-month-disregard-year

slug:
what-is-the-probability-that-at-least-two-persons-out-of-a-group-of-three-persons-were-born-in-the-same-month-disregard-year-39683

question:
<div class="question">What is the probability that at least two persons out of a group of three persons were born in the same month (disregard year)?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{33}{144}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{17}{72}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{144}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{2}{9}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{17}{72}$</span> </div>

answer:
<div class="solution">Probability that no one born in the same month $=\frac{12 \times 11 \times 10}{12 \times 12 \times 12}$<br/>Probability that atleast two are born in same month<br/>$=1-\frac{12 \times 11 \times 10}{12 \times 12 \times 12}$<br/>$=\frac{144-110}{144}=\frac{17}{72}$</div>


title: what-is-the-probability-that-in-a-family-of-4-children-there-will-be-at-least-one-boy
slug: what-is-the-probability-that-in-a-family-of-4-children-there-will-be-at-least-one-boy-33738
tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2008 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the probability that in a family of 4 children there will be at least one boy?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{15}{16}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$\frac{3}{8}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{16}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{7}{8}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{15}{16}$</span> </div>

answer:
<div class="solution">Total possibility of 4 children, either girl or boy is $2^{4}$ $=16$. Out of these there is one possibility in which there will be no boy and only girls. So, total possibility of at least one boy is $16-1=15$<br/>$\Rightarrow \quad \mathrm{P}($ at least one boy $)=\frac{15}{16}$.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch2_P4.db
title:
what-is-the-probability-that-the-sum-of-any-two-different-single-digit-natural-numbers-is-a-prime-number

slug:
what-is-the-probability-that-the-sum-of-any-two-different-single-digit-natural-numbers-is-a-prime-number-65918

question:
<div class="question">What is the probability that the sum of any two different single digit natural numbers is a prime number?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{5}{27}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{7}{18}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{3}$</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">$\frac{7}{18}$</span> </div>

answer:
<div class="solution">Total no. of two different single digit natural number $={ }^{9} \mathrm{C}_{2}=36$<br/>The number of prime number which is sum of two different single digit number. $(3,5,7,11,13 \&amp; 17)=14$<br/>$\therefore$ Required probability $=\frac{14}{36}=\frac{7}{18}$</div>


title: what-is-the-process-by-which-the-secondary-oocyte-ovum-is-released-from-the-ovary
slug: what-is-the-process-by-which-the-secondary-oocyte-ovum-is-released-from-the-ovary-72316
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the process by which the secondary oocyte (ovum) is released from the ovary?</div>

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

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

answer:
<div class="solution">The Graafian follicle ruptures to release the secondary oocyte (ovum) from the ovary through the process called ovulation.</div>


title: what-is-the-process-of-releasing-the-secondary-oocyte-from-the-ovary-called
slug: what-is-the-process-of-releasing-the-secondary-oocyte-from-the-ovary-called-66846
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the process of releasing the secondary oocyte from the ovary called?</div>

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

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

answer:
<div class="solution">The Graafian follicle ruptures to release the secondary oocyte (ovum) from the ovary by the process called ovulation.</div>


title: what-is-the-process-that-allows-a-secondary-cell-to-be-reused-after-use
slug: what-is-the-process-that-allows-a-secondary-cell-to-be-reused-after-use-14068
tags: ['Chemistry', 'Electrochemistry', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the process that allows a secondary cell to be reused after use?</div>

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

answer:
<div class="solution">A secondary cell can be recharged by passing current through it in the opposite direction so that it can be used again.</div>


tags: ['Chemistry', 'Amines', 'NEET']
source_db: MarksBatch2_P4.db
title:
what-is-the-product-formed-when-an-amide-containing-three-carbons-undergoes-hoffmann-bromamide-degradation

slug:
what-is-the-product-formed-when-an-amide-containing-three-carbons-undergoes-hoffmann-bromamide-degradation-38403

question:
<div class="question">What is the product formed when an amide containing three carbons undergoes Hoffmann bromamide degradation?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A primary amine with two carbons</span> </div>

answer:
<div class="solution">In the Hoffmann bromamide degradation, the amine formed contains one carbon less than the amide. So, if the amide has three carbons, the resulting amine will have two carbons.</div>


title: what-is-the-product-obtained-when-nitrile-is-reduced-with-lithium-aluminum-hydride-lialh-4
slug: what-is-the-product-obtained-when-nitrile-is-reduced-with-lithium-aluminum-hydride-lialh-4-96328
tags: ['Chemistry', 'Amines', 'NEET']
answer: <div class="solution">Nitriles, when reduced with LiAlH<sub>4</sub>, produce primary amines.</div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the product obtained when nitrile is reduced with lithium aluminum hydride (LiAlH<sub>4</sub>)?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Secondary amine</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Tertiary amine</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Primary 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">Quaternary ammonium salt</span> </li> </ul>

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


title: what-is-the-product-of-first-2-n-1-terms-of-a-geometric-progression
slug: what-is-the-product-of-first-2-n-1-terms-of-a-geometric-progression-44227
tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the product of first $2 \mathrm{n}+1$ terms of a geometric progression?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The $(2 \mathrm{n}+1)$ th power of the $(\mathrm{n}+1)$ th term of the GP</span> </div>

answer:
<div class="solution">The GP is a, ar, ar $^{2}, \ldots \ldots .$ ar $^{2 \mathrm{n}}$ So, $\mathrm{P}=\mathrm{a}$. ar $\cdot \mathrm{ar}^{2} \cdot \mathrm{ar}^{3} \ldots \ldots \ldots \ldots \mathrm{ar}^{2 n}$<br/>$=a^{2 n+1}, r^{1+2+\ldots}+2 n$<br/>$=a^{(2 n+1)}_{r} \frac{2 n(2 n+1)}{2}=a^{2 n+1} r^{n(2 n+1)}=\left(a r^{n}\right)^{(2 n+1)}$<br/>$=(2 n+1)$ th power of the $(\mathrm{n}+1)$ th term of $\mathrm{GP}$.</div>


title: what-is-the-product-of-the-binary-numbers-100101-and-111
slug: what-is-the-product-of-the-binary-numbers-100101-and-111-71220
question: <div class="question">What is the product of the binary numbers $1001.01$ and 11.1?</div>
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2007 (Phase 1)']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$101110.011$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$100000.011$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$101110.101$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">100000.101</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$100000.011$</span> </div>

answer:
<div class="solution">$1001.01=1 \times 2^{3}+1 \times 2^{0}+1 \times 2^{-2}$<br/>corresponding to number of base 10 .<br/>$=8+1+\frac{1}{4}=\frac{37}{4}=9.25$<br/>and $11.1=1 \times 2^{1}+1 \times 2^{0}+1 \times 2^{-1}$<br/>$=2+1+\frac{1}{2}=\frac{7}{2}=3.5$<br/>Corresponding to the number of base 10 $1001.01 \times 11.1=9.25 \times 3.5=32.375$<br/>From decimal to binary (32) $_{10}=(100000)_{2}$<br/>and $(.375)_{10}=0.25+0.125$<br/>$=\frac{1}{4}+\frac{1}{8}=1 \times 2^{-2}+1 \times 2^{-3}=(0.011)_{2}$<br/>$(32.375)_{10}=(100000.011)_{2}$</div>


tags: ['Mathematics', 'Pair of Lines', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch2_P4.db
title:
what-is-the-product-of-the-perpendiculars-drawn-from-the-points-a-2-b-2-0-upon-the-line-b-x-cos-ay-sin-ab

slug:
what-is-the-product-of-the-perpendiculars-drawn-from-the-points-a-2-b-2-0-upon-the-line-b-x-cos-ay-sin-ab-69436

question:
<div class="question">What is the product of the perpendiculars drawn from the points $\left(\pm \sqrt{a^{2}-b^{2}}, 0\right)$ upon the line $b x \cos \alpha+$ ay sin $\alpha=a b ?$</div>

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

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

answer:
<div class="solution">Given equation of line is $b x \cos \alpha+$ ay $\sin \alpha=a b$ Perpendicular distance from point $\left(\sqrt{\mathrm{a}^{2}-\mathrm{b}^{2}}, 0\right)$ is $d_{1}=\left|\frac{b \cos \alpha \sqrt{a^{2}-b^{2}}+0-a b}{\sqrt{b^{2} \cos ^{2} \alpha+a^{2} \sin ^{2} \alpha}}\right|$<br/>$\left(\because\right.$ distance from $\left(x_{1}, y_{1}\right)$ to $a x+b y+c=0$ is $=\left|\frac{a x_{1}+b y_{1}+c}{\sqrt{a^{2}+b^{2}}}\right|$<br/>Similarly, perpendicular distance from point $\left(-\sqrt{a^{2}-b^{2}}, 0\right)$ is<br/>$d_{2}=\left|\frac{-b \cos \alpha \sqrt{a^{2}-b^{2}}+0-a b}{\sqrt{b^{2} \cos ^{2} \alpha+a^{2} \sin ^{2} \alpha}}\right|$<br/>By product of $\mathrm{d}_{1}$ and $\mathrm{d}_{2}$, we get $=\frac{\left(\mathrm{b} \cos \alpha \sqrt{\mathrm{a}^{2}-\mathrm{b}^{2}}-\mathrm{ab}\right)\left(\mathrm{b} \cos \alpha \sqrt{\mathrm{a}^{2}-\mathrm{b}^{2}}+\mathrm{ab}\right)}{\left(\sqrt{\mathrm{b}^{2} \cos ^{2} \alpha+\mathrm{a}^{2} \sin ^{2} \alpha}\right)\left(\sqrt{ \left.\mathrm{b}^{2} \cos ^{2} \alpha+\mathrm{a}^{2} \sin ^{2} \alpha\right)}\right.}$<br/>$=\frac{\mathrm{b}^{2} \cos ^{2} \alpha\left(\mathrm{a}^{2}-\mathrm{b}^{2}\right)-\mathrm{a}^{2} \mathrm{~b}^{2}}{\mathrm{~b}^{2} \cos ^{2} \alpha+\mathrm{a}^{2} \sin ^{2} \alpha}$<br/>$=\frac{a^{2} b^{2} \cos ^{2} \alpha-b^{4} \cos ^{2} \alpha-a^{2} b^{2}}{b^{2} \cos ^{2} \alpha+a^{2} \sin ^{2} \alpha}$<br/>$=\frac{\mathrm{a}^{2} \mathrm{~b}^{2}\left(\cos ^{2} \alpha-1\right)-\mathrm{b}^{4} \cos ^{2} \alpha}{\mathrm{b}^{2} \cos ^{2} \alpha+\mathrm{a}^{2} \sin ^{2} \alpha}$<br/>$=\frac{-b^{2}\left[a^{2} \sin ^{2} \alpha+b^{2} \cos ^{2} \alpha\right]}{b^{2} \cos ^{2} \alpha+a^{2} \sin ^{2} \alpha}$<br/>Hence, product of the perpendiculars $=-b^{2}=b^{2}$ (since, distance is positive)</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2009 (Phase 2)']
source_db: MarksBatch2_P4.db
title:
what-is-the-product-of-the-perpendiculars-from-the-two-points-b-2-a-2-0-to-the-line-ax-cos-by-sin-ab

slug:
what-is-the-product-of-the-perpendiculars-from-the-two-points-b-2-a-2-0-to-the-line-ax-cos-by-sin-ab-40112

question:
<div class="question">What is the product of the perpendiculars from the two points $\left(\pm \sqrt{b^{2}-a^{2}}, 0\right)$ to the line ax $\cos \phi+$ by $\sin \phi=a b$ ?</div>

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

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

answer:
<div class="solution">Given equation of line is $a x \cos \phi+$ by $\sin \phi-a b=0$ Let $d_{1}$ be the perpendicular distance from<br/>$\left(\sqrt{b^{2}-a^{2}}, 0\right)$ to the line $a x \cos \phi+$ by $\sin \phi-a b=0$<br/>and $d_{2}$ from $\left(-\sqrt{b^{2}-a^{2}}, 0\right)$ to the line $a x \cos \phi+$ by sin $\phi-a b=0$<br/>At point $\left(\sqrt{b^{2}-a^{2}}, 0\right)$<br/>$d_{1}=\frac{a \sqrt{b^{2}-a^{2}} \cos \phi-a b}{\sqrt{a^{2} \cos ^{2} \phi+b^{2} \sin ^{2} \phi}}$<br/>At point $\left(-\sqrt{b^{2}-a^{2}}, 0\right)$<br/>$d_{2}=\frac{-a \sqrt{b^{2}-a^{2}} \cos \phi-a b}{\sqrt{a^{2} \cos ^{2} \phi+b^{2} \sin ^{2} \phi}}$<br/>$\therefore d_{1} d_{2}=-\frac{\left[a^{2}\left(b^{2}-a^{2}\right) \cos ^{2} \phi-a^{2} b^{2}\right]}{a^{2} \cos ^{2} \phi+b^{2} \sin ^{2} \phi}$<br/>$=-\frac{a^{2}\left(-b^{2} \sin ^{2} \phi-a^{2} \cos ^{2} \phi\right)}{a^{2} \cos ^{2} \phi+b^{2} \sin ^{2} \phi}=a^{2}$</div>


title: what-is-the-product-of-the-reaction-between-acetone-and-a-grignard-reagent
slug: what-is-the-product-of-the-reaction-between-acetone-and-a-grignard-reagent-59792
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
answer: <div class="solution">Acetone reacts to form a tertiary alcohol.</div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the product of the reaction between acetone and a Grignard reagent?</div>

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


title: what-is-the-product-of-the-reaction-between-benzene-sulphonyl-chloride-and-a-secondary-amine
slug: what-is-the-product-of-the-reaction-between-benzene-sulphonyl-chloride-and-a-secondary-amine-23023
tags: ['Chemistry', 'Amines', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the product of the reaction between benzene sulphonyl chloride and a secondary amine?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">N,N-diethyl benzene sulphonamide</span> </div>

answer:
<div class="solution">The reaction of benzenesulfonyl chloride with a secondary amine yields N,N-diethyl benzene sulphonamide.</div>


tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2007 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">75</span> </div>
source_db: MarksBatch2_P4.db
title:
what-is-the-product-of-two-parts-of-20-such-that-the-product-of-one-part-and-the-cube-of-the-other-is-maximum

slug:
what-is-the-product-of-two-parts-of-20-such-that-the-product-of-one-part-and-the-cube-of-the-other-is-maximum-65982

question:
<div class="question">What is the product of two parts of 20 , such that the product of one part and the cube of the other is maximum?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">75</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">91</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">84</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">96</span> </li> </ul>

answer:
<div class="solution">Let 20 be divided in two parts such that first part $=\mathrm{x}$ $\therefore \quad$ Second part $=20-\mathrm{x}$<br/>Now, assume that $\mathrm{P}=\mathrm{x}^{3}(20-\mathrm{x})$<br/>$=20 \mathrm{x}^{3}-\mathrm{x}^{4}$<br/>Now, $\frac{\mathrm{dP}}{\mathrm{dx}}=60 \mathrm{x}^{2}-4 \mathrm{x}^{3}$<br/>and $\frac{\mathrm{d}^{2} \mathrm{P}}{\mathrm{dx}^{2}}=120 \mathrm{x}-12 \mathrm{x}^{2}$<br/>Put $\frac{\mathrm{dP}}{\mathrm{dx}}=0$ for maxima or minima<br/>$\Rightarrow \frac{\mathrm{dP}}{\mathrm{dx}}=0$<br/>$\Rightarrow 4 \mathrm{x}^{2}(15-\mathrm{x})=0 \quad \Rightarrow \mathrm{x}=0, \mathrm{x}=15$<br/>$\therefore\left(\frac{\mathrm{d}^{2} \mathrm{P}}{\mathrm{dx}^{2}}\right)_{\mathrm{x}=15}=120 \times 15-12 \times(225)$<br/>$=1800-2700=-900   &lt; 0$<br/>$\therefore \quad P$ is a maximum at $x=15$. $\therefore \quad$ First part $=15$<br/>and second part $=20-15=5$ Required product $=15 \times 5=75$</div>


title: what-is-the-projection-of-the-vector-i-2-j-k-on-the-vector-4-i-4-j-7-k
slug: what-is-the-projection-of-the-vector-i-2-j-k-on-the-vector-4-i-4-j-7-k-97519
tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2011 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the projection of the vector $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ on the<br/>vector $4 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+7 \hat{\mathbf{k}}$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\sqrt{5}}{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{19}{9}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\sqrt{5}}{4}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{11}{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{19}{9}$</span> </div>

answer:
<div class="solution">Let $\vec{a}=\hat{i}-2 \hat{j}+\hat{k}$ and $\vec{b}=4 \hat{i}-4 \hat{j}+7 \hat{k}$<br/>$\therefore \quad$ Projection of $\vec{a}$ on $\vec{b}=\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}$<br/>Now, $\vec{a} \cdot \vec{b}=4(1)+4(2)+1(7)=19$<br/>and $|\vec{b}|=\sqrt{(4)^{2}+(4)^{2}+(7)^{2}}=\sqrt{81}=9$<br/>$\therefore \quad$ Projection of $\vec{a}$ on $\vec{b}=\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}=\frac{19}{9}$</div>


title: what-is-the-propability-that-there-are-5-mondays-in-the-month-of-february-2016
slug: what-is-the-propability-that-there-are-5-mondays-in-the-month-of-february-2016-78830
tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2013 (Phase 2)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the propability that there are 5 Mondays in the month of February 2016 ?</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">$\frac{1}{7}$</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">$\frac{2}{7}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

answer:
<div class="solution">February 2016 has 29 days. $=4$ weeks $+1$ odd day.<br/>Now, probability that 1 odd day is monday $=\frac{1}{7}$.</div>


title: what-is-the-purpose-of-computing-the-average-atomic-mass-of-an-element
slug: what-is-the-purpose-of-computing-the-average-atomic-mass-of-an-element-15907
question: <div class="question">What is the purpose of computing the average atomic mass of an element?</div>
tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">To determine the total number of atoms in the element</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">To establish the most common isotope of the element</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">To account for the presence of isotopes and their relative abundances</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">To simplify the naming of elements</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">To account for the presence of isotopes and their relative abundances</span> </div>

answer:
<div class="solution">Computing the average atomic mass of an element is done to account for the presence of isotopes and their relative abundances.</div>


title: what-is-the-purpose-of-ethical-standards-in-genetic-modification-of-organisms
slug: what-is-the-purpose-of-ethical-standards-in-genetic-modification-of-organisms-11898
tags: ['Biology', 'Biotechnology and Its Applications', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the purpose of ethical standards in genetic modification of organisms?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">To evaluate the morality of human activities that might help or harm living organisms</span> </div>

answer:
<div class="solution">Ethical standards are required to evaluate the morality of human activities that might help or harm living organisms, beyond the biological significance of such things.</div>


title: what-is-the-purpose-of-ex-situ-conservation-1
slug: what-is-the-purpose-of-ex-situ-conservation-1-88341
question: <div class="question">What is the purpose of ex situ conservation?</div>
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">To protect species at risk of extinction in the wild.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">To protect a specific region's biodiversity.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">To save the entire ecosystem.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">To address global conservation problems.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">To protect species at risk of extinction in the wild.</span> </div>

answer:
<div class="solution">Ex situ conservation is the desirable approach when there are situations where an animal or plant is endangered or threatened and needs urgent measures to save it from extinction.</div>


title: what-is-the-purpose-of-nomenclature
slug: what-is-the-purpose-of-nomenclature-70845
question: <div class="question">What is the purpose of nomenclature?</div>
tags: ['Biology', 'The Living World', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">To standardize the naming of living organisms</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">To facilitate the study of organisms</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">To provide scientific names for plants</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">To assign a name to each known organism</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">To standardize the naming of living organisms</span> </div>

answer:
<div class="solution">The purpose of nomenclature is to standardize the naming of living organisms such that a particular organism is known by the same name all over the world.</div>


title: what-is-the-purpose-of-pumping-air-into-the-effluent-in-secondary-treatment
slug: what-is-the-purpose-of-pumping-air-into-the-effluent-in-secondary-treatment-38175
tags: ['Biology', 'Microbes in Human Welfare', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the purpose of pumping air into the effluent in secondary treatment?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">To promote the growth of useful aerobic microbes</span> </div>

answer:
<div class="solution">Air is pumped into the effluent in secondary treatment, allowing vigorous growth of useful aerobic microbes into flocs.</div>


title: what-is-the-purpose-of-secondary-treatment-of-sewage
slug: what-is-the-purpose-of-secondary-treatment-of-sewage-71994
question: <div class="question">What is the purpose of secondary treatment of sewage?</div>
tags: ['Biology', 'Microbes in Human Welfare', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Physical removal of particles</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Removal of organic matter</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Reduction of BOD</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Increase in pollution potential</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Removal of organic matter</span> </div>

answer:
<div class="solution">The primary effluent is passed into large aeration tanks where it is agitated mechanically and air is pumped into it, allowing vigorous growth of useful aerobic microbes.</div>


title: what-is-the-purpose-of-the-formation-of-the-es-complex
slug: what-is-the-purpose-of-the-formation-of-the-es-complex-32792
question: <div class="question">What is the purpose of the formation of the âESâ complex?</div>
tags: ['Biology', 'Biomolecules (B)', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">To stabilize the substrate</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">To form the transition state structure</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">To catalyze the reaction</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">To release the product</span> </li> </ul>

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

answer:
<div class="solution">The formation of the âESâ complex, where E stands for enzyme, is mandatory for the catalyzation of the reaction. The complex formation helps in catalyzing the reaction.</div>


title: what-is-the-purpose-of-the-zona-pellucida-formed-around-the-secondary-oocyte
slug: what-is-the-purpose-of-the-zona-pellucida-formed-around-the-secondary-oocyte-89056
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the purpose of the zona pellucida formed around the secondary oocyte?</div>

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

answer:
<div class="solution">The secondary oocyte forms a new membrane called zona pellucida surrounding it, which helps in the process of fertilization.</div>


title: what-is-the-purpose-of-zncl-2-in-the-reaction-of-primary-and-secondary-alcohols-with-hcl
slug: what-is-the-purpose-of-zncl-2-in-the-reaction-of-primary-and-secondary-alcohols-with-hcl-36283
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the purpose of ZnCl<sub>2</sub> in the reaction of primary and secondary alcohols with HCl?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">ZnCl<sub>2</sub> catalyses the reaction.</span> </div>

answer:
<div class="solution">ZnCl<sub>2</sub> acts as a catalyst in the reaction of primary and secondary alcohols with HCl.</div>


tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch2_P4.db
title:
what-is-the-radius-of-the-circle-passing-through-the-point-2-4-and-having-centre-at-the-intersection-of-the-lines-x-y-4-and-2-x-3-y-7-0

slug:
what-is-the-radius-of-the-circle-passing-through-the-point-2-4-and-having-centre-at-the-intersection-of-the-lines-x-y-4-and-2-x-3-y-7-0-96606

question:
<div class="question">What is the radius of the circle passing through the point $(2,4)$ and having centre at the intersection of the lines $\mathrm{x}-\mathrm{y}$ $=4$ and $2 x+3 y+7=0 ?$</div>

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

answer:
<div class="solution">We have $x-y=4 \&amp; 2 x+3 y+7=0$<br/>On solving, we get, $x=1 \&amp; y=-3$<br/>(these are coordinates of centre of the circle)<br/>$\Rightarrow$ radius $=\sqrt{(2-1)^{2}+(4+3)^{2}}=5 \sqrt{2}$</div>


title: what-is-the-radius-of-the-circle-passing-through-the-points-0-0-a-0-and-0-b
slug: what-is-the-radius-of-the-circle-passing-through-the-points-0-0-a-0-and-0-b-46396
tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the radius of the circle passing through the points $(0,0),(a, 0)$ and $(0, b) ?$</div>

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

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

answer:
<div class="solution">Let $(\mathrm{h}, \mathrm{k})$ be the centre of the circle. Since, circle is passing through $(0,0),(\mathrm{a}, 0)$ and $(0, \mathrm{~b})$, distance between centre and these points would be same and equal to radius. Hence, $h^{2}+k^{2}=(h-a)^{2}+k^{2}=h^{2}+(k-b)^{2}$<br/>$$<br/>\begin{array}{l}<br/>\Rightarrow \mathrm{h}^{2}+\mathrm{k}^{2}=\mathrm{h}^{2}+\mathrm{k}^{2}+\mathrm{a}^{2}-2 \mathrm{ah}=\mathrm{h}^{2}+\mathrm{k}^{2}+\mathrm{b}^{2}-2 \mathrm{bk} \\<br/>\Rightarrow \mathrm{h}^{2}+\mathrm{k}^{2}=\mathrm{h}^{2}+\mathrm{k}^{2}+\mathrm{a}^{2}-2 \mathrm{ah} \\<br/>\Rightarrow \mathrm{h}=\frac{\mathrm{a}}{2}<br/>\end{array}<br/>$$<br/>Similarly, $\mathrm{k}=\frac{\mathrm{b}}{2}$<br/>$\therefore \quad$ Radius of circle $=\sqrt{\mathrm{h}^{2}+\mathrm{k}^{2}}=\frac{1}{2} \sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}}$</div>


title: what-is-the-radius-of-the-circle-touching-x-axis-at-3-0-and-y-axis-at-0-3
slug: what-is-the-radius-of-the-circle-touching-x-axis-at-3-0-and-y-axis-at-0-3-62859
tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the radius of the circle touching $x$ -axis at $(3,0)$ and $y$ -axis at $(0,3)$ ?</div>

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

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

answer:
<div class="solution">Since, circle is touching $x$ -axis at $(3,0)$ and y-axis at $(0$,<br/>3) therefore radius $=3$ unit<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/-AgArA7ACYtGzQbDj2aXiP6uhAI96EjiNBkUGm7SfVg.original.fullsize.png"/></div>


title: what-is-the-radius-of-the-sphere-x-2-y-2-z-2-6-x-8-y-10-z-1-0
slug: what-is-the-radius-of-the-sphere-x-2-y-2-z-2-6-x-8-y-10-z-1-0-82023
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2019 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the radius of the sphere $x^{2}+y^{2}+z^{2}-6 x+8 y-10 z$ $+1=0 ?$</div>

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

answer:
<div class="solution">The equation of sphere is $x^{2}+y^{2}+z^{2}-6 x+8 y-10 z+1=0$<br/>Comparing the equation with general form of sphere, $x^{2}+y^{2}+z^{2}+2 u x+2 v y+2 w z-d-0$<br/>we get, $u=\frac{-6}{2}=-3, v=\frac{8}{2}=4, w=\frac{-10}{2}=5, d=1$<br/>Radius $=\sqrt{u^{2}+v^{2}+w^{2}-d}$<br/>$=\sqrt{(-3)^{2}+(4)^{2}+(5)^{2}-1}$<br/>$=\sqrt{9+16+25-1}=\sqrt{49}=7$</div>


title: what-is-the-radius-of-the-sphere-x-2-y-2-z-2-x-y-z-0
slug: what-is-the-radius-of-the-sphere-x-2-y-2-z-2-x-y-z-0-24646
question: <div class="question">What is the radius of the sphere $x^{2}+y^{2}+z^{2}-x-y-z=0 ?$</div>
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2011 (Phase 1)']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\sqrt{\frac{3}{4}}$</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">$\sqrt{\frac{1}{2}}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\sqrt{\frac{3}{2}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{3}$</span> </li> </ul>

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

answer:
<div class="solution">The given equation of sphere is<br/>$x^{2}+y^{2}+z^{2}-x-y-z=0$<br/>On comparing with<br/>$x^{2}+y^{2}+z^{2}+2 u x+2 v y+2 w z+d=0$<br/>we get, $u=-\frac{1}{2}, v=-\frac{1}{2}, w=-\frac{1}{2}, d=0$<br/>Radius of sphere $=\sqrt{u^{2}+v^{2}+w^{2}-d}$<br/>$=\sqrt{\frac{1}{4}+\frac{1}{4}+\frac{1}{4}}=\sqrt{\frac{3}{4}}$</div>


title: what-is-the-range-of-f-x-cos-2-x-sin-2-x
slug: what-is-the-range-of-f-x-cos-2-x-sin-2-x-45090
question: <div class="question">What is the range of $f(x)=\cos 2 x-\sin 2 x$ ?</div>
tags: ['Mathematics', 'Functions', 'NDA', 'NDA 2011 (Phase 1)']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$[2,4]$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\quad[-1,1]$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$[-\sqrt{2}, \sqrt{2}]$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$(-\sqrt{2}, 2)$</span> </li> </ul>

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

answer:
<div class="solution">Let $f(x)=\cos 2 x-\sin 2 x$<br/>$f(x)=\frac{1}{\sqrt{2}}[\sqrt{2} \cos 2 x-\sin 2 x]$<br/>$f(x)=\sqrt{2}\left[\frac{1}{\sqrt{2}} \cos 2 x-\frac{1}{\sqrt{2}} \sin 2 x\right]$<br/>$f(x)=\sqrt{2}\left[\cos \frac{\pi}{4} \cos 2 x-\sin \frac{\pi}{4} \sin 2 x\right]$<br/>$f(x)=\sqrt{2}\left[\cos \left(\frac{\pi}{4}+2 x\right)\right]$<br/>We know,<br/>$-1 \leq \cos \left(\frac{\pi}{4}+2 x\right) \leq 1$<br/>$\Rightarrow-\sqrt{2} \leq \sqrt{2} \cos \left(\frac{\pi}{4}+2 x\right) \leq \sqrt{2}$<br/>$\Rightarrow-\sqrt{2} \leq f(x) \leq \sqrt{2}$<br/>$\therefore \quad$ Range of $f(x)=[-\sqrt{2}, \sqrt{2}]$</div>


title: what-is-the-range-of-the-function-f-x-x-x-x-0
slug: what-is-the-range-of-the-function-f-x-x-x-x-0-28819
tags: ['Mathematics', 'Functions', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the range of the function $\mathrm{f}(\mathrm{x})=\frac{|\mathrm{x}|}{\mathrm{x}}, \mathrm{x} \neq 0$?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Set of all real numbers</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Set of all integers</span> </li><li class="correct"> <span class="option-label">C</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">D</span> <span class="option-data">$\{-1,0,1\}$</span> </li> </ul>

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

answer:
<div class="solution">As we know<br/>$|\mathrm{x}|=\left\{\begin{array}{ccc}\mathrm{x} &amp; \text { if } &amp; \mathrm{x}&gt;0 \\ -\mathrm{x} &amp; \text { if } &amp; \mathrm{x}   &lt; 0\end{array}\right.$<br/>$\therefore f(x)=\frac{|x|}{x}=\left\{\begin{array}{lll}\frac{x}{x} &amp; \text { if } &amp; x&gt;0 \\ \frac{-x}{x} &amp; \text { if } &amp; x &lt; 0\end{array}\right.$<br/>$=\left\{\begin{array}{ccc}1 &amp; \text { if } &amp; x&gt;0 \\ -1 &amp; \text { if } &amp; x &lt; 0\end{array}\right.$<br/>Hence, Range $=\{-1,1\}$.</div>


title: what-is-the-rangeofthe-function-y-1-x-2-x-2-where-x-r
slug: what-is-the-rangeofthe-function-y-1-x-2-x-2-where-x-r-21001
tags: ['Mathematics', 'Functions', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the rangeofthe function $\mathrm{y}=\frac{\mathrm{x}^{2}}{1+\mathrm{x}^{2}}$, where $\mathrm{X} \in \mathbf{R}$ ?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$[0,1)$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/JsRPB6w_RE0kXcX_qIp4JEDViVeLh_m-vKypcEqtGE8.original.fullsize.png"/><br/><br/>Clearly $0 \leq y &lt; 1$<br/>$\Rightarrow y \in[0,1)$</div>


title: what-is-the-rate-of-change-of-x-2-16-with-respect-to-x-2-at-x-3
slug: what-is-the-rate-of-change-of-x-2-16-with-respect-to-x-2-at-x-3-60387
tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the rate of change of $\sqrt{\mathrm{x}^{2}+16}$ with respect to $\mathrm{x}^{2}$ at $\mathrm{x}=3 ?$</div>

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

answer:
<div class="solution">Let $\mathrm{u}=\sqrt{\mathrm{x}^{2}+16}, \mathrm{v}=\mathrm{x}^{2}$<br/>$\Rightarrow \mathrm{u}^{2}=\mathrm{x}^{2}+16, \quad \frac{\mathrm{dv}}{\mathrm{dx}}=2 \mathrm{x}$<br/>$\Rightarrow 2 \mathrm{u} \frac{\mathrm{du}}{\mathrm{dx}}=2 \mathrm{x}$<br/>$\Rightarrow \frac{\mathrm{du}}{\mathrm{dx}}=\frac{\mathrm{x}}{\sqrt{\mathrm{x}^{2}+16}}$<br/>Now, required rate of change $=\frac{\mathrm{du}}{\mathrm{dv}}$<br/>$=\frac{d u}{d x} \times \frac{d x}{d v}=\frac{x}{\sqrt{x^{2}+16}} \times \frac{1}{2 x}=\frac{1}{2 \sqrt{x^{2}+16}}$<br/>Now, $\left.\frac{d u}{d v}\right|_{x=3}=\frac{1}{2 \times 5}=\frac{1}{10}$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2007 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$5: 4$</span> </div>
source_db: MarksBatch2_P4.db
title:
what-is-the-ratio-in-which-the-line-joining-the-points-2-4-5-and-3-5-4-is-internally-divided-by-the-x-y-plane

slug:
what-is-the-ratio-in-which-the-line-joining-the-points-2-4-5-and-3-5-4-is-internally-divided-by-the-x-y-plane-51786

question:
<div class="question">What is the ratio in which the line joining the points $(2,4,5)$ and $(3,5,-4)$ is internally divided by the $x y$ -plane?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$5: 4$</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">$3: 4$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1: 2$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$7: 5$</span> </li> </ul>

answer:
<div class="solution">Let the line joining the points $(2,4,5)$ and $(3,5,-4)$ is internally divided by the $x y$ - plane in the ratio $k: 1$.<br/>$\therefore \quad$ For xy plane, $z=0$<br/>$\Rightarrow 0=\frac{-\mathrm{k} \times 4+5}{\mathrm{k}+1} \Rightarrow 4 \mathrm{k}=5 \Rightarrow \mathrm{k}=\frac{5}{4}$.<br/>$\mathrm{k}=\frac{5}{4}$ so, ratio is $5: 4$</div>


title: what-is-the-ratio-in-which-the-point-c-7-2-7-20-divides-the-line-joining-the-points-a-2-2-and-b-2-4
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2017 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$3: 4$</span> </div>
source_db: MarksBatch2_P4.db
slug:
what-is-the-ratio-in-which-the-point-c-7-2-7-20-divides-the-line-joining-the-points-a-2-2-and-b-2-4-94062

question:
<div class="question">What is the ratio in which the point $C\left(-\frac{2}{7},-\frac{20}{7}\right)$ divides the line joining the points $\mathrm{A}(-2,-2)$ and $\mathrm{B}(2,-4)$ ?</div>

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

answer:
<div class="solution">$\quad \mathrm{C}=\left(\frac{2 \mathrm{~K}-2}{\mathrm{~K}+1}, \frac{-4 \mathrm{~K}+2}{\mathrm{~K}+1}\right)$<br/>So, $\frac{2 \mathrm{~K}-2}{\mathrm{~K}+1}=\frac{-2}{7}$<br/>$\mathrm{C}\left(\frac{-2}{7}, \frac{-20}{7}\right)$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/UBIde_oRjcTAEKtinIhkEZn0aNXCOejgW9qOxynyv00.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/kHtnlsry-VMsngCqbTIiFlAANSZYzJV01MD-jS5D8qg.original.fullsize.png"/><br/><br/>$\Rightarrow 7 \mathrm{~K}-7=-\mathrm{K}-1$<br/>$\Rightarrow 8 \mathrm{~K}=6 \Rightarrow \mathrm{K}=\frac{3}{4}$<br/>$\therefore \mathrm{K}: 1=\frac{3}{4}: 1=3: 4$</div>


title: what-is-the-ratio-of-coefficient-of-x-15-to-the-term-independent-of-x-in-x-2-x-2-15
slug: what-is-the-ratio-of-coefficient-of-x-15-to-the-term-independent-of-x-in-x-2-x-2-15-50617
tags: ['Mathematics', 'Binomial Theorem', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the ratio of coefficient of $x^{15}$ to the term independent<br/>of $x$ in $\left(x^{2}+\frac{2}{x}\right)^{15} ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 / 64$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$1 / 32$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$1 / 16$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1 / 4$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1 / 32$</span> </div>

answer:
<div class="solution">Given expansion is $\left(x^{2}+\frac{2}{x}\right)^{15}$<br/>$\mathrm{T}_{\mathrm{r}+1}={ }^{15} \mathrm{C}_{r}\left(x^{2}\right)^{15-r}\left(\frac{2}{x}\right)^{r}$<br/>$={ }^{15} \mathrm{C}_{r} x^{30-2 r} 2^{r} \cdot x^{-r}={ }^{15} \mathrm{C}_{\mathrm{r}} . \mathrm{x}^{30-3 r} \cdot 2^{r}$<br/>Now, Above term will be independent of $x$ when $30-3 r=0 \Rightarrow r=10$<br/>$\therefore$ Term independent of $\mathrm{x}={ }^{15} \mathrm{C}_{10} 2^{10}$<br/>Now, coeff of $\mathrm{x}^{15}$ When $30-3 r=15 \Rightarrow r=5$<br/>$\therefore$ Required coeff $={ }^{15} \mathrm{C}_{5} 2^{5}$<br/>Thus, Required Ratio $=\frac{15 \mathrm{C}_{5} \cdot 2^{5}}{15 \mathrm{C}_{10} \cdot 2^{10}}$<br/>$=\frac{\frac{15 !}{5 !(10 !)}}{\frac{15 !}{10 ! 5 !} \times 2^{5}}=\frac{1}{2^{5}}=\frac{1}{32}$</div>


title: what-is-the-real-part-of-sin-x-i-cos-x-3-where-i-1
slug: what-is-the-real-part-of-sin-x-i-cos-x-3-where-i-1-14546
tags: ['Mathematics', 'Complex Number', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the real part of $(\sin x+\mathrm{i} \cos x)^{3}$ where $i=\sqrt{-1}$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-\cos 3 x$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$-\sin 3 x$</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">C</span> <span class="option-data">$\sin 3 x$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\cos 3 x$</span> </li> </ul>

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

answer:
<div class="solution">$\begin{aligned} &amp;(\sin x+i \cos x)^{3} \\ &amp;=\sin ^{3} x+(i)^{3} \cos ^{3} x+3 i(\sin x)(\cos x)(\sin x+i \cos x) \\ &amp;=\sin ^{3} x-i \cos ^{3} x+3 i \sin ^{2} x \cos x-3 \sin x \cos ^{2} x \\ &amp;=\sin ^{3} x-3 \sin x \cos ^{2} x-i \cos x\left(\cos ^{2} x+\sin ^{2} x\right) \\ &amp;=\sin x\left(\sin ^{2} x-3 \cos ^{2} x\right)-i \cos x\left(\cos ^{2} x+3 \sin ^{2} x\right) \\ &amp; \text { Real part of }(\sin x+i \cos x)^{3} \\ &amp;=\sin x\left(\sin ^{2} x-3 \cos ^{2} x\right) \\ &amp;=\sin x\left[\sin ^{2} x-3\left(1-\sin ^{2} x\right)\right] \\ &amp;=\sin x\left[4 \sin ^{2} x-3\right] \\ &amp;=4 \sin ^{3} x-3 \sin x \\ &amp;=-\left(3 \sin x-4 \sin ^{3} x\right)=-\sin 3 x \end{aligned}$<br/>$\therefore$ Option (b) is correct.</div>


title: what-is-the-reason-behind-the-secondary-structure-of-proteins
slug: what-is-the-reason-behind-the-secondary-structure-of-proteins-50362
question: <div class="question">What is the reason behind the secondary structure of proteins?</div>
tags: ['Chemistry', 'Biomolecules', 'JEE Main']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Peptide bond</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Hydrogen bond</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Covalent bond</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Co-ordinate bond</span> </li> </ul>

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

answer:
<div class="solution">Secondary structure is formally defined by the pattern of hydrogen bonds between the amino hydrogen and carboxyl oxygen atoms in the peptide backbone<br/></div>


title: what-is-the-region-that-represents-a-b-if-a-x-y-x-y-4-and-b-x-y-x-y-0
slug: what-is-the-region-that-represents-a-b-if-a-x-y-x-y-4-and-b-x-y-x-y-0-39063
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the region that represents $\mathrm{A} \cap \mathrm{B}$ if $\mathrm{A}=\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}+\mathrm{y} \leq 4\}$ and $\mathrm{B}=\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}+\mathrm{y} \leq 0\} ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\{(x, y) \mid x+y \leq 2\}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\{(x, y) \mid 2 x+y \leq 4\}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\{(x, y) \mid x+y \leq 0\}$</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">$\{(x, y) \mid x+y \leq 4\}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\{(x, y) \mid x+y \leq 0\}$</span> </div>

answer:
<div class="solution">Asgiven $\mathrm{A}=\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}+\mathrm{y} \leq 4\}$<br/>and $B=\{(x, y) \mid x+y \leq 0\}$<br/>Set Acontains all the pairs in the interval $(-\propto, 2)$ andset B contains all the pairs in the interval $(-\infty, 0)$ so, $\mathrm{A} \cap \mathrm{B}$ shows a set containing all the pairs in the interval $[-\infty, 0]$ So, $A \cap B=\{(x, y) \mid x+y \leq 0\}$</div>


title: what-is-the-relationship-between-rna-and-dna
slug: what-is-the-relationship-between-rna-and-dna-67721
question: <div class="question">What is the relationship between RNA and DNA?</div>
tags: ['Biology', 'Molecular Basis of Inheritance', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">RNA is more abundant than DNA</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">DNA is more abundant than RNA</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">RNA and DNA have no relationship</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">They are both genetic materials</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">They are both genetic materials</span> </div>

answer:
<div class="solution">Both RNA and DNA are genetic materials found in living systems. However, DNA acts as the genetic material in most organisms, while RNA mostly functions as a messenger.</div>


tags: ['Chemistry', 's Block Elements', 'NEET']
source_db: MarksBatch2_P4.db
title:
what-is-the-relationship-between-standard-electrode-potential-e-o-and-reducing-power-for-alkali-metals

slug:
what-is-the-relationship-between-standard-electrode-potential-e-o-and-reducing-power-for-alkali-metals-24709

question:
<div class="question">What is the relationship between standard electrode potential (E<sub>o</sub>) and reducing power for alkali metals?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Higher E<sub>o</sub> indicates lower reducing power.</span> </div>

answer:
<div class="solution">In the context of alkali metals, a more negative standard electrode potential (E<sub>o</sub>) indicates higher reducing power. So, higher E<sub>o</sub> values correspond to lower reducing power.</div>


tags: ['Chemistry', 'Electrochemistry', 'NEET']
source_db: MarksBatch2_P4.db
title:
what-is-the-relationship-between-the-emf-of-the-cell-e-cell-and-the-standard-electromotive-force-eo-cell-when-the-concentration-of-all-reacting-specie

slug:
what-is-the-relationship-between-the-emf-of-the-cell-e-cell-and-the-standard-electromotive-force-eo-cell-when-the-concentration-of-all-reacting-specie-40426

question:
<div class="question">What is the relationship between the emf of the cell (E<sub>(cell)</sub>) and the standard electromotive force (Eo<sub>(cell)</sub>) when the concentration of all reacting species is unity?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">E<sub>(cell)</sub> = Eo<sub>(cell)</sub></span> </div>

answer:
<div class="solution">When the concentration of all reacting species is unity, E<sub>(cell)</sub> = Eo<sub>(cell)</sub>.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'NEET']
source_db: MarksBatch2_P4.db
title:
what-is-the-relationship-between-the-gibbs-energy-change-r-g-and-the-equilibrium-constant-k-for-a-reaction-at-standard-state-conditions

slug:
what-is-the-relationship-between-the-gibbs-energy-change-r-g-and-the-equilibrium-constant-k-for-a-reaction-at-standard-state-conditions-19365

question:
<div class="question">What is the relationship  between the Gibbs energy change (â<sub>r</sub>GÂ°) and the equilibrium constant (K) for a reaction at standard state conditions?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">â<sub>r</sub>GÂ° = RT ln K</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">â<sub>r</sub>GÂ° = â RT ln K</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">â<sub>r</sub>GÂ° = 2.303 RT log K</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">â<sub>r</sub>GÂ° = â 2.303 RT log K</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">â<sub>r</sub>GÂ° = â RT ln K</span> </div>

answer:
<div class="solution">The relationship between  the Gibbs energy change (â<sub>r</sub>GÂ°)  and the equilibrium constant (K) for a reaction at standard state conditions  is given by â<sub>r</sub>GÂ° = â RT ln K.</div>


tags: ['Chemistry', 'Electrochemistry']
options: None
correct_option: None
source_db: MarksBatch2_P4.db
title:
what-is-the-relationship-betwen-gibbs-free-energy-of-the-cell-reaction-in-a-galvanic-cell-and-the-emf-of-the-cell-when-will-the-maximum-work-be-obtain

slug:
what-is-the-relationship-betwen-gibbs-free-energy-of-the-cell-reaction-in-a-galvanic-cell-and-the-emf-of-the-cell-when-will-the-maximum-work-be-obtain-27874

question:
<div class="question">What is the relationship betwen Gibbs free energy of the cell reaction in a galvanic cell and the emf of the cell? When will the maximum work be obtained from a galvanic cell?</div>

answer:
<div class="solution">When concentration of all reacting species is unity, then $E_{\text {cell }}=\mathrm{E}^{\circ}$ cell and<br/>Gibbs free energy is given as $\Delta_r G^{\circ}=-n F E_{\text {cell }}^{\circ}$ where, $\Delta_r G^{\circ}=$ Standard Gibbs energy of the reaction $E_{\text {cell }}^{\circ}=$ Emf of the cell<br/>$n F=$ Charge passed<br/>To obtain maximum work from a galvanic cell, charge has to be passed reversibly.<br/>The reversible work done by a galvanic cell is equal to decrease in its Gibbs energy.<br/>$\Delta_r G=-n F E_{\text {cell }}$<br/>As $E_{\text {cell }}$ is an intensive parameter but $\Delta_r G$ is an extensive thermodynamic property and the value depends on $n$.<br/>For reaction,<br/>$\mathrm{Zn}(s)+\mathrm{Cu}^{2+}(a q) \longrightarrow \mathrm{Zn}^{2+}(a q)+\mathrm{Cu}(s)$ in a galvanic cell.<br/>$\Delta_r G=-2 F E_{\text {cell }}[$ Here, $n=2]$</div>


title: what-is-the-result-of-competition-between-closely-related-species
slug: what-is-the-result-of-competition-between-closely-related-species-59539
question: <div class="question">What is the result of competition between closely related species?</div>
tags: ['Biology', 'Organisms and Populations', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Co:existence through resource partitioning</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Competitive exclusion of the inferior 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">Interference competition with abundant resources</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Competitive release through species removal</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Competitive exclusion of the inferior species</span> </div>

answer:
<div class="solution">If two closely related species compete for the same resources, the competitively inferior one will be eliminated eventually, as stated by Gause's Competitive Exclusion Principle.</div>


title: what-is-the-result-of-extinction-of-one-species-in-a-plantpollinator-mutualism
slug: what-is-the-result-of-extinction-of-one-species-in-a-plantpollinator-mutualism-93146
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the result of extinction of one species in a plant:pollinator mutualism?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">The other species in the mutualism becomes extinct</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The other species in the mutualism becomes more abundant</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The other species in the mutualism does not get impacted</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 other species in the mutualism becomes extinct</span> </div>

answer:
<div class="solution">When a species becomes extinct in a plant:pollinator mutualism, other species in the mutualism become extinct.</div>


title: what-is-the-result-of-the-first-meiotic-division-of-a-primary-spermatocyte
slug: what-is-the-result-of-the-first-meiotic-division-of-a-primary-spermatocyte-33109
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the result of the first meiotic division of a primary spermatocyte?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Formation of two equal, diploid secondary spermatocytes</span> </div>

answer:
<div class="solution">A primary spermatocyte undergoes the first meiotic division leading to the formation of two equal, diploid secondary spermatocytes.</div>


title: what-is-the-result-of-the-first-meiotic-division-of-the-primary-oocyte
slug: what-is-the-result-of-the-first-meiotic-division-of-the-primary-oocyte-15587
question: <div class="question">What is the result of the first meiotic division of the primary oocyte?</div>
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Formation of a large haploid secondary oocyte and a tiny first polar body</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The formation of a mature follicle</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The rupture of the Graafian follicle</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Ovulation</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Formation of a large haploid secondary oocyte and a tiny first polar body</span> </div>

answer:
<div class="solution">The first meiotic division of the primary oocyte results in the formation of a large haploid secondary oocyte and a tiny first polar body.</div>


tags: ['Chemistry', 'Aldehydes, Ketones and Carboxylic Acids', 'NEET']
source_db: MarksBatch2_P4.db
title:
what-is-the-result-of-the-reduction-of-the-carbonyl-group-of-aldehydes-and-ketones-with-zincamalgam-and-concentrated-hydrochloric-acid

slug:
what-is-the-result-of-the-reduction-of-the-carbonyl-group-of-aldehydes-and-ketones-with-zincamalgam-and-concentrated-hydrochloric-acid-65894

question:
<div class="question">What is the result of the reduction of the carbonyl group of aldehydes and ketones with zinc-amalgam and concentrated hydrochloric acid?</div>

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

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

answer:
<div class="solution">The reduction of the carbonyl group of aldehydes and ketones with zinc-amalgam and concentrated hydrochloric acid leads to the formation of alkanes.</div>


title: what-is-the-result-of-the-second-meiotic-division-of-the-secondary-spermatocytes
slug: what-is-the-result-of-the-second-meiotic-division-of-the-secondary-spermatocytes-41085
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the result of the second meiotic division of the secondary spermatocytes?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Formation of four equal, haploid spermatozoa</span> </div>

answer:
<div class="solution">The secondary spermatocytes undergo the second meiotic division to produce four equal, haploid spermatids.</div>


title: what-is-the-result-of-the-second-meiotic-division
slug: what-is-the-result-of-the-second-meiotic-division-26161
question: <div class="question">What is the result of the second meiotic division?</div>
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The formation of a diploid zygote</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The fusion of a sperm with an ovum</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">The formation of a second polar body and a haploid ovum</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">The completion of the meiotic division of the secondary oocyte</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The formation of a second polar body and a haploid ovum</span> </div>

answer:
<div class="solution">The second meiotic division is unequal and results in the formation of a second polar body and a haploid ovum.</div>


title: what-is-the-role-of-a-promoter-in-a-transcription-unit
slug: what-is-the-role-of-a-promoter-in-a-transcription-unit-41902
question: <div class="question">What is the role of a promoter in a transcription unit?</div>
tags: ['Biology', 'Molecular Basis of Inheritance', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">To prevent RNA from being translated into protein</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">To define the boundaries of the region of DNA that would be transcribed</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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 initiate the process of replication</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">To catalyze the polymerization of RNA</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">To define the boundaries of the region of DNA that would be transcribed</span> </div>

answer:
<div class="solution">A promoter in a transcription unit helps define the boundaries of the region of DNA that would be transcribed.</div>


title: what-is-the-role-of-a-terminator-in-a-transcription-unit
slug: what-is-the-role-of-a-terminator-in-a-transcription-unit-65651
question: <div class="question">What is the role of a terminator in a transcription unit?</div>
tags: ['Biology', 'Molecular Basis of Inheritance', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">To initiate the process of transcription</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">To define the boundaries of the region of DNA that would be transcribed</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">To mark the end of the segment of DNA that would be transcribed</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">To prevent RNA from being translated into protein</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">To mark the end of the segment of DNA that would be transcribed</span> </div>

answer:
<div class="solution">A terminator in a transcription unit marks the end of the segment of DNA that would be transcribed.</div>


title: what-is-the-role-of-all-nations-in-conserving-biodiversity
slug: what-is-the-role-of-all-nations-in-conserving-biodiversity-73020
question: <div class="question">What is the role of all nations in conserving biodiversity?</div>
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">To conserve biodiversity in their political boundaries</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">To conserve biodiversity in their geographical regions</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">To conserve biodiversity in their local levels</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">A collective responsibility of all nations</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A collective responsibility of all nations</span> </div>

answer:
<div class="solution">Biodiversity knows no political boundaries and its conservation is therefore a collective responsibility of all nations.</div>


title: what-is-the-role-of-feathers
slug: what-is-the-role-of-feathers-60704
question: <div class="question">What is the role of feathers?</div>
tags: ['Biology', 'Animal Kingdom']
options: None
correct_option: None
source_db: MarksBatch2_P4.db
answer:
<div class="solution">Feathers are the epidermal out growths that form distinctive outer covering or plumage in birds.<br/>A variety of role are played by feathers which includes:<br/>(i) They provide life and help in flight, by creating airfoil shape for wings.<br/>(ii) They help in maintaining body temperature.<br/>(iii) Feathers play a vital role in mating by providing secondary sexual that characters in both the sexes the colour and markings determine the alteractiveness of mate.</div>


title: what-is-the-role-of-n-a-d-in-cellular-respiration-1
slug: what-is-the-role-of-n-a-d-in-cellular-respiration-1-55938
tags: ['Biology', 'Respiration in Plants', 'NEET', 'NEET 2018']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the role of <math><mtext>N</mtext><mtext>A</mtext><msup><mrow><mtext>D</mtext></mrow><mrow><mo>+</mo></mrow></msup></math> in cellular respiration?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">It functions as an electron carrier.</span> </div>

answer:
<div class="solution">Nicotinamide adenine dinucleotide is a coenzyme found in all living cells, and it's required for the fundamental biological processes that make life possible. It functions as an electron carrier.</div>


title: what-is-the-role-of-n-a-d-in-cellular-respiration
slug: what-is-the-role-of-n-a-d-in-cellular-respiration-89550
tags: ['Biology', 'Respiration in Plants', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the role of <math><mtext>N</mtext><mtext>A</mtext><msup><mrow><mtext>D</mtext></mrow><mrow><mo>+</mo></mrow></msup></math> in cellular respiration?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">It functions as an electron carrier.</span> </div>

answer:
<div class="solution">Nicotinamide adenine dinucleotide is a coenzyme found in all living cells, and it's required for the fundamental biological processes that make life possible. It functions as an electron carrier</div>


title: what-is-the-role-of-the-pollen-tubes-in-pollination
slug: what-is-the-role-of-the-pollen-tubes-in-pollination-50206
question: <div class="question">What is the role of the pollen tubes in pollination?</div>
tags: ['Biology', 'Plant Kingdom', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">To transport the male gametes to the egg cell</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">To provide nourishment to the developing embryo</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">To enter the embryo-sac and release the male gametes</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">To transport the diploid secondary nucleus to the ovule</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">To enter the embryo-sac and release the male gametes</span> </div>

answer:
<div class="solution">Pollen tubes grow through the tissues of the stigma and style and reach the ovule, where they enter the embryo-sac and release the male gametes for fertilization.</div>


title: what-is-the-role-of-the-structural-gene-in-a-transcription-unit
slug: what-is-the-role-of-the-structural-gene-in-a-transcription-unit-24334
question: <div class="question">What is the role of the structural gene in a transcription unit?</div>
tags: ['Biology', 'Molecular Basis of Inheritance', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">To initiate the process of transcription</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">To define the boundaries of the region of DNA that would be transcribed</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">To encode the information for the synthesis of a particular protein</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">To prevent RNA from being translated into protein</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">To encode the information for the synthesis of a particular protein</span> </div>

answer:
<div class="solution">The structural gene in a transcription unit encodes the information for the synthesis of a particular protein.</div>


title: what-is-the-role-of-the-zygote-in-pollination
slug: what-is-the-role-of-the-zygote-in-pollination-25983
question: <div class="question">What is the role of the zygote in pollination?</div>
tags: ['Biology', 'Plant Kingdom', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">To develop into an embryo</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">) To provide nourishment to the developing embryo</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">To fuse with the diploid secondary nucleus</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">To guide the pollen tubes to the ovules</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">To develop into an embryo</span> </div>

answer:
<div class="solution">The zygote, which is formed from the fusion of the male gamete and egg cell, develops into an embryo with one or two cotyledons.</div>


title: what-is-the-role-of-veterinary-doctors-in-dairy-farming
slug: what-is-the-role-of-veterinary-doctors-in-dairy-farming-24877
question: <div class="question">What is the role of veterinary doctors in dairy farming?</div>
tags: ['Biology', 'Strategies for Enhancement in Food Production', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">They are not important</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">They help to maintain the health of the animals</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">They are mandatory for regular inspections</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">They help to reduce the chance of direct contact between the produce and the handler</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">They are mandatory for regular inspections</span> </div>

answer:
<div class="solution">Regular visits by a veterinary doctor are mandatory in dairy farming to ensure the health of the animals and the quality of the produce.</div>


title: what-is-the-second-most-abundant-element-in-the-earths-crust-by-mass
slug: what-is-the-second-most-abundant-element-in-the-earths-crust-by-mass-43863
question: <div class="question">What is the second most abundant element in the earth's crust by mass?</div>
tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Carbon</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Germanium</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Silicon</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Tin</span> </li> </ul>

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

answer:
<div class="solution">Silicon is the second (27.7% by mass) most abundant element in the earth's crust.</div>


title: what-is-the-secondary-follicle-characterised-by
slug: what-is-the-secondary-follicle-characterised-by-16096
question: <div class="question">What is the secondary follicle characterised by?</div>
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">A fluid filled cavity</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The theca interna</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The zona pellucida</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">The primary follicle</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A fluid filled cavity</span> </div>

answer:
<div class="solution">The secondary follicle is characterised by a fluid filled cavity called antrum.</div>


title: what-is-the-secondary-oocyte-surrounded-by
slug: what-is-the-secondary-oocyte-surrounded-by-80307
question: <div class="question">What is the secondary oocyte surrounded by?</div>
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">The zona pellucida</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The theca externa</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The theca interna</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">A new membrane</span> </li> </ul>

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

answer:
<div class="solution">The secondary oocyte forms a new membrane called zona pellucida surrounding it.</div>


title: what-is-the-secondary-structure-of-nucleic-acids
slug: what-is-the-secondary-structure-of-nucleic-acids-33684
question: <div class="question">What is the secondary structure of nucleic acids?</div>
tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The sequence of nucleotides in the chain</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Double-stranded helical structure</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Hydrogen bonds between pairs of bases</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Complementary base pairing</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Double-stranded helical structure</span> </div>

answer:
<div class="solution">The secondary structure of nucleic acids is the double-stranded helical structure.</div>


title: what-is-the-secondary-structure-of-trna
slug: what-is-the-secondary-structure-of-trna-21413
question: <div class="question">What is the secondary structure of tRNA?</div>
tags: ['Biology', 'Molecular Basis of Inheritance', 'NEET']
answer: <div class="solution">The secondary structure of tRNA is a clover-leaf shape.</div>
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">A straight chain</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">A circular loop</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">A clover-leaf shape</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">A double helix</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A clover-leaf shape</span> </div>


title: what-is-the-secondary-valence-of-a-metal-ion-according-to-alfred-werners-concept
slug: what-is-the-secondary-valence-of-a-metal-ion-according-to-alfred-werners-concept-39457
tags: ['Chemistry', 'Coordination Compounds', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the secondary valence of a metal ion according to Alfred Werner's concept?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The valence responsible for coordination with ligands</span> </div>

answer:
<div class="solution">According to Alfred Werner's concept, the secondary valence of a metal ion is the valence responsible for coordination with ligands.</div>


title: what-is-the-secondary-valence-of-co-3-ion-according-to-werners-theory-in-co-nh-3-4-cl-2
slug: what-is-the-secondary-valence-of-co-3-ion-according-to-werners-theory-in-co-nh-3-4-cl-2-33450
tags: ['Chemistry', 'Coordination Compounds', 'MHT CET', 'MHT CET 2020 (16 Oct Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
answer: <div class="solution">(C)<br/>Secondary valence $=$ Coordination number $=6$</div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the secondary valence of $\mathrm{Co}^{3+}$ ion according to Werner's theory in $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]^{+}$ ?</div>

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


title: what-is-the-set-of-all-points-where-the-function-f-x-1-x-x-is-differentiable
slug: what-is-the-set-of-all-points-where-the-function-f-x-1-x-x-is-differentiable-53758
tags: ['Mathematics', 'Continuity and Differentiability', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the set of all points, where the function<br/>$f(x)=\frac{x}{1+|x|}$ is differentiable?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$(-\infty, \infty)$ 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">$(0, \infty)$ only</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(-\infty, 0) \cup(0, \infty)$ only</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$(-\infty, 0)$ only</span> </li> </ul>

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

answer:
<div class="solution">Given $f(x)=\frac{x}{1+|x|}$<br/>$=\left\{\begin{array}{c}\frac{x}{1-x}, x   &lt; 0 \\ \frac{x}{1+x}, x \geq 0\end{array} \quad\left(\because|x|=\left\{\begin{array}{lll}x &amp; \text { if } \quad x \geq 0 \\ -x &amp; \text { if } \quad x &lt; 0\end{array}\right)\right.\right.$<br/>$\therefore \quad$ LHD $=f^{\prime}\left(0^{-}\right)=\lim _{h \rightarrow 0} \frac{f(0-h)-f(0)}{-h}$<br/>$=\lim _{h \rightarrow 0} \frac{f(-h)-f(0)}{-h}$<br/>and $\mathrm{RHD}=f^{\prime}\left(0^{+}\right)$<br/>$=\lim _{h \rightarrow 0} \frac{f(0+h)-f(0)}{h}$<br/>$\quad$ Since, $\mathrm{LHD}=\mathrm{RHD}$<br/>$\therefore \quad f(x)$ is differentiable at $x=0$<br/>Hence, $f(x)$ is differentiable in $(-\infty, \infty)$.</div>


title: what-is-the-set-of-points-x-y-satisfying-the-equations-x-2-y-2-4-and-x-y-2
slug: what-is-the-set-of-points-x-y-satisfying-the-equations-x-2-y-2-4-and-x-y-2-96945
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2011 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the set of points $(x, y)$ satisfying the equations $x^{2}+y^{2}=4$ and $x+y=2 ?$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\{(0,2),(2,0)\}$</span> </div>

answer:
<div class="solution">The given equations are $x^{2}+v^{2}=4$<br/>and $x+y=2$<br/>$\quad x^{2}+(2-x)^{2}=4$<br/>$\Rightarrow x^{2}+4+x^{2}-4 x=4$<br/>$\Rightarrow 2 x^{2}=4 x$...(i)<br/>$\Rightarrow x=2$<br/>When $x=2$ then $y=2-2=0$.. (ii)<br/>Similarly $y^{2}+(2-y)^{2}=4$<br/>$\Rightarrow y^{2}+4+y^{2}-4 y=4$<br/>$\Rightarrow y=2$ and $x=0$<br/>These equations are satisfied by only $(2,0)$ and $(0,2)$. Hence, required set is $\{(0,2),(2,0)\}$</div>


title: what-is-the-seventeenth-most-abundant-element-by-mass-in-the-earths-crust
slug: what-is-the-seventeenth-most-abundant-element-by-mass-in-the-earths-crust-87391
tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Carbon</span> </div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the seventeenth most abundant element by mass in the earth's crust?</div>

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

answer:
<div class="solution">Carbon is the seventeenth most abundant element by mass in the earth's crust.</div>


title: what-is-the-seventh-term-of-the-sequence-0-3-8-15-24
slug: what-is-the-seventh-term-of-the-sequence-0-3-8-15-24-43553
question: <div class="question">What is the seventh term of the sequence $0,3,8,15,24, \ldots$ ?</div>
tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2013 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">48</span> </div>
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">63</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">48</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">35</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">33</span> </li> </ul>

answer:
<div class="solution">$0+3=3,3+5=8,8+7=15,15+9=24,24+11=35$,<br/>$35+13=48$<br/>Sequence is $0,3,8,15,24,35,48$</div>


title: what-is-the-significance-of-alfred-werners-concept-of-primary-and-secondary-valence
slug: what-is-the-significance-of-alfred-werners-concept-of-primary-and-secondary-valence-50735
tags: ['Chemistry', 'Coordination Compounds', 'NEET']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the significance of Alfred Werner's concept of primary and secondary valence?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">It provided insights into the structures of coordination compounds.</span> </div>

answer:
<div class="solution">Alfred Werner's concept of primary and secondary valence was instrumental in understanding the structures of coordination compounds.</div>


tags: ['Chemistry', 'Amines', 'NEET']
source_db: MarksBatch2_P4.db
title:
what-is-the-significance-of-distinguishing-between-primary-secondary-and-tertiary-amines-in-these-reactions

slug:
what-is-the-significance-of-distinguishing-between-primary-secondary-and-tertiary-amines-in-these-reactions-53607

question:
<div class="question">What is the significance of distinguishing between primary, secondary, and tertiary amines in these reactions?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">It aids in the separation of amine mixtures</span> </div>

answer:
<div class="solution">Distinguishing between primary, secondary, and tertiary amines is important for the separation of amine mixtures.</div>


tags: ['Chemistry', 'Chemical Equilibrium', 'NEET']
source_db: MarksBatch2_P4.db
title:
what-is-the-significance-of-the-intense-activity-at-the-boundary-between-ice-and-water-in-equilibrium

slug:
what-is-the-significance-of-the-intense-activity-at-the-boundary-between-ice-and-water-in-equilibrium-22601

question:
<div class="question">What is the significance of the intense activity at the boundary between ice and water in equilibrium?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">It indicates dynamic equilibrium with equal rates of molecule transfer.</span> </div>

answer:
<div class="solution">The intense activity at the boundary between ice and water is a characteristic of dynamic equilibrium with equal rates of molecule transfer.</div>


tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'NEET']
source_db: MarksBatch2_P4.db
title:
what-is-the-significance-of-the-terms-isolated-gaseous-atom-and-ground-state-while-defining-the-ionisation-enthalpy-and-electron-gain-enthalpy

slug:
what-is-the-significance-of-the-terms-isolated-gaseous-atom-and-ground-state-while-defining-the-ionisation-enthalpy-and-electron-gain-enthalpy-48074

question:
<div class="question">What is the significance of the terms "isolated gaseous atom" and "ground state" while defining the ionisation enthalpy and electron gain enthalpy?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">These terms indicate that the enthalpy values are measured in a vacuum.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">These terms indicate that the enthalpy values are measured at standard temperature and pressure.</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">"Isolated gaseous atom" emphasises that the atom is in its most stable state, and "ground state" indicates that the electron configurations are in their lowest energy states.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">"Isolated gaseous atom" and "ground state" are technical terms without specific significance in the context of ionisation enthalpy and electron gain enthalpy</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">"Isolated gaseous atom" emphasises that the atom is in its most stable state, and "ground state" indicates that the electron configurations are in their lowest energy states.</span> </div>

answer:
<div class="solution">Correct Option is : (C)<br/>"Isolated gaseous atom" emphasises that the atom is in its most stable state, and "ground state" indicates that the electron configurations are in their lowest energy states.</div>


title: what-is-the-sine-of-angle-between-the-vectors-i-2-j-3-k-and-i-2-j-3-k
slug: what-is-the-sine-of-angle-between-the-vectors-i-2-j-3-k-and-i-2-j-3-k-80647
tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2011 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the sine of angle between the vectors $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$<br/>and $-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}} ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\sqrt{\frac{13}{7}}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{\sqrt{13}}{7}$</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">$\frac{13}{\sqrt{7}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\sqrt{13}}{7}$</span> </div>

answer:
<div class="solution">We know that, the angle between the vectors<br/>$a_{1} \hat{i}+b_{1} \hat{j}+c_{1} \hat{k}$ and $a_{2} \hat{i}+b_{2} \hat{j}+c_{2} \hat{k}$ is given by<br/>$\cos \theta=\left[\frac{a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}} \sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}\right]$<br/>$\therefore \quad$ Angle between the vectors $\hat{i}+2 \hat{j}+3 \hat{k}$ and<br/>$-\hat{i}+2 \hat{j}+3 \hat{k}$ is given by<br/>$\cos \theta=\left[\frac{1 \times(-1)+2 \times 2+3 \times 3}{\sqrt{1+4+9} \sqrt{1+4+9}}\right]$<br/>$=\frac{-1+4+9}{14}=\frac{12}{14}=\frac{6}{7}$<br/>Now, $\sin \theta=\sqrt{1-\cos ^{2} \theta}$<br/>$=\sqrt{1-\frac{36}{49}}=\sqrt{\frac{49-36}{49}}=\sqrt{\frac{13}{49}}=\frac{\sqrt{13}}{7}$</div>


title: what-is-the-slope-of-the-line-perpendicular-to-the-line-4-x-3-y-1
slug: what-is-the-slope-of-the-line-perpendicular-to-the-line-4-x-3-y-1-52713
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2010 (Phase 2)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the slope of the line perpendicular to the line $\frac{x}{4}+\frac{y}{3}=1 ?$</div>

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

answer:
<div class="solution">Given equation of the line $\frac{x}{4}+\frac{y}{3}=1$ can be written as $\begin{aligned} 3 x+4 y=12 &amp; \Rightarrow &amp; 4 y &amp;=-3 x+12 \\ &amp; \Rightarrow \quad &amp; y &amp;=\frac{-3}{4} x+\frac{12}{4} \end{aligned}$<br/>The slope of the line $\frac{x}{y}+\frac{y}{3}=1$ is $\frac{-3}{4}$<br/>$\therefore$ Slope of the line perpendicular to this line $=-\left(\frac{-1}{3 / 4}\right)=\frac{4}{3}$</div>


title: what-is-the-slope-of-the-normal-at-the-point-at-2-2-at-of-the-parabola-y-2-4-a-x
slug: what-is-the-slope-of-the-normal-at-the-point-at-2-2-at-of-the-parabola-y-2-4-a-x-36799
tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2006 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$-t$</span> </div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the slope of the normal at the point (at $^{2}, 2$ at) of the parabola $y^{2}=4 a x$ ?</div>

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

answer:
<div class="solution">Equation of parabola is $y^{2}=4 a x$<br/>$2 y \frac{d y}{d x}=4 a$<br/>$\therefore \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{2 \mathrm{a}}{\mathrm{y}}, \quad$ [slope of tangent]<br/>So, slope of normal $=-\left(\frac{\mathrm{dx}}{\mathrm{dy}}\right)_{\left(\mathrm{at}^{2}, 2 \mathrm{at}\right)}$<br/>$=-\left(\frac{\mathrm{y}}{2 \mathrm{a}}\right)=-\frac{2 \mathrm{at}}{2 \mathrm{a}}=-\mathrm{t}$</div>


title: what-is-the-slope-of-the-tangent-to-the-curve-x-t-2-3-t-8-y-2-t-2-2-t-5-at-t-2
slug: what-is-the-slope-of-the-tangent-to-the-curve-x-t-2-3-t-8-y-2-t-2-2-t-5-at-t-2-77271
tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the slope of the tangent to the curve $\mathrm{x}=\mathrm{t}^{2}+3 \mathrm{t}-8, \mathrm{y}=2 \mathrm{t}^{2}-2 \mathrm{t}-5$ at $\mathrm{t}=2 ? \quad$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$7 / 6$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$6 / 7$</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">1</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$5 / 6$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$6 / 7$</span> </div>

answer:
<div class="solution">$\frac{\mathrm{dx}}{\mathrm{dt}}=2 \mathrm{t}+3, \frac{\mathrm{dy}}{\mathrm{dt}}=4 \mathrm{t}-2$<br/>$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{dy} / \mathrm{dt}}{\mathrm{d} \mathrm{x} / \mathrm{dt}}=\frac{4 \mathrm{t}-2}{2 \mathrm{t}+3}$<br/>slope at $t=2=\frac{\mathrm{dy}}{\mathrm{dx}} / \mathrm{t}=2=\frac{4(2)-2}{2(2)+3}=\frac{6}{7}$</div>


title: what-is-the-slope-of-the-tangent-to-the-curve-y-sin-1-sin-2-x-at-x-0
slug: what-is-the-slope-of-the-tangent-to-the-curve-y-sin-1-sin-2-x-at-x-0-80000
tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2014 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the slope of the tangent to the curve $y=\sin ^{1}\left(\sin ^{2} x\right)$ at $x=0 ?$</div>

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

answer:
<div class="solution">$\mathrm{y}=\sin ^{-1}\left(\sin ^{2} \mathrm{x}\right)$<br/>$\frac{d y}{d x}=\frac{2 \sin x \cos x}{\sqrt{1-\sin ^{4} x}} \Rightarrow \frac{d y}{d x}=\frac{\sin 2 x}{\sqrt{1-\sin ^{4} x}}$<br/>at $\mathrm{x}=0, \frac{\mathrm{dy}}{\mathrm{dx}}=0$</div>


title: what-is-the-smallest-natural-number-n-such-that-n-is-divisible-by-990
slug: what-is-the-smallest-natural-number-n-such-that-n-is-divisible-by-990-89263
tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2009 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">11</span> </div>
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the smallest natural number $n$ such that $n !$ is divisible by $990 ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">9</span> </li><li class="correct"> <span class="option-label">B</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><li class=""> <span class="option-label">C</span> <span class="option-data">33</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">99</span> </li> </ul>

answer:
<div class="solution">Consider option 'a' Let us take $n=9$ Since, $9 !=9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1=362880$<br/>which is not divisible by 990 .<br/>Now assume, $n=11$ Since $11 !=39916800$<br/>which is divisible by 990 . Thus, required smallest natural number 11</div>


title: what-is-the-smallest-value-of-m-for-which-f-x-x-2-mx-5-is-increasing-in-the-interval-1-x-2
slug: what-is-the-smallest-value-of-m-for-which-f-x-x-2-mx-5-is-increasing-in-the-interval-1-x-2-38539
tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2008 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the smallest value of $\mathrm{m}$ for which $\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}+\mathrm{mx}+5$ is increasing in the interval $1 \leq \mathrm{x} \leq 2 ?$</div>

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

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

answer:
<div class="solution">$f(x)=x^{2}+m x+5$<br/>Consider, option (c) $\mathrm{m}=-2$. $\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}-2 \mathrm{x}+5 \Rightarrow \mathrm{f}^{\prime}(\mathrm{x})=2 \mathrm{x}-2$<br/>It is clear that $\mathrm{f}^{\prime}(\mathrm{x})&gt;0$ in interval $1 \leq \mathrm{x} \leq 2$. $\therefore \quad \mathrm{m}=-2$</div>


title: what-is-the-solution-of-1-2-x-dy-1-2-y-dx-0
slug: what-is-the-solution-of-1-2-x-dy-1-2-y-dx-0-60029
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the solution of $(1+2 \mathrm{x}) \mathrm{dy}-(1-2 \mathrm{y}) \mathrm{dx}=0 ?$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$x-y-2 x y=c$</span> </div>

answer:
<div class="solution">$\begin{aligned} &amp;(1+2 \mathrm{x}) \mathrm{dy}-(1-2 \mathrm{y}) \mathrm{dx}=0 \Rightarrow(1+2 \mathrm{x}) \mathrm{dy}=(1-2 \mathrm{y}) \mathrm{d} \mathrm{x} \\ &amp; \Rightarrow \frac{\mathrm{dy}}{1-2 \mathrm{y}}=\frac{\mathrm{d} \mathrm{x}}{1+2 \mathrm{x}} \end{aligned}$<br/>Integrating both sides, $\int \frac{\mathrm{dy}}{1-2 \mathrm{y}}=\int \frac{\mathrm{dx}}{1+2 \mathrm{x}}$<br/>$\Rightarrow \frac{-1}{2} \log (1-2 \mathrm{y})=\frac{1}{2} \log (1+2 \mathrm{x})+\frac{1}{2} \log \mathrm{c}$<br/>$\Rightarrow \log (1-2 y)+\log (1+2 x)=\log c$<br/>$\Rightarrow(1+2 x)(1-2 y)=c$<br/>$\Rightarrow 1+2 x-2 y-4 x y=c$<br/>$\Rightarrow 2 x-2 y-4 x y=c$<br/>$\Rightarrow x-y-2 x y=c$</div>


title: what-is-the-solution-of-d-x-d-y-2-y-1-satisfying-y-0-0
slug: what-is-the-solution-of-d-x-d-y-2-y-1-satisfying-y-0-0-84271
question: <div class="question">What is the solution of $\frac{d y}{d x}+2 y=1$ satisfying $y(0)=0$ ?</div>
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$y=\frac{1-e^{-2 x}}{2}$</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">B</span> <span class="option-data">$y=\frac{1+e^{-2 x}}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$y=1+e^{x}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$y=\frac{1+e^{x}}{2}$</span> </li> </ul>

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

answer:
<div class="solution">$\frac{\mathrm{dy}}{\mathrm{dx}}+2 \mathrm{y}=1 \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=1-2 \mathrm{y}$<br/>$\int \frac{\mathrm{dy}}{1-2 \mathrm{y}}=\int \mathrm{dx}$<br/>$-\frac{1}{2} \log |1-2 y|=x+C$<br/>at $\mathrm{x}=0, \mathrm{y}=0$<br/>$-\frac{1}{2} \log 1=0+\mathrm{C} \Rightarrow \mathrm{C}=0$<br/>$1-2 \mathrm{y}=\mathrm{e}^{-2 \mathrm{x}}$<br/>$\mathrm{y}=\frac{1-\mathrm{e}^{-2 \mathrm{x}}}{2}$</div>


