# questions

tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2006 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-probability-that-a-student-passes-in-mathematics-is-49-and-that-he-passes-in-physics-is-25-assuming-that-passing-in-mathematics-and-physics-are-in

slug:
the-probability-that-a-student-passes-in-mathematics-is-49-and-that-he-passes-in-physics-is-25-assuming-that-passing-in-mathematics-and-physics-are-in-88382

question:
<div class="question">The probability that a student passes in mathematics is $4 / 9$ and that he passes in physics is $2 / 5$. Assuming that passing in mathematics and physics are independent of each other, what is the probability that he passes in mathematics but fails in physics?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{4}{15}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$\frac{8}{45}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{26}{45}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{19}{45}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{4}{15}$</span> </div>

answer:
<div class="solution">Probability of passing in mathematics $=\frac{4}{9}$<br/>Probability of passing in physics $=\frac{2}{5}$<br/>Probability of failure in physics $=1-\frac{2}{5}=\frac{3}{5}$ Given that both the events are independent. Required probability $=\frac{4}{9} \times \frac{3}{5}=\frac{4}{15}$</div>


title: the-probability-that-an-ordinary-or-a-nonleap-year-has-53-sunday-is
slug: the-probability-that-an-ordinary-or-a-nonleap-year-has-53-sunday-is-98280
question: <div class="question">The probability that an ordinary or a non-leap year has 53 sunday, is</div>
tags: ['Mathematics', 'Probability', 'JEE Main']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{2}{7}$</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">$\frac{3}{7}$</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">$\frac{1}{7}$</span> </div>

answer:
<div class="solution">In a non-leap year, we have 365 days i.e., 52 weeks and one day. So, we may have any day of seven days. Therefore, 53 Sunday, required probability $=\frac{1}{7}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-probability-that-in-a-random-arrangement-of-the-letters-of-the-word-university-the-two-is-do-not-come-together-is

slug:
the-probability-that-in-a-random-arrangement-of-the-letters-of-the-word-university-the-two-is-do-not-come-together-is-10598

question:
<div class="question">The probability that in a random arrangement of the letters of the word 'UNIVERSITY', the two I's do not come together is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$4 / 5$</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">$1 / 5$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1 / 10$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$9 / 10$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4 / 5$</span> </div>

answer:
<div class="solution">$$<br/>\begin{array}{l}<br/>\because 1 \mathrm{U}, 1 \mathrm{~N}, 2 \mathrm{I}, 1 \mathrm{~V}, 1 \mathrm{E}, 1 \mathrm{R}, 1 \mathrm{~S}, 1 \mathrm{~T}, 1 \mathrm{Y} \\<br/>\therefore \text { Total number of possible arrangements }=\frac{10 !}{2 !} \\<br/>\text { and favourable arrangements }=\frac{10 !}{2 !}-9 ! \\<br/>\therefore \text { Required probability }=\frac{\frac{10 !}{2 !}-9 !}{\frac{10 !}{2 !}} \\<br/>=\frac{9 !(5-1)}{9 ! \times 10} \times 2=\frac{4}{5}<br/>\end{array}<br/>$$</div>


title: the-process-during-which-the-differentiation-occurs-without-any-cell-division
slug: the-process-during-which-the-differentiation-occurs-without-any-cell-division-87926
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">The process during which the differentiation occurs without any cell division</div>

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

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

answer:
<div class="solution">Having completed the first meiotic division, these cells give rise to daughter cells called secondary spermatocytes, which divide to complete meiosis to form round spermatids.<br/><br/>The round spermatids do not divide but undergo a complex metamorphosis, called spermiogenesis, to become spermatozoa that are released into the lumen of the seminiferous tubule by a process called spermiation.</div>


title: the-process-in-which-colloids-when-subjected-to-dc-electric-field-move-towards-an-electrode-is
tags: ['Chemistry', 'Surface Chemistry', 'TS EAMCET', 'TS EAMCET 2022 (20 Jul Shift 2)']
answer: <div class="solution">Electrophoresis</div>
source_db: MarksBatch2_P3.db
slug:
the-process-in-which-colloids-when-subjected-to-dc-electric-field-move-towards-an-electrode-is-23567

question:
<div class="question">The process in which colloids, when subjected to DC electric field move towards an electrode is</div>

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


tags: ['Chemistry', 'Amines', 'AP EAMCET', 'AP EAMCET 2023 (18 May Shift 2)']
source_db: MarksBatch2_P3.db
title:
the-product-of-an-amine-x-with-benzene-sulphonyl-chloride-produces-the-product-which-is-insoluble-in-alkali-the-product-of-x-with-ethanoyl-chloride-is

slug:
the-product-of-an-amine-x-with-benzene-sulphonyl-chloride-produces-the-product-which-is-insoluble-in-alkali-the-product-of-x-with-ethanoyl-chloride-is-71097

question:
<div class="question">The product of an amine ' $\mathrm{X}$ ' with benzene sulphonyl chloride produces the product which is insoluble in alkali. The product of ' $\mathrm{X}$ ' with ethanoyl chloride is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{C}_6 \mathrm{H}_5 \mathrm{NHCOCH}_3$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{C}_6 \mathrm{H}_5 \mathrm{~N}\left(\mathrm{CH}_3\right) \mathrm{COCH}_3$</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">$\mathrm{C}_6 \mathrm{H}_5 \mathrm{~N}\left(\mathrm{CH}_3\right) \mathrm{CH}_2 \mathrm{CH}_3$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{C}_6 \mathrm{H}_5 \mathrm{NHCH}_2 \mathrm{CH}_3$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{C}_6 \mathrm{H}_5 \mathrm{~N}\left(\mathrm{CH}_3\right) \mathrm{COCH}_3$</span> </div>

answer:
<div class="solution">A secondary amine gives an insoluble compound upon reaction with Hinsberg reagent.<br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/I-ni6siPW8v13XX9luknnY99xIzdXlPQ_3k_qhG4yg4.original.fullsize.png"/><br/><br/><br/>Thus, ' $\mathrm{X}$ ' will be<img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/WzejB3igC5sY_TWZymM_CaHioCKU--Jc4h7Wvb-3f54.original.fullsize.png"/><br/></div>


title: the-product-of-first-nine-terms-of-a-gp-is-in-general-equal-to-which-one-of-the-following
slug: the-product-of-first-nine-terms-of-a-gp-is-in-general-equal-to-which-one-of-the-following-90058
tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2008 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The product of first nine terms of a GP is, in general, equal to which one of the following?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The 9 th power of the 5 th term</span> </div>

answer:
<div class="solution">Let a be the first term and $\mathrm{r}$, the common ratio First nine terms of a GP are a, ar, ar $^{2}, \ldots .$ ar $^{8}$.<br/>$$<br/>\begin{aligned}<br/>\therefore \quad \mathrm{P} &amp;=\mathrm{a} . \mathrm{ar} \cdot \mathrm{ar}^{2} \ldots . \mathrm{ar}^{8}=\mathrm{a}^{9} \cdot \mathrm{r}^{1+2+\ldots+8} \\<br/>&amp;=\mathrm{a}^{9} \cdot \mathrm{r}^{\frac{8.9}{2}}=\mathrm{a}^{9} \mathrm{r}^{36}=\left(\mathrm{ar}^{4}\right)^{9}=\left(\mathrm{T}_{5}\right)^{9}<br/>\end{aligned}<br/>$$<br/>$=9$ th power of the 5 th term</div>


title: the-product-of-y-the-perpendiculars-from-the-two-points-4-0-to-the-line-3-x-cos-5-y-sin-15-is
slug: the-product-of-y-the-perpendiculars-from-the-two-points-4-0-to-the-line-3-x-cos-5-y-sin-15-is-20983
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2015 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">9</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The product of $\mathrm{y}$ the perpendiculars from the two points $(\pm 4,0)$ to the line $3 x \cos \phi+5 y \sin \phi=15$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">25</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">16</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">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">D</span> <span class="option-data">8</span> </li> </ul>

answer:
<div class="solution">If length of perpendicular be $\mathrm{p}_{1}$ from the point $(4,0)$ $\begin{aligned} \mathrm{p}_{1} &amp;=\left|\frac{12 \cos \phi-15}{\sqrt{(3 \cos \phi)^{2}+(5 \cos \phi)^{2}}}\right| \\ &amp;=\frac{15-12 \cos \phi}{\sqrt{(3 \cos \phi)^{2}+(5 \cos \phi)^{2}}} \end{aligned}$<br/>If length of perpendicular be $\mathrm{p}_{2}$ from the point $(-4,0)$<br/>$p_{2}=\left|\frac{-12 \cos \phi-15}{\sqrt{(3 \cos \phi)^{2}+(5 \cos \phi)^{2}}}\right|$<br/>$\begin{aligned}=&amp; \frac{(12 \cos \phi+15)}{\sqrt{(3 \cos \phi)^{2}+(5 \sin \phi)^{2}}} \\ \mathrm{p}_{1} \cdot \mathrm{p}_{2} &amp;=\frac{(15-12 \cos \phi)(12 \cos \phi+15)}{(3 \cos \phi)^{2}+(5 \sin \phi)^{2}} \\ &amp;=\frac{\left(225-144 \cos ^{2} \phi\right)}{9 \cos ^{2} \phi+25 \sin ^{2} \phi}=\frac{9\left(25-16 \cos ^{2} \phi\right)}{25-16 \cos ^{2} \phi} \\ &amp;=9 \end{aligned}$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2006 (Phase 1)']
answer: <div class="solution">A simple bar diagram is most suitable for this.</div>
source_db: MarksBatch2_P3.db
title:
the-production-of-food-grains-in-maharashtra-is-given-for-the-12-years-from-1992-to-2003-which-one-of-the-following-representations-is-most-suitable-t

slug:
the-production-of-food-grains-in-maharashtra-is-given-for-the-12-years-from-1992-to-2003-which-one-of-the-following-representations-is-most-suitable-t-28198

question:
<div class="question">The production of food grains in Maharashtra is given for the 12 years from 1992 to 2003 . Which one of the following representations is most suitable to depict the data?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A simple bar diagram</span> </div>


tags: ['Biology', 'Environmental Issues', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-products-resulting-from-atmospheric-reactions-of-hydrocarbons-and-nitrogen-oxides-in-the-presence-of-sunlight-are-called

slug:
the-products-resulting-from-atmospheric-reactions-of-hydrocarbons-and-nitrogen-oxides-in-the-presence-of-sunlight-are-called-19603

question:
<div class="question">The products resulting from atmospheric reactions of hydrocarbons and nitrogen oxides in the presence of sunlight are called:</div>

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

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

answer:
<div class="solution">An air pollutant is a substance in the air that can have adverse effects on humans and the ecosystem. The substance can be solid particles, liquid droplets, or gases. A pollutant can be of natural origin or man-made. Secondary pollutants are not emitted directly. Rather, they form in the air when primary pollutants react or interact. Ground-level ozone is a prominent example of a secondary pollutant.</div>


tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2009 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">200</span> </div>
source_db: MarksBatch2_P3.db
title:
the-profit-function-in-rupees-of-a-firm-selling-x-items-x-0-per-week-is-given-by-p-x-3500-400-x-x-how-many-items-should-the-firm-sell-so-that-the-firm

slug:
the-profit-function-in-rupees-of-a-firm-selling-x-items-x-0-per-week-is-given-by-p-x-3500-400-x-x-how-many-items-should-the-firm-sell-so-that-the-firm-21549

question:
<div class="question">The profit function, in rupees, of a firm selling $x$ items $(x \geq 0)$ per week is given by $\mathrm{P}(\mathrm{x})=-3500+(400-\mathrm{x}) \mathrm{x} . \mathrm{How}$<br/>many items should the firm sell so that the firm has maximum profit?</div>

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

answer:
<div class="solution">$\quad P(x)=-3500+(400-x) x=-3500+400 x-x^{2}$<br/>On differentiating w.r.t. $x$, we get $P^{\prime}(x)=400-2 x$<br/>Put $P^{\prime}(x)=0$ for maxima or minima $\Rightarrow 400-2 x=0$<br/>$\Rightarrow x=200$<br/>Now $P^{\prime \prime}(x)=-2 x$<br/>$\Rightarrow P^{\prime \prime}(200)=-400   &lt; 0$<br/>$\therefore P(x)$ is maximum at $x=200$ Hence 200 items should the firm sell so that the firm has maximum profit.</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-projections-of-a-directed-line-segment-on-the-coordinate-axes-are-12-4-3-respectively-what-are-the-direction-cosines-of-the-line-segment

slug:
the-projections-of-a-directed-line-segment-on-the-coordinate-axes-are-12-4-3-respectively-what-are-the-direction-cosines-of-the-line-segment-75442

question:
<div class="question">The projections of a directed line segment on the coordinate axes are $12,4,3$ respectively. What are the direction cosines of the line segment?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\left\langle\frac{12}{13}, \frac{4}{13}, \frac{3}{13}\right\rangle$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left\langle\frac{12}{13},-\frac{4}{13}, \frac{3}{13}\right\rangle$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left\langle\frac{12}{13},-\frac{4}{13},-\frac{3}{13}\right\rangle$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left\langle-\frac{12}{13},-\frac{4}{13}, \frac{3}{13}\right\rangle$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left\langle\frac{12}{13}, \frac{4}{13}, \frac{3}{13}\right\rangle$</span> </div>

answer:
<div class="solution">Direction cosine of line segment $=\left(\frac{12}{13}, \frac{4}{13}, \frac{3}{13}\right)$<br/>Option (a) is correct.</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-projections-of-a-directed-line-segment-on-the-coordinate-axes-are-12-4-3-respectively-what-is-the-length-of-the-line-segment

slug:
the-projections-of-a-directed-line-segment-on-the-coordinate-axes-are-12-4-3-respectively-what-is-the-length-of-the-line-segment-41682

question:
<div class="question">The projections of a directed line segment on the coordinate axes are $12,4,3$ respectively. What is the length of the line segment?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">19 units</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">17 units</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">15 units</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">13 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">13 units</span> </div>

answer:
<div class="solution">The projection of a directed line segment on the co-ordinate axes are $12,4,3$, respectively. 4e Length of the line segment $=\sqrt{12^{2}+4^{2}+3^{2}}$<br/>$=\sqrt{144+16+9}=\sqrt{169}=13$ units<br/>$\therefore \quad$ Option (d) is correct.</div>


title: the-property-of-colloid-is
slug: the-property-of-colloid-is-19422
question: <div class="question">The property of colloid is</div>
tags: ['Chemistry', 'Surface Chemistry', 'NEET']
answer: <div class="solution">Tyndal effect is scattering of light by colloidal soln.</div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Scattering of light</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">settling under gravity</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Dialysis</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Emulsion</span> </li> </ul>

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


title: the-protective-power-of-a-lyophilic-colloidal-sol-is-expressed-in-terms-of
slug: the-protective-power-of-a-lyophilic-colloidal-sol-is-expressed-in-terms-of-95846
tags: ['Chemistry', 'Surface Chemistry', 'AP EAMCET', 'AP EAMCET 2021 (19 Aug Shift 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The protective power of a lyophilic colloidal sol is expressed in terms of</div>

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

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

answer:
<div class="solution"><p>The protective power of lyophilic colloidal sol is expressed in terms of gold number. Gold number is the number of milligrams of the protective colloid which prevent the coagulation of 10 ml of red gold sol. Smaller the gold number higher the protective power of a colloid.</p></div>


title: the-protein-haemoglobin-found-in-humans-can-be-described-having-a-structure
slug: the-protein-haemoglobin-found-in-humans-can-be-described-having-a-structure-76424
tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">The protein haemoglobin found in humans can be described having a ___________ structure.</div>

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

answer:
<div class="solution">When a protein is made up of two or more than two polypeptide held together variously than it form quaternary structure. Protein haemoglobin has quaternary structure as it is made up of 4 polypeptide or subunits. Two of these are identical to each other. Hence two subunits of alpha type and two subunits of beta type together constitutes the human haemoglobin molecule.</div>


title: the-proteins-with-a-prosthetic-group-are-known-as
slug: the-proteins-with-a-prosthetic-group-are-known-as-78882
question: <div class="question">The proteins with a prosthetic group are known as-</div>
tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Complex proteins</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Conjugated proteins</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Secondary proteins</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Essential proteins</span> </li> </ul>

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

answer:
<div class="solution">Conjugated protein <math><mo>=</mo></math> alpha amino acid <math><mo>+</mo></math> non protein material (prosthetic group)</div>


title: the-qrs-complex-in-a-standard-ecg-represents
slug: the-qrs-complex-in-a-standard-ecg-represents-59899
question: <div class="question">The QRS complex in a standard ECG represents:</div>
tags: ['Biology', 'Body Fluids and Circulation', 'NEET', 'NEET 2020 (Phase 1)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Depolarisation of auricles</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Depolarisation of ventricles</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Repolarisation of ventricles</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Repolarisation of auricles</span> </li> </ul>

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

answer:
<div class="solution"><p>An electrocardiogram (ECG), is a graphical representation of the electrical activity of the heart during a cardiac cycle. The machine used to obtain an electrocardiogram is known as electrocardiography and this technique is called electrocardiography. The interpretation of ECG is as follows:<br/><br/>• The <strong>P wave</strong> is a small upward wave that represents electrical excitation (or depolarization) of the atria which leads to contraction of both the atria.<br/>• The <strong>QRS (wave) complex</strong> represents the depolarization of the ventricles, which initiates the ventricular contraction (ventricular systole). The contraction of the ventricles start shortly after Q and marks the beginning of the systole.<br/>• The <strong>T wave</strong> represents the return of the ventricles from excited (depolarized) to a normal state (i.e., repolarisation). The end of the T wave marks the end of the systole.<br/>• Thus, by counting the number of <strong>QRS complexes</strong> that occur in a given time period, the heartbeat rate of an individual can be determined. </p><p><img src="https://cdn-question-pool.getmarks.app/pyq/neet/d1e53202-c542-4c40-b6d1-c91b38c28afb-image.png" style="width: 335px; height: 210px;"/></p></div>


title: the-quadratic-equation-x-2-b-x-4-0-will-have-real-roots-if
slug: the-quadratic-equation-x-2-b-x-4-0-will-have-real-roots-if-18950
question: <div class="question">The quadratic equation $x^{2}+b x+4=0$ will have real roots if</div>
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2013 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\quad b \leq-4$ only</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$b \geq 4$ only</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$-4   &lt; b &lt; 4$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\quad b \leq-4, b \geq 4$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad b \leq-4, b \geq 4$</span> </div>

answer:
<div class="solution">If root are real $b^{2}-4 \times 4 \geq$<br/>$b^{2} \geq 16$<br/>$b \leq-4, b \geq 4$<br/>$\alpha$ and $\beta$ are roots of given equation. $(a \alpha+b)(a \beta+b)=a^{2} \alpha \beta+a b \alpha+a b \beta+b^{2}$<br/>$=a^{2} \alpha \beta+a b(\alpha+\beta)+b^{2}$<br/>From the given quadratic equation<br/>$\alpha+\beta=\frac{-b}{a}, \alpha \beta=\frac{c}{a}$<br/>$a^{2} \times \frac{c}{a}+a b \times-\frac{b}{a}+b^{2}=a c$</div>


tags: ['Physics', 'Units and Dimensions', 'KVPY', 'KVPY 2011 (SB/SX)']
source_db: MarksBatch2_P3.db
title:
the-quantum-hall-resistance-r-h-is-a-fundamental-constant-with-dimensions-of-resistance-if-h-is-plancks-constant-and-e-the-electron-charge-then-the-di

slug:
the-quantum-hall-resistance-r-h-is-a-fundamental-constant-with-dimensions-of-resistance-if-h-is-plancks-constant-and-e-the-electron-charge-then-the-di-81892

question:
<div class="question">The Quantum Hall Resistance $\mathrm{R}_{\mathrm{H}}$ is a fundamental constant with dimensions of resistance. If $\mathrm{h}$ is Planck's constant and e the electron charge, then the dimension of $\mathrm{R}_{\mathrm{H}}$ is the same as -</div>

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

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

answer:
<div class="solution">$\mathrm{R}=\frac{\mathrm{V}}{\mathrm{i}}=\frac{\mathrm{V} \times \mathrm{i}}{\mathrm{i}^{2}}=\frac{\mathrm{P}}{\mathrm{i}^{2}}$<br/>energy $=\mathrm{h} \mathrm{v}=\frac{\mathrm{h}}{\mathrm{t}}$<br/>Power $=\frac{\text { energy }}{\mathrm{t}}$<br/>$\mathrm{P}=\frac{\mathrm{h}}{\mathrm{t}^{2}}$<br/>$\mathrm{i}=\frac{\mathrm{e}}{\mathrm{t}}$<br/>$\frac{\mathrm{P}}{\mathrm{i}^{2}}=\frac{\mathrm{h}}{\mathrm{e}^{2}}$</div>


title: the-quiescent-centre-in-root-meristem-serves-as-a
slug: the-quiescent-centre-in-root-meristem-serves-as-a-58194
question: <div class="question">The quiescent centre in root meristem serves as a</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'AIIMS', 'AIIMS 2003']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">site for storage of food which is utilized during maturation</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">reservoir of growth hormones</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">reserve for replenishment of damaged cells of the meristem</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">region for absorption of water.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">reserve for replenishment of damaged cells of the meristem</span> </div>

answer:
<div class="solution">A zone of inactive cells is present in the central part of the root apex called quiscent centre. It is a hemispherical region of inactive cells present in between the root cap and the active meristematic region of root apex. This zone contains several hundred cells which are characterized by having lower concentration of DNA, RNA and protein. The quiescent centre acts as reservoir of cells and becomes active whenever the previously active initials get damaged or during the establishment of the secondary roots.</div>


tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-radius-of-a-circle-is-uniformly-increasing-at-the-rate-of-3-cm-s-what-is-the-rate-of-increase-in-area-when-the-radius-is-10-cm

slug:
the-radius-of-a-circle-is-uniformly-increasing-at-the-rate-of-3-cm-s-what-is-the-rate-of-increase-in-area-when-the-radius-is-10-cm-81500

question:
<div class="question">The radius of a circle is uniformly increasing at the rate of $3 \mathrm{~cm} / \mathrm{s}$. What is the rate of increase in area, when the radius is $10 \mathrm{~cm} ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$6 \pi \mathrm{cm}^{2} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$10 \pi \mathrm{cm}^{2} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$30 \pi \mathrm{cm}^{2} / \mathrm{s}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$60 \pi \mathrm{cm}^{2} / \mathrm{s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$60 \pi \mathrm{cm}^{2} / \mathrm{s}$</span> </div>

answer:
<div class="solution">Given $\frac{d r}{d t}=3$<br/>Let $\mathrm{A}=$ Area of circle $=\pi \mathrm{r}^{2}$<br/>$\therefore \frac{\mathrm{d} \mathrm{A}}{\mathrm{dt}}=2 \pi \mathrm{r} \cdot \frac{\mathrm{d} \mathrm{r}}{\mathrm{dt}}=6 \pi \mathrm{r}$<br/>Now, $\left.\frac{\mathrm{d} \mathrm{A}}{\mathrm{dt}}\right|_{\mathrm{r}=10}=6 \times 10 \times \pi=60 \pi \mathrm{cm}^{2} / \mathrm{s}$</div>


title: the-radius-of-the-circle-x-2-y-2-x-c-0-passing-through-the-origin-is
slug: the-radius-of-the-circle-x-2-y-2-x-c-0-passing-through-the-origin-is-96391
tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2013 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The radius of the circle $x^{2}+y^{2}+x+c=0$ passing through the origin is</div>

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

answer:
<div class="solution">Circle is passing through origin then $\mathrm{C}=0$ Now, $x^{2}+y^{2}+x=0$<br/>$\mathrm{x}^{2}+\mathrm{x}+\frac{1}{4}-\frac{1}{4}+\mathrm{y}^{2}=0$<br/>$\left(\mathrm{x}+\frac{1}{2}\right)^{2}+\mathrm{y}^{2}=\left(\frac{1}{2}\right)^{2}$</div>


title: the-radius-of-the-sphere-2015-ii-3-x-2-3-y-2-3-z-2-8-x-4-y-8-z-15-0-is
slug: the-radius-of-the-sphere-2015-ii-3-x-2-3-y-2-3-z-2-8-x-4-y-8-z-15-0-is-36010
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2015 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The radius of the sphere $\quad[2015-I I]$ $3 x^{2}+3 y^{2}+3 z^{2}-8 x+4 y+8 z-15=0$ is</div>

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

answer:
<div class="solution">$3 x^{2}+3 y^{2}+3 z^{2}-8 y+4 y+8 z-15=0$<br/>$\Rightarrow x^{2}+y^{2}+z^{2}-\frac{8}{3} x+\frac{4}{3} y+\frac{8}{3} z-5=0$<br/>$\Rightarrow\left(x-\frac{4}{3}\right)^{2}-\frac{16}{9}+\left(y+\frac{2}{3}\right)^{2}-\frac{4}{9}+\left(z+\frac{4}{3}\right)^{2}-\frac{16}{9}-5=0$<br/>$\Rightarrow\left(x-\frac{4}{3}\right)^{2}+\left(y+\frac{2}{3}\right)^{2}+\left(z+\frac{4}{3}\right)^{2}=(3)^{2}$<br/>So radius is 3 .</div>


title: the-random-or-zigzag-motion-of-the-colloidal-particles-in-the-dispersion-medium-is-referred-to-as
tags: ['Chemistry', 'Surface Chemistry', 'JEE Main']
source_db: MarksBatch2_P3.db
slug:
the-random-or-zigzag-motion-of-the-colloidal-particles-in-the-dispersion-medium-is-referred-to-as-94267

question:
<div class="question">The random or zig-zag motion of the colloidal particles in the dispersion medium is referred to as</div>

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

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

answer:
<div class="solution">Correct option is 3. Brownian movement<br/>Colloidal sol particles in a dispersion medium are continuously bombarded from all sides as a result of which it causes zig-zag motion which is known as Brownian motion</div>


title: the-range-of-frequency-bands-used-for-standard-am-broadcast-is
slug: the-range-of-frequency-bands-used-for-standard-am-broadcast-is-98045
question: <div class="question">The range of frequency bands used for standard AM<br/>broadcast is</div>
tags: ['Physics', 'Communication System', 'TS EAMCET', 'TS EAMCET 2022 (19 Jul Shift 1)']
answer: <div class="solution">No solution. Refer to answer key.</div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">540 â 1600 KHz</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">88 â 108 MHz</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">800 â 900 MHz</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">3.7 â 4.2 GHz</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">540 â 1600 KHz</span> </div>


title: the-rank-of-leftbeginarrayccc2-1-1-0-3-1-1-1-1endarrayright-is
slug: the-rank-of-leftbeginarrayccc2-1-1-0-3-1-1-1-1endarrayright-is-34224
tags: ['Mathematics', 'Matrices', 'AP EAMCET', 'AP EAMCET 2020 (18 Sep Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The rank of \(\left[\begin{array}{ccc}2 &amp; 1 &amp; 1 \\ 0 &amp; 3 &amp; -1 \\ 1 &amp; -1 &amp; 1\end{array}\right]\) is</div>

answer:
<div class="solution">\(\begin{aligned}<br/>&amp; \begin{aligned}<br/>A &amp; =\left[\begin{array}{ccc}<br/>2 &amp; 1 &amp; 1 \\<br/>0 &amp; 3 &amp; -1 \\<br/>1 &amp; -1 &amp; 1<br/>\end{array}\right] \\<br/>R_3 \rightarrow &amp; 2 R_3-R_1 \\<br/>&amp; =\left[\begin{array}{ccc}<br/>2 &amp; 1 &amp; 1 \\<br/>0 &amp; 3 &amp; -1 \\<br/>0 &amp; -3 &amp; 1<br/>\end{array}\right] \\<br/>R_3 \rightarrow &amp; R_3+R_2 \\<br/>&amp; =\left[\begin{array}{ccc}<br/>2 &amp; 1 &amp; 1 \\<br/>0 &amp; 3 &amp; -1 \\<br/>0 &amp; 0 &amp; 0<br/>\end{array}\right]<br/>\end{aligned}<br/>\end{aligned}\)<br/>\(\therefore\) Rank of \(A=2\)<br/>Hence, option (b) is correct.</div>


tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-rate-at-which-light-energy-is-converted-into-chemical-energy-of-organic-molecules-in-the-ecosystem-is

slug:
the-rate-at-which-light-energy-is-converted-into-chemical-energy-of-organic-molecules-in-the-ecosystem-is-42634

question:
<div class="question">The rate at which light energy is converted into chemical energy of organic molecules in the ecosystem is:</div>

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


title: the-rate-at-which-light-energy-is-converted-to-the-chemical-energy-of-organic-molecules-is
slug: the-rate-at-which-light-energy-is-converted-to-the-chemical-energy-of-organic-molecules-is-10048
tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">The rate at which light energy is converted to the chemical energy of organic molecules is:</div>

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

answer:
<div class="solution">The rate at which organic molecules are formed in a green plant is called gross productivity. Gross primary productivity of an ecosystem is the rate of production of organic matter during photosynthesis. A considerable amount of GPP is utilised by plants in respiration.</div>


tags: ['Chemistry', 'Chemical Kinetics', 'KCET', 'KCET 2020']
source_db: MarksBatch2_P3.db
title:
the-rate-constant-of-a-reaction-is-given-by-k-pz-e-e-a-rt-under-standard-notation-in-order-to-speed-up-the-reaction-which-of-the-following-factors-has

slug:
the-rate-constant-of-a-reaction-is-given-by-k-pz-e-e-a-rt-under-standard-notation-in-order-to-speed-up-the-reaction-which-of-the-following-factors-has-19602

question:
<div class="question">The rate constant of a reaction is given by $k=P Z e^{-E_{a} / R T}$ under standard notation. In order to speed up the reaction, which of the following factors has to be decreased?</div>

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

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

answer:
<div class="solution">$\therefore k=P Z e^{-E a / R T}$<br/>The above reaction expression is given in terms of exponents. We have to increase the speed of reaction. So, value of $k$ has to be more and as per the given expression.<br/>$k \propto \frac{1}{e^{E_{a} / R T}}$<br/>if $E a$ decreases, than $\left[e^{E_{a} / R T}\right]$ also decreases and $\left[e^{\frac{1}{E_{a} / R T}}\right]$ increases.<br/>$\therefore k$ also increases</div>


tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-rate-of-conversion-of-light-energy-into-the-chemical-energy-of-organic-molecules-in-an-ecosystem-is-called

slug:
the-rate-of-conversion-of-light-energy-into-the-chemical-energy-of-organic-molecules-in-an-ecosystem-is-called-83831

question:
<div class="question">The rate of conversion of light energy into the chemical energy of organic molecules in an ecosystem is called</div>

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

answer:
<div class="solution">The amount of matter found in the organism is called biomass.<br/><br/>Gross primary production (GPP) is the rate at which an ecosystem's producers capture and store a given amount of chemical energy as biomass in a given length of time. (Definition). It is also the rate of conversion of light energy to chemical energy by producers in an ecosystem.<br/><br/>Total production of organic matter is called gross primary productivity and the energy left after utilization of producers is termed net primary productivity. Community productivity is the difference between GPP and the community respiration. The rate of assimilation of food energy by consumers is called secondary productivity and this energy is available to carnivores as they are the consumers.</div>


title: the-rate-of-formation-of-new-organic-matter-by-rabbit-in-a-grassland-is-called
slug: the-rate-of-formation-of-new-organic-matter-by-rabbit-in-a-grassland-is-called-66961
tags: ['Biology', 'Ecosystem', 'NEET', 'NEET 2012 (Mains)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The rate of formation of new organic matter by rabbit in a grassland, is called</div>

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

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

answer:
<div class="solution">The amount of energy accumulated in green plants through the process of photosynthesis is known as primary productivity. It may gross PP (i.e., the total organic matter synthesized) or Net PP (i.e., the weight of organic matter stored). The rate of resynthesis of organic matter by the consumers is known as secondary productivity.</div>


tags: ['Biology', 'Ecosystem', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">GPP</span> </div>
source_db: MarksBatch2_P3.db
title:
the-rate-of-organic-matter-produced-by-producers-in-their-bodies-per-unit-time-and-area-is-called-as

slug:
the-rate-of-organic-matter-produced-by-producers-in-their-bodies-per-unit-time-and-area-is-called-as-48388

question:
<div class="question">The rate of organic matter produced by producers in their bodies per unit time and area is called as</div>

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

answer:
<div class="solution">The amount of energy accumulation in green plants as biomass or organic matter per unit area over a time period is known as primary productivity. The rate of total capture of energy or the rate of the total production of organic material (biomass) during photosynthesis, is known as gross primary productivity.</div>


title: the-rate-of-synthesis-of-organic-matter-by-consumers-is
slug: the-rate-of-synthesis-of-organic-matter-by-consumers-is-55257
question: <div class="question">The rate of synthesis of organic matter by consumers is</div>
tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">net primary productivity</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">gross primary productivity</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">standing state</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">secondary productivity</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">secondary productivity</span> </div>

answer:
<div class="solution">Carnivores are organisms which obtain nutrient by killing and eating other animals. These form the secondary consumers preceded by the herbivore in the food chain. The rate of assimilation of food energy by consumers is called secondary productivity and this energy is available to carnivores as they are the consumers.<br/><br/>Total production of organic matter is called gross primary productivity and the energy left after utilization of producers is termed net primary productivity. </div>


title: the-ratio-e-w-of-relative-strength-of-electromagnetic-force-e-to-weak-nuclear-force-w-is
slug: the-ratio-e-w-of-relative-strength-of-electromagnetic-force-e-to-weak-nuclear-force-w-is-53952
tags: ['Physics', 'Motion In One Dimension', 'TS EAMCET', 'TS EAMCET 2021 (04 Aug Shift 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mfrac><mi>E</mi><mi>W</mi></mfrac></mfenced></math> of relative strength of electromagnetic force <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>E</mi></mfenced></math> to weak nuclear force <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>W</mi></mfenced></math> is, </div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>10</mn><mn>11</mn></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>10</mn><mn>20</mn></msup></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>10</mn><mrow><mo>-</mo><mn>20</mn></mrow></msup></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>10</mn><mn>11</mn></msup></math></span> </div>

answer:
<div class="solution">The fundamental forces in decreasing order of their magnitude are, strong nuclear force <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>)</mo><mo>&gt;</mo></math>the electromagnetic force <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo> </mo><mo>)</mo><mo>&gt;</mo></math> weak nuclear force <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>13</mn></mrow></msup><mo>)</mo><mo>&gt;</mo></math> gravitational force <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>49</mn></mrow></msup><mo>)</mo></math>. So, the relation between electromagnetic force and weak nuclear force is, <br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>E</mi><mi>W</mi></mfrac><mo>=</mo><mfrac><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><msup><mn>10</mn><mrow><mo>-</mo><mn>13</mn></mrow></msup></mfrac><mo>=</mo><msup><mn>10</mn><mn>11</mn></msup></math>. </div>


tags: ['Physics', 'Waves and Sound', 'NEET', 'NEET 2023 (All India)']
source_db: MarksBatch2_P3.db
title:
the-ratio-of-frequencies-of-fundamental-harmonic-produced-by-an-open-pipe-to-that-of-closed-pipe-having-the-same-length-is

slug:
the-ratio-of-frequencies-of-fundamental-harmonic-produced-by-an-open-pipe-to-that-of-closed-pipe-having-the-same-length-is-88379

question:
<div class="question">The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>:</mo><mn>1</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>:</mo><mn>2</mn></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>:</mo><mn>1</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>:</mo><mn>3</mn></math></span> </li> </ul>

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

answer:
<div class="solution"><blockquote><p>Fundamental frequency of open pipe is given by, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mrow><mi>o</mi><mi>p</mi><mi>e</mi><mi>n</mi></mrow></msub><mo>=</mo><mfrac><mi>v</mi><mrow><mn>2</mn><mi>l</mi></mrow></mfrac></math>.</p><p>Fundamental frequency of closed pipe is given by, </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mrow><mi>c</mi><mi>l</mi><mi>o</mi><mi>s</mi><mi>e</mi><mi>d</mi></mrow></msub><mo>=</mo><mfrac><mi>v</mi><mrow><mn>4</mn><mi>l</mi></mrow></mfrac></math>.</p><p>Therefore,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>f</mi><mrow><mi>o</mi><mi>p</mi><mi>e</mi><mi>n</mi></mrow></msub><msub><mi>f</mi><mrow><mi>c</mi><mi>l</mi><mi>o</mi><mi>s</mi><mi>e</mi><mi>d</mi></mrow></msub></mfrac><mo>=</mo><mfrac><mi>v</mi><mrow><mn>2</mn><mi>l</mi></mrow></mfrac><mo>×</mo><mfrac><mrow><mn>4</mn><mi>l</mi></mrow><mi>v</mi></mfrac><mspace linebreak="newline"></mspace><mo>⇒</mo><msub><mi>f</mi><mrow><mi>o</mi><mi>p</mi><mi>e</mi><mi>n</mi></mrow></msub><mo>:</mo><msub><mi>f</mi><mrow><mi>c</mi><mi>l</mi><mi>o</mi><mi>s</mi><mi>e</mi><mi>d</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>:</mo><mn>1</mn></math></p></blockquote></div>


tags: ['Physics', 'Electromagnetic Induction', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-ratio-of-secondary-and-primary-turns-of-stepup-transformer-is-4-1-if-a-current-of-4-a-is-applied-to-the-primary-the-induced-current-in-secondary-w-1

slug:
the-ratio-of-secondary-and-primary-turns-of-stepup-transformer-is-4-1-if-a-current-of-4-a-is-applied-to-the-primary-the-induced-current-in-secondary-w-1-94988

question:
<div class="question">The ratio of secondary and primary turns of step-up transformer is $4: 1 .$ If a current of 4 A is applied to the primary, the induced current in secondary will be</div>

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

answer:
<div class="solution">$\frac{\mathrm{I}_{\mathrm{S}}}{\mathrm{I}_{\mathrm{P}}}=\frac{\mathrm{N}_{\mathrm{P}}}{\mathrm{N}_{\mathrm{S}}}=\frac{1}{4} \Rightarrow \mathrm{I}_{\mathrm{S}}=\frac{1}{4} \times 4=1 \mathrm{~A}$</div>


tags: ['Physics', 'Electromagnetic Induction', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch2_P3.db
title:
the-ratio-of-secondary-and-primary-turns-of-stepup-transformer-is-4-1-if-a-current-of-4-a-is-applied-to-the-primary-the-induced-current-in-secondary-w

slug:
the-ratio-of-secondary-and-primary-turns-of-stepup-transformer-is-4-1-if-a-current-of-4-a-is-applied-to-the-primary-the-induced-current-in-secondary-w-44966

question:
<div class="question">The ratio of secondary and primary turns of step-up transformer is $4: 1 .$ If a current of 4 A is applied to the primary, the induced current in secondary will be</div>

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

answer:
<div class="solution">$\frac{\mathrm{I}_{\mathrm{S}}}{\mathrm{I}_{\mathrm{P}}}=\frac{\mathrm{N}_{\mathrm{P}}}{\mathrm{N}_{\mathrm{S}}}=\frac{1}{4} \Rightarrow \mathrm{I}_{\mathrm{S}}=\frac{1}{4} \times 4=1 \mathrm{~A}$</div>


title: the-ratio-of-the-strengths-of-the-four-fundamental-forces-in-nature-f-g-f-n-f-e-f-w
slug: the-ratio-of-the-strengths-of-the-four-fundamental-forces-in-nature-f-g-f-n-f-e-f-w-86455
tags: ['Physics', 'Laws of Motion', 'AP EAMCET', 'AP EAMCET 2020 (07 Oct Special)']
answer: <div class="solution">No solution. Refer to answer key.</div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The ratio of the strengths of the four fundamental forces in nature, $\mathrm{F}_{\mathrm{G}}: \mathrm{F}_{\mathrm{N}}: \mathrm{F}_{\mathrm{E}}: \mathrm{F}_{\mathrm{W}}=$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1: 10^{26}: 10^{36}: 10^{38}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1: 10^{36}: 10^{26}: 10^{38}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$1: 10^{38}: 10^{36}: 10^{26}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$10^{38}: 1: 10^{26}: 10^{36}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1: 10^{38}: 10^{36}: 10^{26}$</span> </div>


tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-ration-of-roots-of-the-equations-a-x-2-b-x-c-0-and-px-2-qx-r-0-areequal-ifd-1-and-d-2-are-respective-discriminates-then-what-is-d-2-d-1-equal-to

slug:
the-ration-of-roots-of-the-equations-a-x-2-b-x-c-0-and-px-2-qx-r-0-areequal-ifd-1-and-d-2-are-respective-discriminates-then-what-is-d-2-d-1-equal-to-18731

question:
<div class="question">The ration of roots of the equations $a x^{2}+b x+c=0$ and $\mathrm{px}^{2}+\mathrm{qx}+\mathrm{r}=0$ areequal. IfD $_{1}$ and $\mathrm{D}_{2}$ are respective discriminates, then what is $\frac{\mathrm{D}_{1}}{\mathrm{D}_{2}}$ equal to?</div>

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

answer:
<div class="solution">$\frac{\mathrm{D}_{1}}{\mathrm{D}_{2}}=(\text { ratio of coefficient of } x)^{2}=\frac{b^{2}}{q^{2}}$</div>


title: the-reaction-between-an-ester-and-excess-of-grignard-reagent-shall-finally-result-in-a
slug: the-reaction-between-an-ester-and-excess-of-grignard-reagent-shall-finally-result-in-a-88397
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Main']
source_db: MarksBatch2_P3.db
question:
<div class="question">The reaction between an ester and excess of Grignard reagent shall finally result in a</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">Ketone</span> </li> </ul>

answer:
<div class="solution">The reaction between an ester and excess of Grignard reagent gives tertiary alcohol. Hence, option 3 is correct.<br/><img src="https://cdn-question-pool.getmarks.app/modules/qc/qlJG0RZGF9zLoWr6ddam3TOBfGgP06HNMrjhhfjsnOQ.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 's Block Elements', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-reducing-power-of-a-metal-depends-on-various-factors-suggest-the-factor-which-makes-li-metal-the-strongest-reducing-agent-in-aqueous-solution

slug:
the-reducing-power-of-a-metal-depends-on-various-factors-suggest-the-factor-which-makes-li-metal-the-strongest-reducing-agent-in-aqueous-solution-34406

question:
<div class="question">the reducing power of a metal depends on various factors. Suggest the factor which makes Li metal the strongest reducing agent in aqueous solution</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Sublimation enthalpy</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Ionisation enthalpy</span> </li><li class="correct"> <span class="option-label">C</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">D</span> <span class="option-data">Electron-gain 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">Due to high hydration energy of <math><mi mathvariant="normal">L</mi><msup><mrow><mi mathvariant="normal">i</mi></mrow><mrow><mo>+</mo></mrow></msup></math> cation, the standard reduction potential <math><mi mathvariant="normal">L</mi><msup><mrow><mi mathvariant="normal">i</mi></mrow><mrow><mo>+</mo></mrow></msup></math> is more negative among all alkali metal cations hence Li acts as strong reducing agent in water.</div>


title: the-region-of-the-argand-plane-defined-by-z-i-z-i-4-is
slug: the-region-of-the-argand-plane-defined-by-z-i-z-i-4-is-53022
question: <div class="question">The region of the argand plane defined by $|z-i|+|z+i| \leq 4$ is</div>
tags: ['Mathematics', 'Circle', 'VITEEE', 'VITEEE 2006']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">interior of an ellipse</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">exterior of a circle</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">interior and boundary of an ellipse</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">interior of a parabola</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">interior and boundary of an ellipse</span> </div>

answer:
<div class="solution">Given, $|z-i|+|z+i| \leq 4$ <br/>$\Rightarrow|z-(0+i)|+|z-(0-i)| \leq 0$<br/>This equation represent the interior and boundary of ellipse with foci at $(0,1) \&amp;$ $(0,-1)$, whose major axis is along the $y$-axis.</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-regression-coefficients-of-a-bivariate-distribution-are-064-and-036-then-the-correlation-coefficient-of-the-distribution-is

slug:
the-regression-coefficients-of-a-bivariate-distribution-are-064-and-036-then-the-correlation-coefficient-of-the-distribution-is-27895

question:
<div class="question">The regression coefficients of a bivariate distribution are $=0.64$ and $-0.36$. Then the correlation coefficient of the distribution is $\quad$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.48$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$-0.48$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.50$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-0.50$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-0.48$</span> </div>

answer:
<div class="solution">Let $\mathrm{b}_{1}$ $b_{2}=-0.36$<br/>$r=\pm \sqrt{-0.64 \times-0.36}=\pm 0.48$<br/>$\mathrm{b}_{1}   &lt; 0 \&amp; \mathrm{~b}_{2}$<br/>$ &lt; 0$<br/>ã¹ $\mathrm{r}=-0.48$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2014 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: MarksBatch2_P3.db
title:
the-regression-lines-will-be-perpendicular-to-each-other-jf-the-coefficient-of-correlation-r-is-equal-to

slug:
the-regression-lines-will-be-perpendicular-to-each-other-jf-the-coefficient-of-correlation-r-is-equal-to-30505

question:
<div class="question">The regression lines will be perpendicular to each other jf the coefficient of correlation $r$ is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1 only</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1 or $-1$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$-1$ only</span> </li><li class="correct"> <span class="option-label">D</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> </ul>

answer:
<div class="solution">When regression lines perpendicular to each other then angle will be<br/>$\tan \theta=\left\{\left(\frac{1-r^{2}}{r}\right)\left(\frac{\sigma_{x} \cdot \sigma_{y}}{\sigma_{x}^{2}+\sigma_{y}^{2}}\right)\right\}$<br/>$\Rightarrow \tan \frac{\pi}{2}=\left(\frac{1-r^{2}}{r}\right)\left(\frac{\sigma_{x} \cdot \sigma_{y}}{\sigma_{x}^{2}+\sigma_{y}^{2}}\right)$<br/>$\Rightarrow \mathrm{r} .\left(\sigma_{\mathrm{x}}^{2}+\sigma_{\mathrm{y}}^{2}\right)=0$</div>


title: the-relation-has-the-same-father-as-over-the-set-of-children-is
slug: the-relation-has-the-same-father-as-over-the-set-of-children-is-40528
question: <div class="question">The relation 'has the same father as' over the set of children is:</div>
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">only reflexive</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">only symmetric</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">only transitive</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">an equivalence relation</span> </li> </ul>

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

answer:
<div class="solution">The relation 'has the same father as' over the set of children is onlyreflexive. $(\because$ In reflexivity an element isrelated to itself)</div>


title: the-relation-r-1-1-2-2-3-3-1-2-2-3-1-3-on-a-set-a-1-2-3-is
slug: the-relation-r-1-1-2-2-3-3-1-2-2-3-1-3-on-a-set-a-1-2-3-is-49965
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2010 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The relation $R=\{(1,1),$,<br/>$(2,2),(3,3)(1,2),(2,3)$<br/>$(1,3)\}$ on a set $\mathrm{A}=\{1,2,3\}$ is</div>

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

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

answer:
<div class="solution">Let $\mathrm{R}=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}$<br/>Reflexive Since, IR $1,2 \mathrm{R} 2,3 \mathrm{R} 3$ in the set $\mathrm{R}$ $\mathrm{R}$ is reflexive relation Symmetric Since $1 \mathrm{R} 2$ but 2 is not related to 1 in $\mathrm{R}$ $\mathrm{R}$ isnot symmetric relation. Transitive $\mathbb{1 R} 2,2 \mathrm{R} 3 \Rightarrow 1 \mathrm{R}^{3}$<br/>$\mathrm{R}$ is transitive relation Hence, $\mathrm{R}$ isreflexive and transitive only.</div>


title: the-relation-r-in-the-set-z-of-integers-given-by-r-a-b-a-b-is-divisible-by-5-is
slug: the-relation-r-in-the-set-z-of-integers-given-by-r-a-b-a-b-is-divisible-by-5-is-61610
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2013 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The relation $R$ in the set $Z$ of integers given by $R=\{(a, b)$ $a-b$ is divisible by 5 \}is</div>

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

answer:
<div class="solution">For reflexive:<br/>$(a, a)=a-a=0$ is divisible by 5 . For symmetric:<br/>If $(a-b)$ is divisible by 5 , then $b-a=-(a-b)$ is also divisible by 5 . Thus relation is symmetric.<br/>For transitive If $(a-b)$ and $(b-c)$ is divisible by 5 Then $(\mathrm{a}-\mathrm{c})$ is also divisible by 5 .<br/>Thusrelation is transitive $\mathrm{R}$ is an equivalence relation.</div>


title: the-relation-s-is-defined-on-the-set-of-integers-z-as-x-s-y-if-integer-x-devides-integer-y-then
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch2_P3.db
slug:
the-relation-s-is-defined-on-the-set-of-integers-z-as-x-s-y-if-integer-x-devides-integer-y-then-83502

question:
<div class="question">The relation $S$ is defined on the set of integers $Z$ as $x S y$ if integer $x$ devides integer $y$. Then</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$s$ is only reflexive and transitive</span> </div>

answer:
<div class="solution">The relation $\mathrm{S}$ is defined on the set of integers $\mathrm{Z}$ and xSy, if integer $x$ divides integer $y$ Reflexive: Since, every integer divides itself integer $\mathrm{x}$ divides integer $\mathrm{x}$ $\Rightarrow x$ Sx<br/>Hence, $\mathrm{S}$ is reflexive.<br/>Symmetric : Let $\mathrm{x}, \mathrm{y} \in \mathrm{Z}$ such that $\mathrm{xSy}$<br/>L.e., integer $\mathrm{x}$ divides integer $\mathrm{y}$ Now, this does notimplies that integer ydivides integer $\mathrm{x}$<br/>e.g. Take $x=2$ and $y=4$ Then, 2 divides 4 but 4 does not divides 2 .<br/>Thus, $\mathrm{S}$ is not symmetric.<br/>Transitive : Let $x, y, z \in Z$ such that $x$ Sy and $y S z$. $\Rightarrow$ integer $x$ divides integer $y$ and integer y divides integer $\Rightarrow$ integer $\mathrm{x}$ divides integer $\mathrm{z}$ $\Rightarrow \mathrm{xSz}$<br/>Hence, $\mathrm{S}$ is transitive</div>


title: the-relationship-between-standard-reduction-potential-of-cell-and-equilibrium-constant-is-shown-by
tags: ['Chemistry', 'Electrochemistry', 'JEE Main']
source_db: MarksBatch2_P3.db
slug:
the-relationship-between-standard-reduction-potential-of-cell-and-equilibrium-constant-is-shown-by-41937

question:
<div class="question">The relationship between standard reduction potential of cell and equilibrium constant is shown by</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$E_{\text {cell }}^0=\frac{n}{0.059} \log K_c$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$E_{\text {cell }}^0=\frac{0.059}{n} \log K_c$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$E_{\text {cell }}^0=0.059 n \log K_c$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$E_{\text {cell }}^0=\frac{\log K_c}{n}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$E_{\text {cell }}^0=\frac{0.059}{n} \log K_c$</span> </div>

answer:
<div class="solution">$E_{\text {cell }}^o=\frac{2.303 R T}{n F} \log K=\frac{0.0591}{n} \log K_c$ at $298 K$.</div>


title: the-relationship-between-the-pair-of-compounds-shown-above-are-respectively-1
slug: the-relationship-between-the-pair-of-compounds-shown-above-are-respectively-1-66293
tags: ['Chemistry', 'General Organic Chemistry', 'WBJEE', 'WBJEE 2023']
source_db: MarksBatch2_P3.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/UR93AqaeijC-N-W4Fup8KBSN1n_5uhZMrj1oRSQ4Q2k.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/X2wBV1YcmKAAR0P-TVDbJTefeNtLOskP6-GbxJ9pDqs.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/s8NdadrbSaE3c21NF4mA6RyzpaEwb0VpQDI69jMwFFM.original.fullsize.png"/><br/><br/>The relationship between the pair of compounds shown above are respectively,</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">enantiomer, homomer (identical), diastereomer</span> </div>

answer:
<div class="solution">Hint : <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/Hon4bbF8sUxKvGWb_OiZAXkjn4abqmGb6rppTVMu0mo.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/hZNpmVAyBWANNYvjExgRzAUGoGFGhVnTzSujtZ-3Js8.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/ZweCLfI5aH4DBPEC2PvARSRt9pabUoPQd-Lcd5q1M4A.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">85.5</span> </div>
source_db: MarksBatch2_P3.db
title:
the-relative-abundance-of-two-isotopes-of-an-element-with-atomic-weight-85-and-87-is-75-and-25-respectively-then-calculate-the-average-atomic-weight-o

slug:
the-relative-abundance-of-two-isotopes-of-an-element-with-atomic-weight-85-and-87-is-75-and-25-respectively-then-calculate-the-average-atomic-weight-o-48231

question:
<div class="question">The relative abundance of two isotopes of an element with atomic weight <math><mn>85</mn></math> and <math><mn>87</mn></math> is <math><mn>75</mn><mi mathvariant="normal">%</mi></math> and <math><mn>25</mn><mi mathvariant="normal">%</mi></math> respectively. Then calculate the average atomic weight of element</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">86.0</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">85.5</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">75.5</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">40.0</span> </li> </ul>

answer:
<div class="solution">Average atomic weight of element <math><mo>=</mo><mfrac><mrow><mn>85</mn><mo>Ã</mo><mn>3</mn><mo>+</mo><mn>87</mn><mo>Ã</mo><mn>1</mn></mrow><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mn>85.5</mn></math></div>


title: the-remainder-and-the-quotient-of-the-binary-division-101110-2-110-are-respectively
slug: the-remainder-and-the-quotient-of-the-binary-division-101110-2-110-are-respectively-12430
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The remainder and the quotient of the binary division $\begin{array}{ll}(101110)_{2} \div(110), \text { are respectively } &amp; \end{array}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(111)_{2}$ and $(100)_{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$(100)_{2}$ and $(111)_{2}$</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">$(101)_{2}$ and $(101)_{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$(100)_{2}$ and $(100)$.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(100)_{2}$ and $(111)_{2}$</span> </div>

answer:
<div class="solution">$(101110)_{2}=1 \times 2^{5}+0 \times 2^{4}+1 \times 2^{3}+1 \times 2^{2}+1 \times 2^{1}+0 \times 2^{0}$<br/>$=32+0+8+4+2+0$<br/>$=(46)_{10}$<br/>Similarly, $(110)_{2}=1 \times 2^{2}+1 \times 2^{1}+0 \times 2^{4}$<br/>$=4+2$<br/>$=(6)_{10}$<br/>Quotient $=7$ Remainder $=4$ $(7)_{10}=(111)_{2}$ and $(4)_{10}=(100)_{2}$</div>


title: the-right-option-for-the-statement-tyndall-effect-is-exhibited-by-is
slug: the-right-option-for-the-statement-tyndall-effect-is-exhibited-by-is-82261
tags: ['Chemistry', 'Surface Chemistry', 'NEET', 'NEET 2021']
source_db: MarksBatch2_P3.db
question:
<div class="question">The right option for the statement "Tyndall effect is exhibited by", is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>NaCl</mi></math> solution</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Glucose solution</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Starch solution</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Urea solution</span> </li> </ul>

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

answer:
<div class="solution">Tyndall effect is exhibited by colloidal solutions and not true solutions. Starch solution is colloid, so it will exhibit the Tyndall effect.</div>


tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-roots-of-a-x-2-b-x-c-0-are-r-and-s-for-the-roots-of-x-2-p-x-q-0-to-be-r-2-and-s-2-what-must-be-the-value-of-p

slug:
the-roots-of-a-x-2-b-x-c-0-are-r-and-s-for-the-roots-of-x-2-p-x-q-0-to-be-r-2-and-s-2-what-must-be-the-value-of-p-37524

question:
<div class="question">The roots of $A x^{2}+B x+C=0$ are $r$ and $s$. For the roots of $x^{2}+p x+q=0$ to be $r^{2}$ and $s^{2}$, what must be the value of $p$</div>

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

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

answer:
<div class="solution">Since, $r$ and $s$ are the roots of $A x^{2}+B x+C=0$, then<br/>$r+s=-\frac{B}{A}$ and $r s=\frac{C}{A}$<br/>Now, Given roots of $x^{2}+p x+q=0$ be $r^{2}$ and $s^{2}$<br/>$\Rightarrow r^{2}+s^{2}=-p$ and $r^{2} s^{2}=q$<br/>$\Rightarrow \frac{B^{2}}{A^{2}}-\frac{2 C}{A}=-p$<br/>$\Rightarrow \frac{B^{2}-2 A C}{A^{2}}=-p$<br/>$\Rightarrow \quad p=\frac{2 A C-B^{2}}{A^{2}}$</div>


title: the-roots-of-the-equation-1-t-1-1-t-1-1-1-1-1-t-1-0-are
slug: the-roots-of-the-equation-1-t-1-1-t-1-1-1-1-1-t-1-0-are-63919
tags: ['Mathematics', 'Determinants', 'NDA', 'NDA 2013 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$-1,2$</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The roots of the equation $\left|\begin{array}{ccc}1 &amp; \mathrm{t}-1 &amp; 1 \\ \mathrm{t}-1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; \mathrm{t}-1\end{array}\right|=0$ are</div>

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

answer:
<div class="solution">$\begin{array}{ll} &amp; 1(\mathrm{t}-2)-(\mathrm{t}-1)\left[(\mathrm{t}-1)^{2}-1\right]+1(\mathrm{t}-2)=0 \\ \Rightarrow &amp; (\mathrm{t}-2)-\mathrm{t}(\mathrm{t}-1)(\mathrm{t}-2)+(\mathrm{t}-2)=0 \\ &amp; \Rightarrow(\mathrm{t}-2)[1-(\mathrm{t}-1)(\mathrm{t})+1]=0 \\ &amp; \Rightarrow(\mathrm{t}-2)\left(\mathrm{t}^{2}-\mathrm{t}-2\right)=0 \\ &amp; \Rightarrow(\mathrm{t}-2)(\mathrm{t}-2)(\mathrm{t}+1)=0 \\ &amp; \Rightarrow \mathrm{t}=2, \mathrm{t}=-1\end{array}$<br/>Hence, required roots are $-1,2 .$</div>


title: the-roots-of-the-equation-2-a-2-x-2-2-ab-x-b-2-0-when-and-b-0-are
slug: the-roots-of-the-equation-2-a-2-x-2-2-ab-x-b-2-0-when-and-b-0-are-35796
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The roots of the equation $2 a^{2} x^{2}-2 a b x+b^{2}=0$ when. and $b&gt;0$ are</div>

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

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

answer:
<div class="solution">We have, $2 a^{2} x^{2}-2 a b x+b^{2}=0$ Discriminent, $\mathrm{D}=(-2 \mathrm{ab})^{2}-4\left(2 \mathrm{a}^{2}\right)\left(\mathrm{b}^{2}\right)$<br/>$=4 a^{2} b^{2}-8 a^{2} b^{2}=-4 a^{2} b^{2}   &lt; 0$<br/>Roots are always complex.</div>


title: the-roots-of-the-equation-q-r-x-2-r-p-x-p-q-0-are
slug: the-roots-of-the-equation-q-r-x-2-r-p-x-p-q-0-are-13167
question: <div class="question">The roots of the equation $(q-r) x^{2}+(r-p) x+(p-q)=0$ are</div>
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(\mathrm{r}-\mathrm{p}) /(\mathrm{q}-\mathrm{r}), 1 / 2$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$(\mathrm{p}-\mathrm{q}) /(\mathrm{q}-\mathrm{r}), \mathrm{j}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(q-r) /(p-q)$,</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$(r-p) /(p-q), 1 / 2$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(\mathrm{p}-\mathrm{q}) /(\mathrm{q}-\mathrm{r}), \mathrm{j}$</span> </div>

answer:
<div class="solution">Given equation, $(q-r) x^{2}+(r-p) x+(p-q)=0$<br/>On observing the equation, it is clear that 1 is root of equation. If $x=1$, then $q-r+r-p+p-q=0$<br/>1 is one root of given equation. Since, the given equation is quadratic equation, we<br/>know that product of roots is $\frac{\mathrm{c}}{\mathrm{a}}$<br/>Let the second root be $\alpha$.<br/>$\therefore \quad(1)(\alpha)=\frac{\mathrm{p}-\mathrm{q}}{\mathrm{q}-\mathrm{r}} \Rightarrow \alpha=\frac{\mathrm{p}-\mathrm{q}}{\mathrm{q}-\mathrm{r}}$</div>


title: the-roots-of-the-equation-x-2-8-x-16-0
slug: the-roots-of-the-equation-x-2-8-x-16-0-84309
question: <div class="question">The roots of the equation $x^{2}-8 x+16=0$</div>
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2013 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">are imaginary</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">are distinct and real</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">are equal and real</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">cannot be ascertained</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">are equal and real</span> </div>

answer:
<div class="solution">Discriminant, $\mathrm{D}=(-8)^{2}-4 \times 16=0$ Roots are real and equal</div>


title: the-roots-of-the-equation-x-x-1-1-1-0-are-independent-of
slug: the-roots-of-the-equation-x-x-1-1-1-0-are-independent-of-43136
tags: ['Mathematics', 'Determinants', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The roots of the equation $\left|\begin{array}{lll}x &amp; \alpha &amp; 1 \\ \beta &amp; x &amp; 1 \\ \beta &amp; \gamma &amp; 1\end{array}\right|=0$ are independent of</div>

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

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

answer:
<div class="solution">Given $\left|\begin{array}{lll}x &amp; \alpha &amp; 1 \\ \beta &amp; x &amp; 1 \\ \beta &amp; \gamma &amp; 1\end{array}\right|=0$<br/>$\Rightarrow x(x-\gamma)-\alpha(0)+1(\gamma \beta-x \beta)=0$<br/>$\Rightarrow x^{2}-x \gamma+\gamma \beta-x \beta=0$<br/>$\Rightarrow x^{2}-(\gamma+\beta) x+\gamma \beta=0$<br/>$\Rightarrow x=\frac{(\gamma+\beta) \pm \sqrt{\gamma^{2}+\beta^{2}-2 \gamma \beta}}{2}$<br/>( $\because$ roots of Quad. eqn. $a x^{2}+b x+c=0$ are<br/>$\left.\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}\right)$<br/>$\Rightarrow x=\frac{(\gamma+\beta) \pm(\gamma-\beta)}{2}$<br/>$\Rightarrow x=\frac{\gamma+\beta+\gamma-\beta}{2}, \frac{\gamma+\beta-\gamma+\beta}{2}$<br/>$\Rightarrow x=\gamma, \beta .$<br/>Hence, roots of the equation $\left|\begin{array}{lll}x &amp; \alpha &amp; 1 \\ \beta &amp; x &amp; 1 \\ \beta &amp; \gamma &amp; 1\end{array}\right|=0$ are<br/>independent of $\alpha$.</div>


title: the-roots-ofthe-equation-x-p-x-q-r-2-where-p-q-r-are-real-are
slug: the-roots-ofthe-equation-x-p-x-q-r-2-where-p-q-r-are-real-are-59432
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2009 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The roots ofthe equation $(x-p)(x-q)=r^{2}$, where $p, q, r$ are<br/>real, are</div>

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

answer:
<div class="solution">Given, equation is $(x-p)(x-q)=$ Now, $\begin{aligned} D &amp;=\sqrt{(p+q)^{2}-4\left(p q-r^{2}\right)} \\ &amp;=\sqrt{(p-q)^{2}+4 r^{2}} \geq 0 \end{aligned}$<br/>Hence, roots are always real</div>


title: the-roots-that-originate-from-the-base-of-the-stem-are
slug: the-roots-that-originate-from-the-base-of-the-stem-are-37661
question: <div class="question">The roots that originate from the base of the stem are</div>
tags: ['Biology', 'Morphology of Flowering Plants', 'NEET', 'NEET 2020 (Phase 1)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Primary roots</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Prop roots</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Lateral roots</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Fibrous roots</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Fibrous roots</span> </div>

answer:
<div class="solution"><p>In the majority of dicot plants, the root system is formed by the direct elongation of the radicle into the <strong>primary root</strong>. Branches of the primary root are called <strong>secondary roots</strong>. These in turn branch to form tertiary roots. The primary root and its branches constitute the <strong>taproot</strong> system.</p><p><strong>Prop roots:</strong> In trees like the banyan and Indian rubber plant, many adventitious roots arise from the horizontal branches of the stem and grow vertically downwards. They become thick pillar-like and provide mechanical support to the huge trees.</p><p><strong>Stilt/Fibrous roots:</strong> These are small roots growing obliquely from the basal nodes of the main stem. Like prop roots, they also provide mechanical support. </p></div>


title: the-scalar-triple-product-a-b-c-of-three-vectors-a-b-c-determines
slug: the-scalar-triple-product-a-b-c-of-three-vectors-a-b-c-determines-50604
tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The scalar triple product $(\vec{A} \times \vec{B}) \cdot \vec{C}$ of three vectors<br/>$\vec{A}, \vec{B}, \vec{C}$ determines</div>

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

answer:
<div class="solution">The scalar triple product $(\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{B}}) \cdot \overrightarrow{\mathbf{C}}$ of three vectors<br/>$\overrightarrow{\mathbf{A}}, \overrightarrow{\mathbf{B}}, \overrightarrow{\mathbf{C}}$ determines volume of a parallelopiped.</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-scores-of-15-students-in-an-examination-were-recorde-as-10-5-8-16-18-20-8-10-16-20-18-11-16-14-and-12-afte-calculating-the-mean-median-and-mode-an

slug:
the-scores-of-15-students-in-an-examination-were-recorde-as-10-5-8-16-18-20-8-10-16-20-18-11-16-14-and-12-afte-calculating-the-mean-median-and-mode-an-41308

question:
<div class="question">The scores of 15 students in an examination were recorde as $10,5,8,16,18,20,8,10,16,20,18,11,16,14$ and 12 . Afte calculating the mean, median and mode, an error is found One of the values is wrongly written as 16 instead of 18 Which of the following measures of central tendency w1 change?</div>

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

answer:
<div class="solution">Mean of the scores $=\frac{202}{15}$ Mean of the correct scores $=\frac{200}{15}$<br/>i.e., Mean changes. Median is same for both cases i.e., 14 Mode is proportional to mean.</div>


tags: ['Mathematics', 'Statistics', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$6$</span> </div>
source_db: MarksBatch2_P3.db
title:
the-sd-of-15-items-is-6-and-if-each-item-is-decreased-or-increased-by-1-then-standard-deviation-will-be

slug:
the-sd-of-15-items-is-6-and-if-each-item-is-decreased-or-increased-by-1-then-standard-deviation-will-be-49105

question:
<div class="question">The S.D of 15 items is 6 and if each item is decreased or increased by 1 , then standard deviation will be</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">$7$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$91 / 15$</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>

answer:
<div class="solution">If each item of a data is increased or decreased by the same constant, the standard deviation of the data remains unchanged.</div>


title: the-second-degree-equation-x24-y22-x4-y20-represents
slug: the-second-degree-equation-x24-y22-x4-y20-represents-45365
question: <div class="question">The second degree equation \(x^{2}+4 y^{2}-2 x-4 y+2=0\) represents</div>
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">A point</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">An ellipse of semi-major axis 1</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">An ellipse with eccentricity $\frac{\sqrt{3}}{2}$</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">A point</span> </div>

answer:
<div class="solution">$\left(x^{2}-2 x+1\right)+\left(4 y^{2}-4 y+1\right)=0$<br/>$\Rightarrow(x-1)^{2}+(2 y-1)^{2}=0$<br/>$\Rightarrow \quad x=1, y=\frac{1}{2}$<br/>It is a point.</div>


title: the-second-maturation-division-of-the-mammalian-ovum-occurs
slug: the-second-maturation-division-of-the-mammalian-ovum-occurs-96173
question: <div class="question">The second maturation division of the mammalian ovum occurs</div>
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Shortly after ovulation before the ovum makes entry into the Fallopian tube</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Until the nucleus of the sperm has fused with that of the ovum</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">In the Graffian follicle following the first maturation division.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">After the ovum has been penetrated by a sperm</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">After the ovum has been penetrated by a sperm</span> </div>

answer:
<div class="solution">Oogenesis starts with the division of oogonia (gamete mother cells) giving rise to primary oocyte which enters into prophase - I of the meiotic division and gets temporarily arrested at this stage. These primary oocyte gets surrounded by primary, secondary, and tertiary follicles respectively. The tertiary follicle grows in size and completes its first meiotic division to give rise to the haploid secondary oocyte. This secondary oocyte forms a new membrane called zona pellucida surrounding it. During fertilization, the sperm enters into the cytoplasm of the ovum through the zona pellucida and the plasma membrane. This induces the completion of the meiotic division (2<sup>nd</sup> division) of the secondary oocyte. The second meiotic division is also unequal and results in the formation of a second polar body and a haploid ovum (ootid).</div>


tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-second-meiotic-division-of-p-is-unequal-and-results-in-the-formation-of-q-select-the-appropriate-option-for-p-and-q

slug:
the-second-meiotic-division-of-p-is-unequal-and-results-in-the-formation-of-q-select-the-appropriate-option-for-p-and-q-47402

question:
<div class="question">The second meiotic division of <math><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mi mathvariant="normal">P</mi><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo></math> is unequal and results in the formation of <math><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mi mathvariant="normal">Q</mi><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_.</mo></math><br/> <br/>
Select the appropriate option for P and Q.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">P-secondary spermatocytes; Q-spermatids</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">P-primary oocyte; Q-ovum</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">P-secondary oocyte; Q-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">D</span> <span class="option-data">P-primary spermatocytes; Q-spermatids</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">P-secondary oocyte; Q-polar body</span> </div>

answer:
<div class="solution">The entry of sperm into the cytoplasm of secondary oocytes brings the signal to induce the completion of the meiotic division. The second meiotic division of secondary oocyte is unequal which results in the formation of a large size haploid ovum and a tiny haploid cell called a polar body.</div>


tags: ['Physics', 'Waves and Sound', 'AIIMS', 'AIIMS 2010']
source_db: MarksBatch2_P3.db
title:
the-second-overtone-of-an-open-pipe-has-the-same-frequency-as-the-first-overtone-of-a-closed-pipe-2-m-long-the-length-of-the-open-pipe-is

slug:
the-second-overtone-of-an-open-pipe-has-the-same-frequency-as-the-first-overtone-of-a-closed-pipe-2-m-long-the-length-of-the-open-pipe-is-48471

question:
<div class="question">The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe $2 \mathrm{~m}$ long. The length of the open pipe is</div>

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

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

answer:
<div class="solution">Let $L$ be the length of the open pipe. The fundamental frequency of the open pipe is given by<br/>$v=\frac{v}{2 L}, v=$ velocity of sound in air<br/>The second overtone of the open pipe has a<br/><br/><br/>frequency $3 v_O=\frac{3 v}{2 L_O} \mathrm{~Hz}$<br/>The length of the closed pipe $L_C=2 \mathrm{~m}$.<br/>The fundamental frequency of the closed pipe is given by $v=\frac{v}{4 L}$<br/><br/>The first overtone of the closed pipe has a frequency<br/>$$<br/>3 v_C=\frac{3 v}{4 L_C}=\frac{3 v}{4 \times 2}=\frac{3 v}{8} \mathrm{~Hz}<br/>$$<br/>Now $3 v_O=3 v_C$ or $\frac{3 v}{2 L_O}=\frac{3 v}{8}$<br/>or $2 L_O=8$ or $L_O=4 \mathrm{~m}$</div>


title: the-second-trophic-level-in-a-lake-is
slug: the-second-trophic-level-in-a-lake-is-72659
question: <div class="question">The second trophic level in a lake is ___.</div>
tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Phytoplankton</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Zooplankton</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Benthos</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Fishes</span> </li> </ul>

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

answer:
<div class="solution">Zooplankton forms the secondary trophic level in a lake as they are the primary consumers in food chain that is aquatic, feeding upon Phytoplankton.</div>


tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-secondary-metabolites-belonging-to-same-category-are-a-abrin-b-vinblastin-c-rubber-d-ricin-e-carotenoids

slug:
the-secondary-metabolites-belonging-to-same-category-are-a-abrin-b-vinblastin-c-rubber-d-ricin-e-carotenoids-24487

question:
<div class="question">The secondary metabolites belonging to same category are<br/>
a. Abrin<br/>
b. Vinblastin<br/>
c. Rubber<br/>
d. Ricin<br/>
e. Carotenoids</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">a, b only</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">a, b, c only</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">a, d 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">D</span> <span class="option-data">a, c, e only</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">a, d only</span> </div>

answer:
<div class="solution"><p style="text-align: justify;">In animal tissues, one notices the presence of all such<br/>categories of compounds like nitrogen bases, nucleosides or nucleotides, etc. These are called primary metabolites. However, when one analyses plant, fungal, and microbial cells, one would see thousands of compounds other than these called primary metabolites, e.g. alkaloids, flavonoids, rubber, essential oils, antibiotics, colored pigments, scents, gums, spices. These are called secondary metabolites. A list of secondary metabolites is given in the table below.</p><table border="1" cellpadding="1" cellspacing="1" style="width: 500px;"> <tbody> <tr> <td style="text-align: center;">Pigments</td> <td style="text-align: center;">Carotenoids, Anthocyanins,<br/>			etc.</td> </tr> <tr> <td style="text-align: center;">Alkaloids</td> <td style="text-align: center;">Morphine, Codeine, etc.</td> </tr> <tr> <td style="text-align: center;">Terpenoides </td> <td style="text-align: center;">Monoterpenes, Diterpenes etc.<br/>			 </td> </tr> <tr> <td style="text-align: center;">Essential oils </td> <td style="text-align: center;">Lemon grass oil, etc.<br/>			 </td> </tr> <tr> <td style="text-align: center;"><strong>Toxins</strong></td> <td style="text-align: center;"><strong>Abrin, Ricin</strong></td> </tr> <tr> <td style="text-align: center;">Lectins</td> <td style="text-align: center;">Concanavalin A</td> </tr> <tr> <td style="text-align: center;">Drugs</td> <td style="text-align: center;">Vinblastin, curcumin, etc.</td> </tr> <tr> <td style="text-align: center;">Polymeric<br/>			substances</td> <td style="text-align: center;">Rubber, gums, cellulose</td> </tr> </tbody></table><p> </p></div>


title: the-secondary-precursors-of-photochemical-smog-are
slug: the-secondary-precursors-of-photochemical-smog-are-59474
question: <div class="question">The secondary precursors of photochemical smog are</div>
tags: ['Chemistry', 'Environmental Chemistry', 'AP EAMCET', 'AP EAMCET 2021 (23 Aug Shift 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{SO}_2$ and $\mathrm{NO}_2$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{NO}_2$ and hydrocarbons</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{NO}_2$ and PAN</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{O}_3$ and PAN</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution">The primary precursors of photochemical smog are $\mathrm{NO}_2$ and hydrocarbons. The secondary precursors are ozone and PAN (peroxyacyl nitrates).</div>


title: the-secondary-productivity-means
slug: the-secondary-productivity-means-79746
question: <div class="question">The secondary productivity means</div>
tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Rate of increase in the biomass of autotrophs</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Rate of increase in biomass of heterotrophs</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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 rate at which the organic molecules are formed in an autotrophs.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">The rate at which the organic molecules are used in an autotrophs</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Rate of increase in biomass of heterotrophs</span> </div>

answer:
<div class="solution">Secondary productivity is the rate at which organic matter or biomass is stored at the level of consumers.</div>


title: the-secondary-structure-of-a-protein-refers-to-1
slug: the-secondary-structure-of-a-protein-refers-to-1-86098
question: <div class="question">The secondary structure of a protein refers to</div>
tags: ['Chemistry', 'Biomolecules', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">fixed configuration of the polypeptide backbone</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\alpha$ -helical backbone</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">hydrophobic interactions</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">sequence of $\alpha$ -amino acids.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\alpha$ -helical backbone</span> </div>

answer:
<div class="solution">The secondary structure of a protein refers to the shape in which a long peptide chain can exist. There are two different conformations of the peptide linkage present in protein are $\alpha$ -helix and $\beta$ -conformation. The $\alpha$ -helix always has a right handed arrangement. In $\beta$ -conformation all peptide chains are streched out to nearly maximum extension and then laid side by side held together by intermolecular hydrogen bonds. The structure resembles the pleated folds of drapery and therefore is known as $\beta$ -pleated shelt.</div>


title: the-secondary-structure-of-a-protein-refers-to-2
slug: the-secondary-structure-of-a-protein-refers-to-2-95422
question: <div class="question">The secondary structure of a protein refers to</div>
tags: ['Chemistry', 'Biomolecules', 'VITEEE', 'VITEEE 2011']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\alpha$-helical backbone</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">hydrophobic interactions</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">sequence of $\alpha$-amino acids</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">fixed configuration of the polypeptide backbone</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\alpha$-helical backbone</span> </div>

answer:
<div class="solution">Secondary structure involves $\alpha$-helical and $\beta$-pleated sheet like structure. Where as Primary strucure involves sequence of $\alpha$-amino acids polypeptide chain.</div>


title: the-secondary-structure-of-a-protein-refers-to
slug: the-secondary-structure-of-a-protein-refers-to-71493
question: <div class="question">The secondary structure of a protein refers to</div>
tags: ['Chemistry', 'Biomolecules', 'JEE Main', 'JEE Main 2007']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\alpha$-helical backbone<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>hydrophobic interactions<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>sequence of $\alpha$-amino acids<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>fixed configuration of the polypeptide backbone</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\alpha$-helical backbone<br/></span> </div>

answer:
<div class="solution">Secondary structure of proteins involves $\alpha$-helical back bond and $\beta$-sheet structures. These structures are formed as a result of $\mathrm{H}$-bonding between different peptide groups.<br/>Hence, (A) is correct</div>


title: the-secondary-structure-of-protein-is-stabilised-by
slug: the-secondary-structure-of-protein-is-stabilised-by-52190
question: <div class="question">The secondary structure of protein is stabilised by:</div>
tags: ['Chemistry', 'Biomolecules', 'JEE Main', 'JEE Main 2021 (16 Mar Shift 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Peptide bond</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">glycosidic bond</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Hydrogen bonding</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">van der Waals forces</span> </li> </ul>

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

answer:
<div class="solution"><p>The secondary structure of protein includes two type :</p><p>(a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math>-Helix</p><p>(b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi></math>-pleated sheet</p><p>In <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math>-Helix structure, the poly peptide chain is coil around due to presence of Intramolecular <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">H</mi></math>-Bonding.</p></div>


title: the-secondary-structure-of-proteins-is-derived-from
slug: the-secondary-structure-of-proteins-is-derived-from-10275
question: <div class="question">The secondary structure of proteins is derived from</div>
tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Hydrogen bonding</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Peptide linkage</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Folding of chains</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Disulphide linkage</span> </li> </ul>

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

answer:
<div class="solution">Peptide linkages give rise to primary structure of protein and the arrangement of polypeptide chains assumed as a result of hydrogen bonding is called secondary structure of proteins. Folding of chains and disulphide linkage etc. give rise to tertiary structure of protein. <br/><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/5505bd62-d8e2-4d19-bac7-e401c2aed041.png" style="width:2.88681in;height:3.73333in"/></div>


tags: ['Chemistry', 'Coordination Compounds', 'JEE Main', 'JEE Main 2021 (18 Mar Shift 2)']
source_db: MarksBatch2_P3.db
title:
the-secondary-valency-and-the-number-of-hydrogen-bonded-water-molecules-in-cuso-4-5-h-2-o-respectively-are

slug:
the-secondary-valency-and-the-number-of-hydrogen-bonded-water-molecules-in-cuso-4-5-h-2-o-respectively-are-43130

question:
<div class="question">The secondary valency and the number of hydrogen bonded water molecule(s) in <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CuSO</mi><mn>4</mn></msub><mo>·</mo><mn>5</mn><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi></math>, respectively, are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></p></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span> </div>

answer:
<div class="solution"><p>In <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CuSO</mi><mn>4</mn></msub><mo>.</mo><mn>5</mn><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cu</mi></math> is coordinated with 4 water molecules and two more oxygen atoms from Sulphate ion.</p><p>Now fifth water molecule is hydrogen-bonded and is deeply embedded in a crystal. It is not coordinated.</p><p>Only 4 water molecules are coordinated and the fifth is the only hydrogen bonded.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/8d6a163e-4a00-4045-9e8e-b1eff983dacb-image.png" style="width: 382px; height: 256px;"/></p></div>


title: the-secondary-valency-of-platinum-in-tetra-amminedichloroplatinum-iv-chloride-is
slug: the-secondary-valency-of-platinum-in-tetra-amminedichloroplatinum-iv-chloride-is-42845
tags: ['Chemistry', 'Coordination Compounds', 'KCET', 'KCET 2012']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The secondary valency of platinum in tetra amminedichloroplatinum (IV) chloride is</div>

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

answer:
<div class="solution">Secondary valency corresponds to the coordination number. The formula of the given complex is $\left[\mathrm{Pt} \mathrm{Cl}_{2}\left(\mathrm{NH}_{3}\right)_{4}\right] \mathrm{Cl}_{2}$.<br/>In it coordination number of $\mathrm{Pt}=2+4=6$<br/>$\therefore$ Secondary valency of Pt $=6$.</div>


tags: ['Physics', 'Electromagnetic Induction', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-selfinductance-of-two-coils-of-a-transformer-is-20-mh-and-30-mh-what-is-the-resistance-between-them-1

slug:
the-selfinductance-of-two-coils-of-a-transformer-is-20-mh-and-30-mh-what-is-the-resistance-between-them-1-92178

question:
<div class="question">The self-inductance of two coils of a transformer is $20 \mathrm{mH}$ and $30 \mathrm{mH}$. What is the resistance between them?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1.5 \Omega$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$600 \Omega$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Infinite</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Infinite</span> </div>

answer:
<div class="solution">Transformers are built in such a way that both primary and secondary coils are well insulated from each other. Hence, resistance between them is considered to be infinite.</div>


tags: ['Physics', 'Electromagnetic Induction', 'AP EAMCET', 'AP EAMCET 2021 (25 Aug Shift 1)']
source_db: MarksBatch2_P3.db
title:
the-selfinductance-of-two-coils-of-a-transformer-is-20-mh-and-30-mh-what-is-the-resistance-between-them

slug:
the-selfinductance-of-two-coils-of-a-transformer-is-20-mh-and-30-mh-what-is-the-resistance-between-them-24350

question:
<div class="question">The self-inductance of two coils of a transformer is $20 \mathrm{mH}$ and $30 \mathrm{mH}$. What is the resistance between them?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1.5 \Omega$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$600 \Omega$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Infinite</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Infinite</span> </div>

answer:
<div class="solution">Transformers are built in such a way that both primary and secondary coils are well insulated from each other. Hence, resistance between them is considered to be infinite.</div>


title: the-sequence-of-basic-strength-of-alky1-amines-follows-the-order
slug: the-sequence-of-basic-strength-of-alky1-amines-follows-the-order-28610
question: <div class="question">The sequence of basic strength of alky1 amines follows the order</div>
tags: ['Chemistry', 'Amines', 'VITEEE', 'VITEEE 2006']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{RNH}_{2} &lt; \mathrm{R}_{2} \mathrm{NH}&gt;\mathrm{R}_{3} \mathrm{~N}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{R}_{2} \mathrm{NH}_{2} &lt; \mathrm{R}_{2} \mathrm{NH} &lt; \mathrm{R}_{3} \mathrm{~N}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{R}_{2} \mathrm{NH} &lt; \mathrm{RNH}_{2} &lt; \mathrm{R}_{3} \mathrm{~N}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{RNH}_{2} &lt; \mathrm{R}_{2} \mathrm{NH} &lt; \mathrm{R}_{3} \mathrm{~N}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{RNH}_{2} &lt; \mathrm{R}_{2} \mathrm{NH}&gt;\mathrm{R}_{3} \mathrm{~N}$</span> </div>

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


title: the-set-a-x-x-4-4-can-also-be-represented-by
slug: the-set-a-x-x-4-4-can-also-be-represented-by-48372
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The set $\mathrm{A}=\{\mathrm{x}: \mathrm{x}+4=4\}$ can also be represented by</div>

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

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

answer:
<div class="solution">Let $\begin{aligned} \mathrm{A} &amp;=\{\mathrm{x}: \mathrm{x}+4=4\}=\{\mathrm{x}: \mathrm{x}=4-4\} \\ &amp;=\{\mathrm{x}: \mathrm{x}=0\}=\{0\} \end{aligned}$<br/>Let the people who read all three papers $\mathrm{A}, \mathrm{B}, \mathrm{C}=\mathrm{x} \%$ So, people who read only A and $\mathrm{B}$ not $\mathrm{C}=(30-\mathrm{x}) \%$ People who read only $\mathrm{B}$ and $\mathrm{C}$, not $\mathrm{A}=(28-\mathrm{x}) \%$ People who read only A and $\mathrm{C}$, not $\mathrm{B}=(36-\mathrm{x}) \%$<br/>Venn diagram representing these is shown below<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/r-uhoc5Zo9l-I_Pt5zloxmoc8AkgtksdgyMeO5CENUI.original.fullsize.png"/><br/><br/>Remaining numbers in circles are filled asshown below.<br/>People who read only $\mathrm{A}+30-\mathrm{x}+\mathrm{x}+36-\mathrm{x}=42$<br/>People reading only $\mathrm{A}=42-30-36+\mathrm{x}=(\mathrm{x}-24) \%$<br/>Similarly, people who read only $\mathrm{B}=51-(30-\mathrm{x}+\mathrm{x}+28-\mathrm{x})$<br/>$=51-(58-x)=51-58+x=(x-7) \%$<br/>People who read only $\mathrm{C}=68-(36-\mathrm{x}+\mathrm{x}+28-\mathrm{x})$<br/>$68-(64-x)=(x+4) \%$<img src="https://cdn-question-pool.getmarks.app/pyq/nda/OoXimeMc8H5F7rop6cTJkvxEIiFzG1R_vpnk8k4eHH8.original.fullsize.png"/><br/><br/>Let $x \%$ people read all the three newspap<br/>$8 \%$ people do not read any newspapers. $(x-24)+(x-7)+(x+4)+(30-x)+(36-x)+(28-x)+x=92$<br/>$x+98-31=92$<br/>$x=92-67=25$</div>


title: the-set-of-all-points-where-the-function-f-x-1-e-x-2-is-differentiable-is
slug: the-set-of-all-points-where-the-function-f-x-1-e-x-2-is-differentiable-is-61532
tags: ['Mathematics', 'Continuity and Differentiability', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The set of all points, where the function $f(\mathrm{x})=\sqrt{1-\mathrm{e}^{-\mathrm{x}^{2}}}$ is differentiable, is</div>

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

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

answer:
<div class="solution">$\mathrm{f}(\mathrm{x})=\sqrt{1-\mathrm{e}^{-\mathrm{x}^{2}}}$<br/>$\mathrm{f}^{\prime}(\mathrm{x})=\frac{1}{2 \sqrt{1-\mathrm{e}^{-\mathrm{x}^{2}}}} \cdot\left(-\mathrm{e}^{-\mathrm{x}^{2}}\right)(-2 \mathrm{x})$<br/>$f^{\prime}(x)=\frac{x e^{-x^{2}}}{\sqrt{1-e^{-x^{2}}}}$<br/>$\mathrm{f}^{\prime}(\mathrm{x})$ is defined for all values of $\mathrm{x}$, except $0 .$ $\therefore \mathrm{f}(\mathrm{x})$ is differentiable on $(-\infty, 0) \cup(0, \infty)$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2018 (Phase 2)']
answer: <div class="solution">By definition.</div>
source_db: MarksBatch2_P3.db
title:
the-set-of-bivariate-observation-x-1-y-1-x-2-y-2-xn-yn-are-such-that-all-the-values-are-distinct-and-all-the-observations-fall-on-a-straight-line-with

slug:
the-set-of-bivariate-observation-x-1-y-1-x-2-y-2-xn-yn-are-such-that-all-the-values-are-distinct-and-all-the-observations-fall-on-a-straight-line-with-98326

question:
<div class="question">The set of bivariate observation $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right),\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right), \ldots . .(\mathrm{xn}, \mathrm{yn})$<br/>are such that all the values are distinct and all the observations fall on a straight line with non-zero slope. Then the possible values of the correlation coefficient between and $\mathrm{y}$ are $\quad\mathrm{}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0 and 1 only</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">0 and $-1$ only</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">0,1 and $-1$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$-1$ and 1 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> </ul>

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


tags: ['Biology', 'Chemical Coordination and Integration', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-set-of-hormones-which-lead-to-the-formation-of-secondary-messengers-like-cyclic-amp-during-their-mode-of-action-is

slug:
the-set-of-hormones-which-lead-to-the-formation-of-secondary-messengers-like-cyclic-amp-during-their-mode-of-action-is-67068

question:
<div class="question">The set of hormones which lead to the formation of secondary messengers like cyclic AMP during their mode of action is:</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">LH, FSH, ACTH</span> </div>

answer:
<div class="solution">All water-soluble hormones must bind to their specific membrane-bound or extracellular receptors on target cells. This results in the formation of the hormone-receptor complex. Hormones which interact with membrane-bound receptors normally do not enter the target cell, but generate second messengers (e.g., cyclic AMP, IP<sub>3</sub>, Ca<sup>++</sup> etc) which in turn regulate cellular metabolism. E.g. peptide, polypeptide, protein hormones (e.g., insulin, glucagon, pituitary hormones, hypothalamic hormones, etc.)</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-shadow-of-a-tower-standing-on-a-level-plane-is-found-to-be-50-m-longer-when-the-suns-elevation-is-3-0-than-when-it-is-6-0-the-height-of-the-tower-

slug:
the-shadow-of-a-tower-standing-on-a-level-plane-is-found-to-be-50-m-longer-when-the-suns-elevation-is-3-0-than-when-it-is-6-0-the-height-of-the-tower-84586

question:
<div class="question">The shadow of a tower standing on a level plane is found to be $50 \mathrm{~m}$ longer when the Sun's elevation is $30^{\circ}$ than when it is $60^{\circ}$. The height of the tower is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$25 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$25 \sqrt{3} \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$50 \mathrm{~m}$</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">$25 \sqrt{3} \mathrm{~m}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/o-fZUbBSmxQr2pB0Bw9vv3Em_XNo0YlN1607Z2k6-cM.original.fullsize.png"/><br/><br/>Let $\mathrm{AB}$ be the tower and $\mathrm{AC} \&amp; \mathrm{AD}$ be the shadows of the tower. Let $\mathrm{h}$ be the height of the tower. $\operatorname{In} \Delta \mathrm{ABC}, \tan 60^{\circ}=\frac{\mathrm{h}}{\mathrm{x}}$<br/>$\operatorname{In} \Delta \mathrm{ABD}, \tan 30^{\circ}=\frac{\mathrm{h}}{\mathrm{x}+50}$<br/>(i) $\div$ (ii) $\Rightarrow \frac{\sqrt{3}}{\frac{1}{\sqrt{3}}}=\frac{\mathrm{x}+50}{\mathrm{x}}$<br/>$\Rightarrow 3 \mathrm{x}=\mathrm{x}+50$<br/>$\Rightarrow \quad \mathrm{x}=25^{\circ}$<br/>$\Rightarrow \quad \mathrm{h}=\mathrm{x} \sqrt{3}=25 \sqrt{3}$</div>


tags: ['Physics', 'Mathematics in Physics']
options: None
correct_option: None
answer: <div class="solution">(b)</div>
source_db: MarksBatch2_P3.db
title:
the-shells-of-crabs-found-around-a-particular-coastal-location-in-japan-seem-mostly-to-resemble-the-legendary-face-of-a-samurai-given-below-are-two-ex

slug:
the-shells-of-crabs-found-around-a-particular-coastal-location-in-japan-seem-mostly-to-resemble-the-legendary-face-of-a-samurai-given-below-are-two-ex-37256

question:
<div class="question">The shells of crabs found around a particular coastal location in Japan seem mostly to resemble the legendary face of a Samurai. Given below are two explanations of this observed fact. Which of these strikes you as a scientific explanation?<br/>(a) A tragic sea accident several centuries ago drawned a young Samurai. As a tribute to his bravery, nature through its inscrutable ways immortalised his face by imprinting it on the crab shells in that area.<br/>(b) After the sea tragedy, fishermen in that area, in a gesture to honour to their dead hero, let free any crab shell caught by them which accidentally had a shape resembling the face of a samurai. Consequently the particular shape of the crab shell survived longer and therefore in course of time the shape was genetically propagated. This is an example of evalution by artificial selection.<br/>[Note : This interesting illustration taken from Carl Sagan's 'The Cosmos' highlights the fact that often strange and inexplicable facts which on the first sight appear 'supernatural' actually turn out to have simple scientific explanations. Try to think out other examples of this kind].</div>


tags: ['Mathematics', 'Properties of Triangles', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-sides-a-b-c-of-a-triangle-abc-are-in-arithmetic-progression-and-a-is-the-smallest-side-what-is-cos-a-equal-to

slug:
the-sides-a-b-c-of-a-triangle-abc-are-in-arithmetic-progression-and-a-is-the-smallest-side-what-is-cos-a-equal-to-15773

question:
<div class="question">The sides $a, b, c$ of a triangle $\mathrm{ABC}$ are in arithmetic progression and ' $a$ ' is the smallest side. What is $\cos A$ equal to?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{4 c-3 b}{2 c}$</span> </div>

answer:
<div class="solution">Given a, b, c are in arithmetic progression. <br/>$\therefore 2 b=a+c$ ...(i)<br/>Now, we know<br/>$\cos A=\frac{b^{2}+c^{2}-a^{2}}{2 b c}$<br/>$=\frac{b^{2}+c^{2}-(2 b-c)^{2}}{2 b c}($ from 1$)$<br/>$=\frac{b^{2}+c^{2}-4 b^{2}-c^{2}+4 b c}{2 b c}$<br/>$=\frac{-3 b^{2}+4 b c}{2 b c}=\frac{4 c-3 b}{2 c}$</div>


title: the-similarity-of-bone-structure-in-the-forelimbs-of-many-vertebrates-is-an-example-of
slug: the-similarity-of-bone-structure-in-the-forelimbs-of-many-vertebrates-is-an-example-of-33516
tags: ['Biology', 'Evolution', 'NEET', 'NEET 2018']
source_db: MarksBatch2_P3.db
question:
<div class="question">The similarity of bone structure in the forelimbs of many vertebrates is an example of:</div>

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

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

answer:
<div class="solution"><p dir="ltr">The similarity of bone structure in the forelimbs of many vertebrates is an example of homology, The homologous organs have the same fundamental structure but are adapted to perform different functions, eg. forelimbs of man, cheetah, whale, and bat.<br/>Analogous organs show convergent evolution. These organs have similar functions but are different in their structural details and origin. Development of different functional structures from a common ancestral form is called adaptive radiation.</p></div>


title: the-simultaneous-equations-3-x-5-y-7-and-6-x-10-y-18-have
slug: the-simultaneous-equations-3-x-5-y-7-and-6-x-10-y-18-have-85612
question: <div class="question">The simultaneous equations $3 x+5 y=7$ and $6 x+10 y=18$ have</div>
tags: ['Mathematics', 'Determinants', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">no solution</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">infinitely many solutions</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">unique solution</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">any finite number of solutions</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">no solution</span> </div>

answer:
<div class="solution">Given system of equations $3 x+5 y=7$ and $6 x+10 y=18$<br/>This system can be written as $A X=B$ where<br/>$A=\left(\begin{array}{cc}3 &amp; 5 \\ 6 &amp; 10\end{array}\right), X=\left(\begin{array}{l}x \\ y\end{array}\right), B=\left(\begin{array}{c}7 \\ 18\end{array}\right)$<br/>Now, $|A|=30-30=0$<br/>and $(\operatorname{adj} A) B=\left(\begin{array}{cc}10 &amp; -5 \\ -6 &amp; 3\end{array}\right)\left(\begin{array}{c}7 \\ 18\end{array}\right)=\left(\begin{array}{c}-20 \\ -96\end{array}\right) \neq 0$<br/>$\therefore$ system of equations is inconsistent. $\Rightarrow$ system of equations have no solution.</div>


title: the-sine-of-the-angle-between-vectors-a-2-i-6-j-3-k-and-b-4-i-3-j-k
slug: the-sine-of-the-angle-between-vectors-a-2-i-6-j-3-k-and-b-4-i-3-j-k-23124
tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The sine of the angle between vectors $\vec{a}=2 \hat{i}-6 \hat{j}-3 \hat{k}$ and $\vec{b}=4 \hat{i}+3 \hat{j}-\hat{k}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{\sqrt{26}}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{5}{\sqrt{26}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$\frac{5}{26}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{26}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{5}{\sqrt{26}}$</span> </div>

answer:
<div class="solution">Given, $\vec{a}=2 \hat{i}-6 \hat{j}-3 \hat{k}$<br/>$\vec{b}=4 \hat{i}+3 \hat{j}-\hat{k}$<br/>$\vec{a} \cdot \vec{b}=(2 \hat{i}-6 \hat{j}-3 \hat{k}) \cdot(4 \hat{i}+3 \hat{j}-\hat{k})$<br/>$=(2)(4)+(-6)(3)+(-3)(-1)$<br/>$=8-18+3=-7$<br/>$\Rightarrow|\vec{a}||\vec{b}| \cos \theta=-7 \Rightarrow \cos \theta=\frac{-7}{|\vec{a}||\vec{b}|}$<br/>$=\frac{-7}{\sqrt{49} \sqrt{26}}=\frac{-1}{\sqrt{26}}$<br/>$\sin \theta=\sqrt{1-\cos ^{2} \theta}=\sqrt{1-\left(\frac{-1}{\sqrt{26}}\right)^{2}}=\sqrt{1-\frac{1}{26}}$<br/>$=\sqrt{\frac{25}{26}}=\frac{5}{\sqrt{26}}$</div>


tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-sines-of-two-angles-of-a-triangle-are-equal-to-513-and-99101-what-is-the-cosine-of-the-third-angle

slug:
the-sines-of-two-angles-of-a-triangle-are-equal-to-513-and-99101-what-is-the-cosine-of-the-third-angle-85728

question:
<div class="question">The sines of two angles of a triangle are equal to $5 / 13$ and $99 / 101 .$ What is the cosine of the third angle?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$255 / 1313$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$265 / 1313$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$275 / 1313$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">7701313</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$255 / 1313$</span> </div>

answer:
<div class="solution">Let $\sin \theta=\frac{5}{13}$ and $\sin \phi=\frac{99}{101}$<br/>$\therefore \cos \{\pi-(\theta+\phi)\}$<br/>$=-\cos (\theta+\phi)$<br/>$=-\{\cos \theta \cos \phi-\sin \theta \sin \phi\}$<br/>$=-\left\{\sqrt{1-\frac{25}{169}} \sqrt{1-\left(\frac{99}{101}\right)^{2}}-\frac{5}{13} \times \frac{99}{101}\right\}$<br/>$=-\left\{\frac{12}{13} \times \frac{20}{101}-\frac{5}{13} \times \frac{99}{101}\right\}$<br/>$=-\left\{\frac{240}{1313}-\frac{495}{1313}\right\}=\frac{255}{1313}$</div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-sixth-term-of-an-ap-is-2-and-its-common-difference-is-greater-than-1-what-is-the-common-difference-of-the-ap-so-that-the-product-of-the-first-four

slug:
the-sixth-term-of-an-ap-is-2-and-its-common-difference-is-greater-than-1-what-is-the-common-difference-of-the-ap-so-that-the-product-of-the-first-four-80015

question:
<div class="question">The sixth term of an AP is 2 and its common difference is greater than 1<br/>What is the common difference of the AP so that the product of the first, fourth and fifth terms is greatest? $\quad[2016-I I]$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$8 / 5$</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">$9 / 5$</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">$11 / 5$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$8 / 5$</span> </div>

answer:
<div class="solution">Let first term $=\mathrm{a} \&amp;$ common difference $=\mathrm{x}$<br/>$\therefore \quad a+5 x=2 \Rightarrow a=2-5 x$<br/>$\begin{aligned} &amp; \text { Let } \mathrm{P}=\mathrm{T}_{1} \times \mathrm{T}_{4} \times \mathrm{T}_{5} \\ \Rightarrow &amp; \mathrm{P}=\mathrm{a}(\mathrm{a}+3 \mathrm{x})(\mathrm{a}+4 \mathrm{x}) \\ \Rightarrow &amp; \mathrm{P}=(2-5 \mathrm{x})(2-5 \mathrm{x}+3 \mathrm{x})(2-5 \mathrm{x}+4 \mathrm{x}) \\ \Rightarrow &amp; \mathrm{P}=-10 \mathrm{x}^{3}+34 \mathrm{x}^{2}-32 \mathrm{x}+8 \\ &amp; \frac{d p}{d x}=0 \Rightarrow 15 \mathrm{x}^{2}-34 \mathrm{x}+16=0 \\ &amp; \Rightarrow(5 \mathrm{x}-8)(3 \mathrm{x}-2)=0 \\ \Rightarrow &amp; \mathrm{x}=\frac{8}{5},\left[\because x=\frac{2}{3}   &lt; 1\right] \end{aligned}$</div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2016 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$-6$</span> </div>
source_db: MarksBatch2_P3.db
title:
the-sixth-term-of-an-ap-is-2-and-its-common-difference-is-greater-than-1-what-is-the-first-term-of-the-ap-so-that-the-product-of-the-first-fourth-and-

slug:
the-sixth-term-of-an-ap-is-2-and-its-common-difference-is-greater-than-1-what-is-the-first-term-of-the-ap-so-that-the-product-of-the-first-fourth-and-83527

question:
<div class="question">The sixth term of an AP is 2 and its common difference is greater than 1<br/>What is the first term of the AP so that the product of the first, fourth and fifth terms is greatest? $\quad[2016-I I]$</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">$-6$</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">C</span> <span class="option-data">$-8$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-10$</span> </li> </ul>

answer:
<div class="solution">Since, $\mathrm{a}=2-5 \mathrm{x}$<br/>$\Rightarrow \quad a=2-5\left(\frac{8}{5}\right)$<br/>$\Rightarrow \quad a=-6$</div>


title: the-smallest-positive-divisor-greater-than-1-of-a-composite-number-a-is
slug: the-smallest-positive-divisor-greater-than-1-of-a-composite-number-a-is-76227
tags: ['Mathematics', 'Basic of Mathematics', 'KCET', 'KCET 2013']
source_db: MarksBatch2_P3.db
question:
<div class="question">The smallest positive divisor greater than 1 of a composite number $a$ is</div>

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

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

answer:
<div class="solution">By property, the smallest positive divisor greater than 1 of a composite number $a$ is less than or equal to $\sqrt{a}$, which is standard result.</div>


title: the-smallest-positive-integer-n-for-which-1-i-1-i-n-1-is
slug: the-smallest-positive-integer-n-for-which-1-i-1-i-n-1-is-83716
tags: ['Mathematics', 'Complex Number', 'NDA', 'NDA 2017 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The smallest positive integer $n$ for which $\left(\frac{1+i}{1-i}\right)^{n}=1$, is</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">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">8</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">16</span> </li> </ul>

answer:
<div class="solution">$\left(\frac{1+\mathrm{i}}{1-\mathrm{i}}\right)^{\mathrm{n}}=1$<br/>We know, $\mathrm{i}^{2}=-1$ and $\mathrm{i}^{4}=1$. Now, rationalise the denominator.<br/>$\left(\frac{(1+i)(1+i)}{(1-i)(1+i)}\right)^{n}=\left(\frac{1+2 i+i^{2}}{1-i^{2}}\right)^{n}=\left(\frac{1+2 i-i}{1-(-1)}\right)^{n}=\left(\frac{2 i}{2}\right)^{n}=-i^{n}$<br/>The smallest positive integer for which $\mathrm{i}^{\mathrm{n}}=1$ is 4</div>


tags: ['Mathematics', 'Complex Number', 'NDA', 'NDA 2011 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch2_P3.db
title:
the-smallest-positive-integral-value-of-n-for-which-1-i-1-i-n-is-purely-imaginary-with-positive-imaginary-part-is

slug:
the-smallest-positive-integral-value-of-n-for-which-1-i-1-i-n-is-purely-imaginary-with-positive-imaginary-part-is-25267

question:
<div class="question">The smallest positive integral value of $n$ for which $\left(\frac{1-i}{1+i}\right)^{n}$ is purely imaginary with positive imaginary part is</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">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">4</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">5</span> </li> </ul>

answer:
<div class="solution">$\begin{aligned} &amp;\left(\frac{1-i}{1+i}\right)^{n}=\left[\frac{(1-i)^{2}}{(1+i)(1-i)}\right]^{n} \\ &amp;=\left[\frac{1+i^{2}-2 i}{1-i^{2}}\right]^{n}=\left(\frac{-2 i}{2}\right)^{n}=(-i)^{n} \\ &amp; \text { For } n=3 \end{aligned}$<br/>$(-i)^{n}=(-i)^{3}=-i \times-i \times-i=-i^{3}=-(-i)=i$<br/>Which is purely imaginary with positive imaginarypart. <br/>Hence, $n=3$.</div>


title: the-softiron-is-a-suitable-material-for-making-an-electromagnet-this-is-because-softiron-has
slug: the-softiron-is-a-suitable-material-for-making-an-electromagnet-this-is-because-softiron-has-33512
tags: ['Physics', 'Magnetic Properties of Matter', 'JEE Main', 'JEE Main 2022 (24 Jun Shift 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The soft-iron is a suitable material for making an electromagnet. This is because soft-iron has</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">high permeability and low retentivity.</span> </div>

answer:
<div class="solution">Electromagnets are made of soft iron because of its high permeability and low retentivity. High permeability means that the core provides complete linkage of magnetic flux of the primary coil to the secondary coil.  The determination of the magnetism left in the material after the removal of the magnetizing field is known as retentivity. The required condition for the operation of electromagnets is the fast reversal of polarity, so high retentivity is undesirable. So, soft iron core has high permeability and low retentivity.</div>


tags: ['Chemistry', 'Solutions', 'TS EAMCET', 'TS EAMCET 2020 (14 Sep Shift 2)']
source_db: MarksBatch2_P3.db
title:
the-solubility-product-of-a-sparingly-soluble-a-b-2-salt-is-256-1-0-4-m-3-at-2-5-c-the-k-f-of-water-is-18-k-kg-mol-1-the-depression-in-freezing-point-

slug:
the-solubility-product-of-a-sparingly-soluble-a-b-2-salt-is-256-1-0-4-m-3-at-2-5-c-the-k-f-of-water-is-18-k-kg-mol-1-the-depression-in-freezing-point-33824

question:
<div class="question">The solubility product of a sparingly soluble $A B_2$ salt is $2.56 \times 10^{-4} \mathrm{M}^3$ at $25^{\circ} \mathrm{C}$. The $K_f$ of water is $1.8 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$. The depression in freezing point of a standard solution of $A B_2$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0.432 K</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">0.216 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">0.108 K</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">13.824 K</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">0.216 K</span> </div>

answer:
<div class="solution">Let, solubility of $A B_2$ (1:2 type electrolyte) is pure water $=5 \mathrm{~mol} \mathrm{~L}^{-1}=5 \mathrm{M}$<br/>$\Rightarrow K_{\mathrm{sp}}=4 S^3=2.56 \times 10^{-4} \mathrm{M}^3$ (given)<br/>$\therefore S=0.04 \mathrm{M}=0.04 \mathrm{~m}$ (molal) under standard condition of the solution.<br/>Depression of freezing point,<br/>$\Delta T_f=K_f \times m \times i=1.8 \times 0.04 \times 3=0.216 \mathrm{~K}$<br/>$\left[\because\right.$ Assuming complete dissociation of $A B_2$,<br/>van't Hoff factor, $i=3]$</div>


title: the-solution-of-d-x-d-y-x-is
slug: the-solution-of-d-x-d-y-x-is-50206
question: <div class="question">The solution of $\frac{d y}{d x}=|x|$ is: $\quad$</div>
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$y=\frac{x|x|}{2}+c$</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">$y=\frac{|x|}{2}+c$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$y=\frac{x^{2}}{2}+c$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$y=\frac{x^{3}}{2}+c$<br/>Where $c$ is an arbitary constant</span> </li> </ul>

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

answer:
<div class="solution">$\frac{d y}{d x}=|x|$<br/>$\frac{d y}{d x}=x$ for $x \geq 0 ; \frac{d y}{d x}=-x$ for $x   &lt; 0$<br/>$\int \mathrm{dy}=\int \mathrm{x} \mathrm{dx}$<br/>$\mathrm{y}=\frac{\mathrm{x}^{2}}{2}+\mathrm{C}_{1} \quad \ldots(\mathrm{i}) ; \int \mathrm{dy}=-1 \mathrm{x} \mathrm{d} \mathrm{x}$<br/>$\mathrm{y}=-\frac{\mathrm{x}^{2}}{2}+\mathrm{C}_{1}$<br/>From (i) and (ii)<br/>$\mathrm{y}=\frac{\mathrm{x}|\mathrm{x}|}{2}+\mathrm{C}$</div>


title: the-solution-of-dx-dy-1-x-2-y-2-x-2-y-2-is
slug: the-solution-of-dx-dy-1-x-2-y-2-x-2-y-2-is-40125
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The solution of $\frac{\mathrm{dy}}{\mathrm{dx}}=\sqrt{1-\mathrm{x}^{2}-\mathrm{y}^{2}+\mathrm{x}^{2} \mathrm{y}^{2}}$ is</div>

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

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

answer:
<div class="solution">$\quad \because \frac{d y}{d x}=\sqrt{1-x^{2}-y^{2}+x^{2} y^{2}}$<br/>$\frac{d y}{d x}=\sqrt{\left(1-x^{2}\right)\left(1-y^{2}\right)}$<br/>$\Rightarrow \frac{d y}{\sqrt{1-y^{2}}}=\sqrt{1-x^{2}} \cdot d x$<br/>$=\int \frac{\mathrm{dy}}{\sqrt{1-\mathrm{y}^{2}}}=\int \sqrt{1-\mathrm{x}^{2}} \cdot \mathrm{dx}$<br/>[integrating $\mathrm{b} / \mathrm{s}$ ]<br/>$=\sin ^{-1}\left(\frac{\mathrm{y}}{1}\right)=\frac{\mathrm{x}}{2} \sqrt{1-\mathrm{x}^{2}}+\frac{1}{2} \sin ^{-1}\left(\frac{\mathrm{x}}{1}\right)+\mathrm{c}$<br/>$=2 \sin ^{-1} \mathrm{y}=\mathrm{x} \sqrt{1-\mathrm{x}^{2}}+\sin ^{-1} \mathrm{x}+\mathrm{c}$</div>


title: the-solution-of-the-differential-equation-d-x-d-y-cos-y-x-1-is
slug: the-solution-of-the-differential-equation-d-x-d-y-cos-y-x-1-is-89299
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The solution of the differential equation <br/>$\frac{d y}{d x}=\cos (\mathrm{y}-\mathrm{x})+1$ is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{e}^{\mathrm{x}}[\sec (\mathrm{y}-\mathrm{x})-\tan (\mathrm{y}-\mathrm{x})]=\mathrm{c}$</span> </div>

answer:
<div class="solution">$\frac{d y}{d x}=\cos (y-x)+1$<br/>Let $y-x=t \Rightarrow \frac{d y}{d x}-1=\frac{d t}{d x}$<br/>$\therefore(1) \Rightarrow \frac{d t}{d x}+1=\cos t+1$<br/>$\Rightarrow \frac{d t}{d x}=\cos t$<br/>$\Rightarrow \sec t . d t=1 . d x$<br/>$\Rightarrow \int \sec t \cdot d t=\int 1 \cdot d x$<br/>$\Rightarrow \log |\operatorname{sect}+\tan t|=x+c$<br/>$\Rightarrow-\log |\sec t-\tan t|=x+c$<br/>$\Rightarrow \log |\sec t-\tan t|=-x-c$<br/>$\Rightarrow \log (\sec (y-x)-\tan (y-x)=-x-c$<br/>$\Rightarrow \sec (y-x)-\tan (y-x)=e^{-x} \cdot e^{-c}$<br/>$\Rightarrow e^{x}(\sec (y-x)-\tan (y-x))=c$</div>


title: the-solution-of-the-differential-equation-dx-dy-x-y-x-y-2-is
slug: the-solution-of-the-differential-equation-dx-dy-x-y-x-y-2-is-60068
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The solution of the differential equation $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{y} \phi^{\prime}(\mathrm{x})-\mathrm{y}^{2}}{\phi(\mathrm{x})}$<br/>is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{y}=\frac{\phi(\mathrm{x})}{\mathrm{x}+\mathrm{c}}$</span> </div>

answer:
<div class="solution">$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{y} \phi^{\prime}(\mathrm{x})-\mathrm{y}^{2}}{\phi(\mathrm{x})}=\frac{\mathrm{y} \phi^{\prime}(\mathrm{x})}{\phi(\mathrm{x})}-\frac{\mathrm{y}^{2}}{\phi(\mathrm{x})}$<br/>$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{y}^{2} \cdot \phi^{\prime}(\mathrm{x})}{\mathrm{y} \cdot \phi(\mathrm{x})}-\frac{\mathrm{y}^{2}}{\phi(\mathrm{x})}$<br/>$\Rightarrow \frac{1}{\mathrm{y}^{2}}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)=\frac{\phi^{\prime}(\mathrm{x})}{\mathrm{y} \cdot \phi(\mathrm{x})}-\frac{1}{\phi(\mathrm{x})}$<br/>$\Rightarrow \frac{1}{\mathrm{y}^{2}}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)-\frac{1}{\mathrm{y}} \cdot \frac{\phi^{\prime}(\mathrm{x})}{\phi(\mathrm{x})}=\frac{-1}{\phi(\mathrm{x})}$<br/>Let $\mathrm{t}=\frac{-1}{\mathrm{y}} \Rightarrow \frac{\mathrm{dt}}{\mathrm{dx}}=\frac{1}{\mathrm{y}^{2}}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)$<br/>$\Rightarrow \frac{\mathrm{dt}}{\mathrm{dx}}+\mathrm{t} \cdot \frac{\phi^{\prime}(\mathrm{x})}{\phi(\mathrm{x})}=\frac{-1}{\phi(\mathrm{x})}$<br/>$\mathrm{IF}=\mathrm{e}^{\int \frac{\phi^{\prime}(\mathrm{x})}{\phi(\mathrm{x})} \cdot \mathrm{dx}}=\mathrm{e}^{\log \phi(\mathrm{x})}=\phi(\mathrm{x})$<br/>Solution of differential equation is<br/>$\mathrm{t} \cdot \phi(\mathrm{x})=\int \frac{-1}{\phi(\mathrm{x})} \times \phi(\mathrm{x}) \cdot \mathrm{dx}$<br/>$\Rightarrow \frac{-1}{y} \phi(x)=-x-c \Rightarrow \frac{\phi(x)}{y}=x+c \Rightarrow y=\frac{\phi(x)}{x}+c$</div>


tags: ['Mathematics', 'Basic of Mathematics', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-solution-of-the-simultaneous-linear-equations-2-x-y-6-and-3-y-8-4-x-will-also-be-satisfied-by-which-one-of-the-following-linear-equations

slug:
the-solution-of-the-simultaneous-linear-equations-2-x-y-6-and-3-y-8-4-x-will-also-be-satisfied-by-which-one-of-the-following-linear-equations-65936

question:
<div class="question">The solution of the simultaneous linear equations $2 \mathrm{x}+\mathrm{y}=6$ and $3 \mathrm{y}=8+4 \mathrm{x}$ will also be satisfied by which one of the following linear equations?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\quad x+y=5$</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">$2 x+y=5$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\quad 2 x-3 y=10$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 x+3 y=6$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad x+y=5$</span> </div>

answer:
<div class="solution">Given equations $2 \mathrm{x}+\mathrm{y}=6 \Rightarrow 2 \mathrm{x}=6-\mathrm{y}$...(1)<br/>and $3 y=8+2(2 x)$<br/>$\Rightarrow 3 y=8+2(6-y)$ (from(1))<br/>$\Rightarrow 3 y=8+12-2 y$<br/>$\Rightarrow \mathrm{y}=4$ and $\mathrm{x}=1$<br/>Now, equation given in option (a) is satisfied by $\mathrm{x}=1$ and $\mathrm{y}=4$</div>


title: the-solution-of-which-of-the-following-will-be-nonconducting
slug: the-solution-of-which-of-the-following-will-be-nonconducting-14757
question: <div class="question">The solution of which of the following will be non-conducting?</div>
tags: ['Chemistry', 'Coordination Compounds', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/6c222ca0-aea7-4f0c-9f41-258a0629873f.png" style="max-width:100%; object-fit:contain"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/dcbd71a5-543c-4d27-9881-00948f4156dc.png" style="max-width:100%; object-fit:contain"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/aa0bc65f-ed4d-4934-adfe-2fd974206d80.png" style="max-width:100%; object-fit:contain"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/61fe786a-1ea1-4c29-93f4-ede876b43162.png" style="max-width:100%; object-fit:contain"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/aa0bc65f-ed4d-4934-adfe-2fd974206d80.png" style="max-width:100%; object-fit:contain"/></span> </div>

answer:
<div class="solution">Using Werner's theory in this complex all the chlorine atoms are showing secondary valency so they cannot be precipitated.<br/><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/3df7811d-fb13-460d-98d9-0310d6c7fb5b.png" style="max-width:100%; object-fit:contain"/></div>


tags: ['Biology', 'Organisms and Populations', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-species-of-organisms-which-plays-a-vital-role-in-controlling-the-relative-abundance-of-other-species-in-a-community-are-called

slug:
the-species-of-organisms-which-plays-a-vital-role-in-controlling-the-relative-abundance-of-other-species-in-a-community-are-called-40994

question:
<div class="question">The species of organisms which plays a vital role in controlling the relative abundance of other species in a community are called</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Edge species</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Keystone 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">Pioneer species</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Seral species</span> </li> </ul>

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

answer:
<div class="solution">The species that plays an important role in the functioning and stability of the ecosystem by controlling the relative abundance of other species in a community is called keystone species.</div>


tags: ['Biology', 'Biodiversity and its Conservation', 'NEET', 'NEET 2023 (Manipur)']
source_db: MarksBatch2_P3.db
title:
the-species-of-plants-that-plays-a-vital-role-in-controlling-the-relative-abundance-of-other-species-in-a-community-is-called

slug:
the-species-of-plants-that-plays-a-vital-role-in-controlling-the-relative-abundance-of-other-species-in-a-community-is-called-57303

question:
<div class="question">The species of plants that plays a vital role in controlling the relative abundance of other species in a community is called<img src="https://cdn-question-pool.getmarks.app/pyq/neet/FzZ9NmvT7Pw_kx-PbnQw1SNtjbimpbAWNNCKcT4UfcA.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Exotic species</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Keystone 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">Alien species</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Endemic species</span> </li> </ul>

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

answer:
<div class="solution">A species of plant that play vital role in controlling relative abundance of other species in a community is called keystone species. They are important for overall structure and function of an ecosystem. Exotic species or Alien species are organisms that have been introduced into an area outside their normal distribution. Endemic species exist only in one particular geographical region or area.</div>


title: the-species-which-by-definition-has-zero-standard-molar-enthalpy-of-formation-at-298-k-is
slug: the-species-which-by-definition-has-zero-standard-molar-enthalpy-of-formation-at-298-k-is-23279
tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The species which by definition has zero standard molar enthalpy of formation at $298 \mathrm{~K}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{Br}_2(g)$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{Cl}_2(g)$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{H}_2 \mathrm{O}(g)$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{CH}_4(g)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{Cl}_2(g)$<br/></span> </div>

answer:
<div class="solution">$\Delta H_f^{\circ}\left(\mathrm{Cl}_2, g\right)=0$<br/>$\Delta H_f^{\circ}$ of elements in their standard state is taken to be zero. $\mathrm{Cl}_2$ is gas, $\mathrm{Br}_2$ is liquid and $\mathrm{I}_2$ is solid at room temperature.<br/>Energetics<br/>Conceptual, implication of rules/laws III</div>


title: the-species-which-is-going-to-become-extinct-due-to-lack-of-proper-care-would-be-called
slug: the-species-which-is-going-to-become-extinct-due-to-lack-of-proper-care-would-be-called-73023
tags: ['Biology', 'Biodiversity and its Conservation', 'JIPMER', 'JIPMER 2005']
source_db: MarksBatch2_P3.db
question:
<div class="question">The species, which is going to become extinct due to lack of proper care would be called</div>

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

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

answer:
<div class="solution">Taxa whose numbers have been reduced to a critical level or whose habitats have been so drastically reduced that they are deemed to be in immediate danger of extinction are called endangered animals. e.g. Lion tailed macaque, Crocodile, Musk deer, Rhino, etc.</div>


tags: ['Physics', 'Units and Dimensions', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-speed-of-light-c-gravitational-constant-g-and-plancks-constant-h-are-taken-as-fundamental-units-in-a-system-the-dimensions-of-time-in-this-new-sys-1

slug:
the-speed-of-light-c-gravitational-constant-g-and-plancks-constant-h-are-taken-as-fundamental-units-in-a-system-the-dimensions-of-time-in-this-new-sys-1-55770

question:
<div class="question"><div> <p align="left" style="text-align:left;"><span>The speed of light <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>c</mi></mfenced></math>, gravitational constant <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtext mathvariant="italic">G</mtext></mfenced></math> and Planckâs constant <math> <mrow> <mfenced> <mi>h</mi> </mfenced></mrow> </math> are taken as fundamental units in a system. The dimensions of time in this new system should be:</span></p> </div> </div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><div><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <msup> <mi>G</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext>â</mtext><msup> <mi>h</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext>â</mtext><msup> <mi>c</mi> <mrow> <mfrac> <mrow> <mo>â</mo><mn>5</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </math> </span></p></div></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><div><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <msup> <mi>G</mi> <mrow> <mfrac> <mrow> <mo>−</mo><mn>1</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </msup> <mtext> </mtext><msup> <mi>h</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext> </mtext><msup> <mi>c</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </math> </span></p></div></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><div><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <msup> <mi>G</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext> </mtext><msup> <mi>h</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext> </mtext><msup> <mi>c</mi> <mrow> <mfrac> <mrow> <mo>−</mo><mn>3</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </math> </span></p></div></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><div><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <msup> <mi>G</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext> </mtext><msup> <mi>h</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext> </mtext><msup> <mi>c</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </math> </span></p></div></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><div><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <msup> <mi>G</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext>â</mtext><msup> <mi>h</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext>â</mtext><msup> <mi>c</mi> <mrow> <mfrac> <mrow> <mo>â</mo><mn>5</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </math> </span></p></div></span> </div>

answer:
<div class="solution"><div><p align="left" style="text-align:left;"><span>Let time,  <math> <mrow> <mi>T</mi><mo>â</mo><msup> <mi>c</mi> <mi>X</mi> </msup> <msup> <mi>G</mi> <mi>Y</mi> </msup> <msup> <mi>h</mi> <mi>Z</mi> </msup> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mo>â</mo><mi>T</mi><mo>=</mo><mi>k</mi><msup> <mi>c</mi> <mi>X</mi> </msup> <msup> <mi>G</mi> <mi>Y</mi> </msup> <msup> <mi>h</mi> <mi>Z</mi> </msup> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span>Taking dimensions on both sides</span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mo stretchy="false">[</mo><msup> <mi>M</mi> <mn>0</mn> </msup> <msup> <mi>L</mi> <mn>0</mn> </msup> <msup> <mi>T</mi> <mn>1</mn> </msup> <mo stretchy="false">]</mo><mo>=</mo><msup> <mrow> <mo stretchy="false">[</mo><mi>L</mi><msup> <mi>T</mi> <mrow> <mo>â</mo><mn>1</mn> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <mi>X</mi> </msup> <msup> <mrow> <mo stretchy="false">[</mo><msup> <mi>M</mi> <mrow> <mo>â</mo><mn>1</mn> </mrow> </msup> <msup> <mi>L</mi> <mn>3</mn> </msup> <msup> <mi>T</mi> <mrow> <mo>â</mo><mn>2</mn> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <mi>Y</mi> </msup> <msup> <mrow> <mo stretchy="false">[</mo><mi>M</mi><msup> <mi>L</mi> <mn>2</mn> </msup> <msup> <mi>T</mi> <mrow> <mo>â</mo><mn>1</mn> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <mi>Z</mi> </msup> </mrow> </math> </span></p><p align="left" style="text-align:left;"><i><span>i.e.,</span></i></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mo stretchy="false">[</mo><msup> <mi>M</mi> <mn>0</mn> </msup> <msup> <mi>L</mi> <mn>0</mn> </msup> <msup> <mi>T</mi> <mn>1</mn> </msup> <mo stretchy="false">]</mo><mo>=</mo><mo stretchy="false">[</mo><msup> <mi>M</mi> <mrow> <mo>â</mo><mi>Y</mi><mo>+</mo><mi>Z</mi> </mrow> </msup> <msup> <mi>L</mi> <mrow> <mi>X</mi><mo>+</mo><mn>3</mn><mi>Y</mi><mo>+</mo><mn>2</mn><mi>Z</mi> </mrow> </msup> <msup> <mi>T</mi> <mrow> <mo>â</mo><mi>X</mi><mo>â</mo><mn>2</mn><mi>Y</mi><mo>â</mo><mi>Z</mi> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span>Equating powers of <math> <mrow> <mi>M</mi><mo>,</mo><mtext> </mtext><mi>L</mi></mrow></math>, and <math> <mi>T</mi></math>, on both sides, we get â</span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mo>â</mo><mi>Y</mi><mo>+</mo><mi>Z</mi><mo>=</mo><mn>0</mn><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mn>...</mn><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>X</mi><mo>+</mo><mn>3</mn><mi>Y</mi><mo>+</mo><mn>2</mn><mi>Z</mi><mo>=</mo><mn>0</mn><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mn>...</mn><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mo>â</mo><mi>X</mi><mo>â</mo><mn>2</mn><mi>Y</mi><mo>â</mo><mi>Z</mi><mo>=</mo><mn>1</mn><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mn>...</mn><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span>From equation (i)</span></p><p align="left" style="text-align:left;"><span>Adding (2) and (3) </span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>Y</mi><mo>+</mo><mi>Z</mi><mo>=</mo><mn>1</mn> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span>or           <math> <mrow> <mn>2</mn><mi>Y</mi><mo>=</mo><mn>1</mn><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mrow><mo>(</mo> <mrow> <mo>âµ</mo><mtext>â</mtext><mtext>â</mtext><mi>Z</mi><mo>=</mo><mi>Y</mi> </mrow> <mo>)</mo></mrow> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mo>â´</mo><mi>Z</mi><mo>=</mo><mi>Y</mi><mo>=</mo><mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span>Putting these values in (2), we get â</span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>X</mi><mo>+</mo><mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>+</mo><mn>1</mn><mo>=</mo><mn>0</mn><mtext>â</mtext><mtext>â</mtext><mi>or</mi><mtext>â</mtext><mtext>â</mtext><mi>X</mi><mo>=</mo><mfrac> <mrow> <mo>â</mo><mn>5</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span>Hence,  <math> <mrow> <mo stretchy="false">[</mo><mi>T</mi><mo stretchy="false">]</mo><mo>=</mo><mo stretchy="false">[</mo><msup> <mi>G</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext>â</mtext><msup> <mi>h</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext>â</mtext><msup> <mi>c</mi> <mrow> <mfrac> <mrow> <mo>â</mo><mn>5</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> </math> </span></p></div></div>


tags: ['Physics', 'Units and Dimensions', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-speed-of-light-c-gravitational-constant-g-and-plancks-constant-h-are-taken-as-fundamental-units-in-a-system-the-dimensions-of-time-in-this-new-sys

slug:
the-speed-of-light-c-gravitational-constant-g-and-plancks-constant-h-are-taken-as-fundamental-units-in-a-system-the-dimensions-of-time-in-this-new-sys-27365

question:
<div class="question"><div> <p align="left" style="text-align:left;"><span>The speed of light <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>c</mi></mfenced></math>, gravitational constant <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtext mathvariant="italic">G</mtext></mfenced></math> and Planckâs constant <math> <mrow> <mfenced> <mi>h</mi> </mfenced></mrow> </math> are taken as fundamental units in a system. The dimensions of time in this new system should be:</span></p> </div> </div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><div><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <msup> <mi>G</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext>â</mtext><msup> <mi>h</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext>â</mtext><msup> <mi>c</mi> <mrow> <mfrac> <mrow> <mo>â</mo><mn>5</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </math> </span></p></div></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><div><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <msup> <mi>G</mi> <mrow> <mfrac> <mrow> <mo>−</mo><mn>1</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </msup> <mtext> </mtext><msup> <mi>h</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext> </mtext><msup> <mi>c</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </math> </span></p></div></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><div><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <msup> <mi>G</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext> </mtext><msup> <mi>h</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext> </mtext><msup> <mi>c</mi> <mrow> <mfrac> <mrow> <mo>−</mo><mn>3</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </math> </span></p></div></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><div><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <msup> <mi>G</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext> </mtext><msup> <mi>h</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext> </mtext><msup> <mi>c</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </math> </span></p></div></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><div><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <msup> <mi>G</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext>â</mtext><msup> <mi>h</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext>â</mtext><msup> <mi>c</mi> <mrow> <mfrac> <mrow> <mo>â</mo><mn>5</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </math> </span></p></div></span> </div>

answer:
<div class="solution"><div><p align="left" style="text-align:left;"><span>Let time,  <math> <mrow> <mi>T</mi><mo>â</mo><msup> <mi>c</mi> <mi>X</mi> </msup> <msup> <mi>G</mi> <mi>Y</mi> </msup> <msup> <mi>h</mi> <mi>Z</mi> </msup> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mo>â</mo><mi>T</mi><mo>=</mo><mi>k</mi><msup> <mi>c</mi> <mi>X</mi> </msup> <msup> <mi>G</mi> <mi>Y</mi> </msup> <msup> <mi>h</mi> <mi>Z</mi> </msup> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span>Taking dimensions on both sides</span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mo stretchy="false">[</mo><msup> <mi>M</mi> <mn>0</mn> </msup> <msup> <mi>L</mi> <mn>0</mn> </msup> <msup> <mi>T</mi> <mn>1</mn> </msup> <mo stretchy="false">]</mo><mo>=</mo><msup> <mrow> <mo stretchy="false">[</mo><mi>L</mi><msup> <mi>T</mi> <mrow> <mo>â</mo><mn>1</mn> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <mi>X</mi> </msup> <msup> <mrow> <mo stretchy="false">[</mo><msup> <mi>M</mi> <mrow> <mo>â</mo><mn>1</mn> </mrow> </msup> <msup> <mi>L</mi> <mn>3</mn> </msup> <msup> <mi>T</mi> <mrow> <mo>â</mo><mn>2</mn> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <mi>Y</mi> </msup> <msup> <mrow> <mo stretchy="false">[</mo><mi>M</mi><msup> <mi>L</mi> <mn>2</mn> </msup> <msup> <mi>T</mi> <mrow> <mo>â</mo><mn>1</mn> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <mi>Z</mi> </msup> </mrow> </math> </span></p><p align="left" style="text-align:left;"><i><span>i.e.,</span></i></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mo stretchy="false">[</mo><msup> <mi>M</mi> <mn>0</mn> </msup> <msup> <mi>L</mi> <mn>0</mn> </msup> <msup> <mi>T</mi> <mn>1</mn> </msup> <mo stretchy="false">]</mo><mo>=</mo><mo stretchy="false">[</mo><msup> <mi>M</mi> <mrow> <mo>â</mo><mi>Y</mi><mo>+</mo><mi>Z</mi> </mrow> </msup> <msup> <mi>L</mi> <mrow> <mi>X</mi><mo>+</mo><mn>3</mn><mi>Y</mi><mo>+</mo><mn>2</mn><mi>Z</mi> </mrow> </msup> <msup> <mi>T</mi> <mrow> <mo>â</mo><mi>X</mi><mo>â</mo><mn>2</mn><mi>Y</mi><mo>â</mo><mi>Z</mi> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span>Equating powers of <math> <mrow> <mi>M</mi><mo>,</mo><mtext> </mtext><mi>L</mi></mrow></math>, and <math> <mi>T</mi></math>, on both sides, we get â</span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mo>â</mo><mi>Y</mi><mo>+</mo><mi>Z</mi><mo>=</mo><mn>0</mn><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mn>...</mn><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>X</mi><mo>+</mo><mn>3</mn><mi>Y</mi><mo>+</mo><mn>2</mn><mi>Z</mi><mo>=</mo><mn>0</mn><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mn>...</mn><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mo>â</mo><mi>X</mi><mo>â</mo><mn>2</mn><mi>Y</mi><mo>â</mo><mi>Z</mi><mo>=</mo><mn>1</mn><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mn>...</mn><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span>From equation (i)</span></p><p align="left" style="text-align:left;"><span>Adding (2) and (3) </span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>Y</mi><mo>+</mo><mi>Z</mi><mo>=</mo><mn>1</mn> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span>or           <math> <mrow> <mn>2</mn><mi>Y</mi><mo>=</mo><mn>1</mn><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mrow><mo>(</mo> <mrow> <mo>âµ</mo><mtext>â</mtext><mtext>â</mtext><mi>Z</mi><mo>=</mo><mi>Y</mi> </mrow> <mo>)</mo></mrow> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mo>â´</mo><mi>Z</mi><mo>=</mo><mi>Y</mi><mo>=</mo><mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span>Putting these values in (2), we get â</span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mi>X</mi><mo>+</mo><mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>+</mo><mn>1</mn><mo>=</mo><mn>0</mn><mtext>â</mtext><mtext>â</mtext><mi>or</mi><mtext>â</mtext><mtext>â</mtext><mi>X</mi><mo>=</mo><mfrac> <mrow> <mo>â</mo><mn>5</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span>Hence,  <math> <mrow> <mo stretchy="false">[</mo><mi>T</mi><mo stretchy="false">]</mo><mo>=</mo><mo stretchy="false">[</mo><msup> <mi>G</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext>â</mtext><msup> <mi>h</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mtext>â</mtext><msup> <mi>c</mi> <mrow> <mfrac> <mrow> <mo>â</mo><mn>5</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> </math> </span></p></div></div>


title: the-sporophylls-forms-a-distinct-compact-structures-called
slug: the-sporophylls-forms-a-distinct-compact-structures-called-31548
question: <div class="question">The sporophylls forms a distinct compact structures called ________ .</div>
tags: ['Biology', 'Plant Kingdom', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">calyptra</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">indusium</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">stobili cones</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">sporangium</span> </li> </ul>

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

answer:
<div class="solution">The sporophytes bear sporangia that are subtended by leaf-like appendages called sporophylls. In some cases, sporophylls may form distinct compact structures called strobili or cones, especially in <em>Selaginella, Equisetum</em>. The sporangia produce spores by meiosis in spore mother cells. The spores germinate to give rise to the inconspicuous, small but multicellular prothallus.</div>


title: the-stability-of-a-lyophobic-colloid-is-due-to
slug: the-stability-of-a-lyophobic-colloid-is-due-to-71924
question: <div class="question">The stability of a lyophobic colloid is due to</div>
tags: ['Chemistry', 'Surface Chemistry', 'KCET', 'KCET 2013']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">adsorption of covalent molecules on the colloid</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">the size of the particles</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">the charge on the particles</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Tyndall effect</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">the charge on the particles</span> </div>

answer:
<div class="solution">The stability of a lyophobic colloidal solution is due to the fact that the colloidal particles in the sol are electrically charged. The particles, therefore repel one another and do not coalesce (come close together) to form large non-colloidal particles Colloidal particles carry either positive or negative charge. All the dispersed particles in a colloidal solution carry the same charge while the dispersion medium has an equal and opposite charge.</div>


tags: ['Chemistry', 'Electrochemistry', 'KVPY', 'KVPY 2015 (SB/SX)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$37.3$</span> </div>
source_db: MarksBatch2_P3.db
title:
the-standard-cell-potential-for-z-n-z-n-2-c-u-2-c-u-is-110-v-when-the-cell-is-completely-discharged-lo-g-zn-2-cu-2-is-closest-to

slug:
the-standard-cell-potential-for-z-n-z-n-2-c-u-2-c-u-is-110-v-when-the-cell-is-completely-discharged-lo-g-zn-2-cu-2-is-closest-to-76237

question:
<div class="question">The standard cell potential for $Z n\left|Z n^{2+} \| C u^{2+}\right| C u$ is $1.10 \mathrm{~V}$. When the cell is completely discharged, $\log \left[\mathrm{Zn}^{2+}\right] /\left[\mathrm{Cu}^{2+}\right]$ is closest to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$37.3$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.026$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$18.7$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.052$</span> </li> </ul>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/kvpy/cpDoECTOHzkJmj3n8vCowJnCEXW4LP_Bm796Ub76718.original.fullsize.png"/></div>


tags: ['Chemistry', 'Electrochemistry', 'NEET', 'NEET 2024 (Re-NEET)']
source_db: MarksBatch2_P3.db
title:
the-standard-cell-potential-of-the-following-cell-zn-zn-2-aq-fe-2-aq-fe-is-032-v-calculate-the-standard-gibbs-energy-change-for-the-reaction-zn-s-fe-2

slug:
the-standard-cell-potential-of-the-following-cell-zn-zn-2-aq-fe-2-aq-fe-is-032-v-calculate-the-standard-gibbs-energy-change-for-the-reaction-zn-s-fe-2-66425

question:
<div class="question">The standard cell potential of the following cell $\mathrm{Zn}\left|\mathrm{Zn}^{2+}(\mathrm{aq})\right| \mathrm{Fe}^{2+}(\mathrm{aq}) \mid \mathrm{Fe}$ is 0.32 V . Calculate the standard Gibbs energy change for the reaction :<br/>$\mathrm{Zn}(\mathrm{s})+\mathrm{Fe}^{2+}(\mathrm{aq}) \rightarrow \mathrm{Zn}^{2+}(\mathrm{aq})+\mathrm{Fe}(\mathrm{s})$<br/>(Given : $1 \mathrm{~F}=96487 \mathrm{C}$ )</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$-61.75 \mathrm{~kJ} \mathrm{~mol}^{-1}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$+5.006 \mathrm{~kJ} \mathrm{~mol}^{-1}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$-5.006 \mathrm{~kJ} \mathrm{~mol}^{-1}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$+61.75 \mathrm{~kJ} \mathrm{~mol}^{-1}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-61.75 \mathrm{~kJ} \mathrm{~mol}^{-1}$</span> </div>

answer:
<div class="solution">$\Delta_r G^{\ominus}=-n F E_{\text {cell }}^{\ominus}$<br/>For the given reaction, $n=2$<br/>$\therefore \quad \Delta_{\mathrm{r}} \mathrm{G}^{\ominus}=-2 \times 96487 \times 0.32$<br/>$=-61751.68 \mathrm{~J} \mathrm{~mol}^{-1}$<br/>$=-61.751 \mathrm{~kJ} \mathrm{~mol}^{-1}$</div>


tags: ['Mathematics', 'Statistics', 'AP EAMCET', 'AP EAMCET 2020 (22 Sep Shift 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P3.db
title:
the-standard-deviation-and-mean-of-five-observations-are-0-and-9-respectively-if-one-of-the-observations-is-changed-such-that-the-mean-of-the-new-set-

slug:
the-standard-deviation-and-mean-of-five-observations-are-0-and-9-respectively-if-one-of-the-observations-is-changed-such-that-the-mean-of-the-new-set-90836

question:
<div class="question">The standard deviation and mean of five observations are 0 and 9 respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10 , then their standard deviation is</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">0</span> </li> </ul>

answer:
<div class="solution">Let the five observations are $x_1, x_2, x_3, x_4, x_5$.<br/>So, mean $=\frac{x_1+x_2+x_3+x_4+x_5}{5}=9$<br/>(given)<br/>$\Rightarrow \quad x_1+x_2+x_3+x_4+x_5=45$<br/>and standard deviation $=\sum_{i=1}^5 \sqrt{\frac{\left(9-x_i\right)^2}{5}}=0$ (given)<br/>$\Rightarrow \quad \sum_{i=1}^5\left(9-x_i\right)^2=0 \Rightarrow x_i=9 \forall i$<br/>Now, let observation $x_5$ is changed with $y$, so<br/>$$<br/>\begin{array}{lrr}<br/>\text { mean }=\frac{x_1+x_2+x_3+x_4+y}{5}=10 &amp; \text { (given) } \\<br/>\Rightarrow &amp; x_1+x_2+x_3+x_4+y=50 &amp; \\<br/>\Rightarrow &amp; 45-x_5+y=50 &amp; \text { (from Eq. (i)) } \\<br/>\Rightarrow &amp; x_5+5=y \Rightarrow y=14 &amp; \left\{\because x_5=9\right\}<br/>\end{array}<br/>$$<br/>(given)<br/><br/>Now, the changed standard deviation is<br/>$$<br/>\begin{aligned}<br/>&amp; \sqrt{\frac{\left(10-x_1\right)^2+\left(10-x_2\right)^2+\left(10-x_3\right)^2}{\frac{+\left(10-x_4\right)^2+(10-y)^2}{5}}} \\<br/>= &amp; \sqrt{\frac{1+1+1+1+16}{5}}=\sqrt{\frac{20}{5}}=\sqrt{4}=2<br/>\end{aligned}<br/>$$</div>


title: the-standard-deviation-is-to-the-mean-deviation-taken-from-the-arithmetic-mean
slug: the-standard-deviation-is-to-the-mean-deviation-taken-from-the-arithmetic-mean-10898
tags: ['Mathematics', 'Statistics']
options: None
correct_option: None
answer: <div class="solution">greater than or equal</div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The standard deviation is to the mean deviation taken from the arithmetic mean.</div>


title: the-standard-deviation-of-5-scores-1-2-3-4-5-is-a-the-value-of-a-is-1
slug: the-standard-deviation-of-5-scores-1-2-3-4-5-is-a-the-value-of-a-is-1-71265
tags: ['Mathematics', 'Statistics', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value"><br/>2</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The standard deviation of 5 scores $1,2,3,4,5$ is $\sqrt{a}$. The value of ' $a$ ' is</div>

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

answer:
<div class="solution"><br/>$\begin{aligned} &amp; \text { Mean }(\bar{x})=\frac{1+2+3+4+5}{5}=3 \\ &amp; \text { S.D }=\sigma=\sqrt{\frac{1}{5}(1+4+9+16+25)-9}=\sqrt{11-9} \\ &amp; =\sqrt{2}\end{aligned}$</div>


title: the-standard-deviation-of-a-a-d-a-2-d-a-2-n-d-is
slug: the-standard-deviation-of-a-a-d-a-2-d-a-2-n-d-is-22311
question: <div class="question">The standard deviation of $a, a+d, a+2 d, \ldots, a+2 n d$ is</div>
tags: ['Mathematics', 'Statistics', 'TS EAMCET', 'TS EAMCET 2016']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$n d$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$n^2 d$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\sqrt{\frac{n(n+1)}{3}} d$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\sqrt{\frac{n(n+3)}{3}} d$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\sqrt{\frac{n(n+1)}{3}} d$</span> </div>

answer:
<div class="solution">Given series,<br/>$$<br/>a, a+d, a+2 d, \ldots, a+2 n d<br/>$$<br/>Here, $\quad a+2 n d=a+(m-1) d$<br/>$$<br/>\begin{array}{rlrl}<br/>\Rightarrow &amp; &amp; 2 n d=(m-1) d \\<br/>\Rightarrow &amp; 2 n=m-1 \\<br/>\Rightarrow &amp; &amp; 2 n+1=m<br/>\end{array}<br/>$$<br/>$$<br/>\begin{aligned}<br/>&amp; \therefore \text { Standard deviation }=\sqrt{\frac{(2 n+1)^2-1}{12} d^2} \\<br/>&amp;=\sqrt{\frac{(2 n+1-1)(2 n+1+1)}{12} d^2} \\<br/>&amp;=\sqrt{\frac{(2 n+2) 2 n}{12} d^2}=\sqrt{\frac{(n+1) n}{3} d}<br/>\end{aligned}<br/>$$</div>


tags: ['Mathematics', 'Statistics']
options: None
correct_option: None
answer: <div class="solution">Independent</div>
source_db: MarksBatch2_P3.db
title:
the-standard-deviation-of-a-data-is-of-any-change-in-origin-but-is-on-the-change-of-scalethe-sum-of-the-squares-of-the-deviations-of-the-values-of-the

slug:
the-standard-deviation-of-a-data-is-of-any-change-in-origin-but-is-on-the-change-of-scalethe-sum-of-the-squares-of-the-deviations-of-the-values-of-the-14799

question:
<div class="question">The standard deviation of a data is of any change in origin, but is on the change of scale.The sum of the squares of the deviations of the values of the variable is when taken about their arithmentic mean.</div>


tags: ['Mathematics', 'Statistics', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-standard-deviation-of-a-distribution-is-30-if-each-observation-is-increased-by-5-then-the-new-standard-deviation-will-be

slug:
the-standard-deviation-of-a-distribution-is-30-if-each-observation-is-increased-by-5-then-the-new-standard-deviation-will-be-70795

question:
<div class="question">The standard deviation of a distribution is <math><mn>30.</mn></math> If each observation is increased by <math><mn>5</mn></math>, then the new standard deviation will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mn>32</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>28</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mn>27</mn></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">None of these</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">S.D. of a series is unaltered if each observation is increased (or reduced) by the same scalar quantity, S.D. is independent of change of origin.<br/>Hence, S.D. will be the same.<br/><math><mo>â´</mo></math> S.D. <math><mo>=</mo><mn>30</mn></math></div>


title: the-standard-deviation-of-first-10-multiples-of-4-is
slug: the-standard-deviation-of-first-10-multiples-of-4-is-82884
question: <div class="question">The standard deviation of first 10 multiples of 4 is</div>
tags: ['Mathematics', 'Statistics', 'AP EAMCET', 'AP EAMCET 2022 (07 Jul Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$11.5$</span> </div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$7$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$8$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$11.5$</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">D</span> <span class="option-data">$14$</span> </li> </ul>

answer:
<div class="solution">Entries are $4,8,12,16,20,24,28,32,36,40$.<br/>$$<br/>\begin{aligned}<br/>\text { Variance } &amp; =\frac{\sum_{i=1}^{10}(4 i)^2}{10}-\left(\frac{\sum_{i=1}^{10} 4 i}{10}\right)^2 \\<br/>&amp; =\frac{16 \times 10 \times 11 \times 21}{60}-\left(\frac{4 \times 55}{10}\right)^2 \\<br/>&amp; =132<br/>\end{aligned}<br/>$$<br/>$\therefore$ Standard deviation $=\sqrt{132} \approx 11.5$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2006 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P3.db
title:
the-standard-deviation-of-n-observations-x-1-x-2-x-n-is-6-the-standard-deviation-of-another-set-of-n-observations-y-1-y-2-y-n-is-8-what-is-the-standar

slug:
the-standard-deviation-of-n-observations-x-1-x-2-x-n-is-6-the-standard-deviation-of-another-set-of-n-observations-y-1-y-2-y-n-is-8-what-is-the-standar-59803

question:
<div class="question">The standard deviation of $\mathrm{n}$ observations $\mathrm{x}_{1}, \mathrm{x}_{2}, \ldots \ldots \mathrm{x}_{\mathrm{n}}$ is $6 .$ The standard deviation of another set of $\mathrm{n}$ observations $\mathrm{y}_{1}$, $\mathrm{y}_{2}$<br/>$\mathrm{y}_{\mathrm{n}}$ is $8 .$ What is the standard deviation of $\mathrm{n}$ observations $\mathrm{x}_{1}-\mathrm{y}_{1}, \mathrm{x}_{2}-\mathrm{y}_{2}, \ldots \ldots . ., \mathrm{x}_{\mathrm{n}}-\mathrm{y}_{\mathrm{n}} ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">10</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">7</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">14</span> </li><li class="correct"> <span class="option-label">D</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> </ul>

answer:
<div class="solution">The standard deviation of n observation $\mathrm{x}_{1}, \mathrm{x}_{2}$, $\mathrm{x}_{\mathrm{n}}$ is 6 and of $\mathrm{y}_{1}, \mathrm{y}_{2}, \ldots \ldots, \mathrm{y}_{n}$ is 8, then the standard<br/>deviation of n observation $\mathrm{x}_{1}-\mathrm{y}_{1}, \mathrm{x}_{2}-\mathrm{y}_{2}, \mathrm{x}_{3}-\mathrm{y}_{3}, \ldots \ldots$<br/>$x_{n}-y_{n}$ is $8-6=2$.</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2010 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-standard-deviation-of-some-consecutive-integers-is-found-to-be-2-which-of-the-following-statements-best-describes-the-nature-of-the-consecutive-in

slug:
the-standard-deviation-of-some-consecutive-integers-is-found-to-be-2-which-of-the-following-statements-best-describes-the-nature-of-the-consecutive-in-19953

question:
<div class="question">The standard deviation of some consecutive integers is found to be $2 .$ Which of the following statements best describes the nature of the consecutive integers?</div>

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

answer:
<div class="solution">Since, the standard deviation of same consecutive integers is 2, these integers are any set of seven consecutive integers.</div>


title: the-standard-deviation-of-the-data-6-7-8-9-10-is
slug: the-standard-deviation-of-the-data-6-7-8-9-10-is-73246
question: <div class="question">The standard deviation of the data $6,7,8,9$, 10 is</div>
tags: ['Mathematics', 'Functions', 'KCET', 'KCET 2020']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\sqrt{2}$</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">B</span> <span class="option-data">$\sqrt{10}$</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">10</span> </li> </ul>

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

answer:
<div class="solution">Given data $6,7,8,9,10$<br/>$\begin{aligned}<br/>\bar{x} &amp;=\frac{6+7+8+9+10}{5}=8 \\<br/>\mathrm{SD} &amp;=\sqrt{\frac{\sum x_{i}^{2}}{n}-(\bar{x})^{2}} \\<br/>\mathrm{SD} &amp;=\sqrt{\frac{6^{2}+7^{2}+8^{2}+9^{2}+10^{2}}{5}-(8)^{2}} \\<br/>\mathrm{SD} &amp;=\sqrt{\frac{36+49+64+81+100-320}{5}} \\<br/>\mathrm{SD} &amp;=\sqrt{\frac{330-320}{5}}=\sqrt{\frac{10}{5}}=\sqrt{2}<br/>\end{aligned}$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-standard-deviation-of-the-first-n-natural-numbers-can-be-obtained-using-which-one-of-the-following-formulae

slug:
the-standard-deviation-of-the-first-n-natural-numbers-can-be-obtained-using-which-one-of-the-following-formulae-33783

question:
<div class="question">The standard deviation $\sigma$ of the first N natural numbers can be obtained using which one of the following formulae:</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$=\sqrt{\frac{N^{2}-1}{12}}$</span> </div>

answer:
<div class="solution">$\sigma^{2}=\frac{1}{\mathrm{n}} \sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{x}_{\mathrm{i}}^{2}-\left(\frac{1}{\mathrm{n}} \cdot \sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{x}_{\mathrm{i}}\right)^{2}$<br/>$=\frac{1}{n}\left(1^{2}+2^{2}+3^{2}+\ldots+n^{2}\right)-\left(\frac{1}{n}(1+2+3+\ldots .+n)\right)^{2}$<br/>$=\frac{1}{n} \frac{n(n+1)(2 n+1)}{6}-\left(\frac{1}{n} \cdot \frac{n(n+1)}{2}\right)^{2}$<br/>$=\frac{\mathrm{n}^{2}-1}{12} \quad \therefore \sigma=\sqrt{\frac{\mathrm{n}^{2}-1}{12}} .$</div>


tags: ['Mathematics', 'Statistics', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-standard-deviation-of-the-following-distribution-beginarraycccc-hline-ci-06-612-1218-hline-mathrmfmathrmi-2-4-6-hline-endarray-is-1

slug:
the-standard-deviation-of-the-following-distribution-beginarraycccc-hline-ci-06-612-1218-hline-mathrmfmathrmi-2-4-6-hline-endarray-is-1-58985

question:
<div class="question">The standard deviation of the following distribution<br/>\begin{array}{|c|c|c|c|}<br/>\hline C.I. &amp; 0-6 &amp; 6-12 &amp; 12-18 \\<br/>\hline \mathrm{f}_{\mathrm{i}} &amp; 2 &amp; 4 &amp; 6 \\<br/>\hline<br/>\end{array}<br/>is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5 \sqrt{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\sqrt {5}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$2\sqrt {5}$</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">D</span> <span class="option-data">$20$</span> </li> </ul>

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

answer:
<div class="solution">\begin{array}{|c|c|c|c|c|c|}<br/>\hline C.I. &amp; \mathbf{f}_{\mathbf{i}} &amp; \boldsymbol{x}_{\mathbf{i}} &amp; \boldsymbol{x}_{\mathbf{i}}^{\mathbf{2}} &amp; \mathbf{f}_{\mathbf{i}} \boldsymbol{x}_{\mathbf{i}} &amp; \mathbf{f}_{\mathbf{i}} \boldsymbol{x}_{\mathbf{i}}^{\mathbf{2}} \\<br/>\hline 0-6 &amp; 2 &amp; 3 &amp; 9 &amp; 6 &amp; 18 \\<br/>\hline 6-12 &amp; 4 &amp; 9 &amp; 81 &amp; 36 &amp; 324 \\<br/>\hline 12-18 &amp; 6 &amp; 15 &amp; 225 &amp; 90 &amp; 1350 \\<br/>\hline Total &amp; \mathbf{1 2} &amp; &amp; &amp; \mathbf{1 3 2} &amp; \mathbf{1 6 9 2} \\<br/>\hline<br/>\end{array}<br/>Here $\sum \mathrm{f}_{\mathrm{i}}=12, \sum \mathrm{f}_{\mathrm{i}} x_{\mathrm{i}}=132, \sum \mathrm{f}_{\mathrm{i}} x_{\mathrm{i}}^2=1692$<br/>$\begin{aligned}<br/>\therefore \quad \mathrm{V}(\mathrm{X}) &amp; =\frac{1692}{12}-\left(\frac{132}{12}\right)^2 \\<br/>&amp; =141-121 \\<br/>&amp; =20<br/>\end{aligned}$<br/>$\therefore \quad$ Standard deviation $=\sqrt{20}=2 \sqrt{5}$</div>


tags: ['Mathematics', 'Statistics', 'MHT CET', 'MHT CET 2023 (09 May Shift 1)']
source_db: MarksBatch2_P3.db
title:
the-standard-deviation-of-the-following-distribution-beginarraycccc-hline-ci-06-612-1218-hline-mathrmfmathrmi-2-4-6-hline-endarray-is

slug:
the-standard-deviation-of-the-following-distribution-beginarraycccc-hline-ci-06-612-1218-hline-mathrmfmathrmi-2-4-6-hline-endarray-is-82454

question:
<div class="question">The standard deviation of the following distribution<br/>\begin{array}{|c|c|c|c|}<br/>\hline C.I. &amp; 0-6 &amp; 6-12 &amp; 12-18 \\<br/>\hline \mathrm{f}_{\mathrm{i}} &amp; 2 &amp; 4 &amp; 6 \\<br/>\hline<br/>\end{array}<br/>is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5 \sqrt{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\sqrt {5}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$2\sqrt {5}$</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">D</span> <span class="option-data">$20$</span> </li> </ul>

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

answer:
<div class="solution">\begin{array}{|c|c|c|c|c|c|}<br/>\hline C.I. &amp; \mathbf{f}_{\mathbf{i}} &amp; \boldsymbol{x}_{\mathbf{i}} &amp; \boldsymbol{x}_{\mathbf{i}}^{\mathbf{2}} &amp; \mathbf{f}_{\mathbf{i}} \boldsymbol{x}_{\mathbf{i}} &amp; \mathbf{f}_{\mathbf{i}} \boldsymbol{x}_{\mathbf{i}}^{\mathbf{2}} \\<br/>\hline 0-6 &amp; 2 &amp; 3 &amp; 9 &amp; 6 &amp; 18 \\<br/>\hline 6-12 &amp; 4 &amp; 9 &amp; 81 &amp; 36 &amp; 324 \\<br/>\hline 12-18 &amp; 6 &amp; 15 &amp; 225 &amp; 90 &amp; 1350 \\<br/>\hline Total &amp; \mathbf{1 2} &amp; &amp; &amp; \mathbf{1 3 2} &amp; \mathbf{1 6 9 2} \\<br/>\hline<br/>\end{array}<br/>Here $\sum \mathrm{f}_{\mathrm{i}}=12, \sum \mathrm{f}_{\mathrm{i}} x_{\mathrm{i}}=132, \sum \mathrm{f}_{\mathrm{i}} x_{\mathrm{i}}^2=1692$<br/>$\begin{aligned}<br/>\therefore \quad \mathrm{V}(\mathrm{X}) &amp; =\frac{1692}{12}-\left(\frac{132}{12}\right)^2 \\<br/>&amp; =141-121 \\<br/>&amp; =20<br/>\end{aligned}$<br/>$\therefore \quad$ Standard deviation $=\sqrt{20}=2 \sqrt{5}$</div>


tags: ['Mathematics', 'Statistics', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">9</span> </div>
answer: <div class="solution">No solution. Refer to answer key.</div>
source_db: MarksBatch2_P3.db
title:
the-standard-deviation-of-the-following-distribution-is-class-interval-frequency-0-10-1-10-20-3-20-30-4-30-40-2-1

slug:
the-standard-deviation-of-the-following-distribution-is-class-interval-frequency-0-10-1-10-20-3-20-30-4-30-40-2-1-87188

question:
<div class="question">The standard deviation of the following distribution is<br/>$\begin{array}{|l|c|c|c|c|}<br/>\hline \begin{array}{l}<br/>\text { Class interval } \\<br/>\end{array} &amp; 0-10 &amp; 10-20 &amp; 20-30 &amp; 30-40 \\<br/>\hline \begin{array}{l}<br/>\text { Frequency } \\<br/>\end{array} &amp; 1 &amp; 3 &amp; 4 &amp; 2 \\<br/>\hline<br/>\end{array}$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">9</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">8</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">7</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">6</span> </li> </ul>


tags: ['Mathematics', 'Statistics', 'AP EAMCET', 'AP EAMCET 2017 (24 Apr Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">9</span> </div>
answer: <div class="solution">No solution. Refer to answer key.</div>
source_db: MarksBatch2_P3.db
title:
the-standard-deviation-of-the-following-distribution-is-class-interval-frequency-0-10-1-10-20-3-20-30-4-30-40-2

slug:
the-standard-deviation-of-the-following-distribution-is-class-interval-frequency-0-10-1-10-20-3-20-30-4-30-40-2-50221

question:
<div class="question">The standard deviation of the following distribution is<br/>$\begin{array}{|l|c|c|c|c|}<br/>\hline \begin{array}{l}<br/>\text { Class interval } \\<br/>\end{array} &amp; 0-10 &amp; 10-20 &amp; 20-30 &amp; 30-40 \\<br/>\hline \begin{array}{l}<br/>\text { Frequency } \\<br/>\end{array} &amp; 1 &amp; 3 &amp; 4 &amp; 2 \\<br/>\hline<br/>\end{array}$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">9</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">8</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">7</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">6</span> </li> </ul>


