# questions

title: can-competition-occur-when-resources-are-abundant
slug: can-competition-occur-when-resources-are-abundant-28778
question: <div class="question">Can competition occur when resources are abundant?</div>
tags: ['Biology', 'Organisms and Populations', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">No, competition can only occur when resources are limiting.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Yes, competition can occur even if resources are abundant.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Competition only occurs in laboratory experiments.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Competition occurs only when resources are limited in nature.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Yes, competition can occur even if resources are abundant.</span> </div>

answer:
<div class="solution">Resources need not be limiting for competition to occur; in interference competition, the feeding efficiency of one species might be reduced due to the interfering and inhibitory presence of the other species, even if resources (food and space) are abundant.</div>


title: cannot-be-prepared-by-1
slug: cannot-be-prepared-by-1-21666
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Main', 'JEE Main 2019 (12 Jan Shift 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question"><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/fde1fbe8-dfd1-4698-aa5a-de564ad642d3-image.png" style="width: 214px; height: 122px;"/></p><p>cannot be prepared by:</p></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>HCHO</mi><mo>+</mo><mi>PhCH</mi><mfenced separators="|"><msub><mi>CH</mi><mn>3</mn></msub></mfenced><msub><mi>CH</mi><mn>2</mn></msub><mi>MgX</mi></math></span> </div>

answer:
<div class="solution"><p> The given compound is tertiary alcohol and formaldehyde forms secondary alcohol on reaction with Grignard reagent.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/4346e290-a9ff-4491-a02a-b0cd97d28ca0-image.png" style="width: 395px; height: 514px;"/></p><p> </p></div>


title: carbohydrates-are-the-most-abundant-biomolecule-present-on-earth-they-are-produced-by
slug: carbohydrates-are-the-most-abundant-biomolecule-present-on-earth-they-are-produced-by-36923
tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch1_P2.db
question:
<div class="question">Carbohydrates are the most abundant biomolecule present on earth. They are produced by</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">some bacteria, algae and green plant cells.</span> </div>

answer:
<div class="solution">Carbohydrates are organic compounds synthesized bychlorophyll containing photosynthetic cells of some bacteria, algae and green plant cells. Certain photoautotrophic bacteria e.g., Green sulphur bacteria and purple sulphur bacteria contain pigments like chlorobium chlorophyll and acteriochlorophyll respectively that helps them in photosynthesis.</div>


title: carbohydrates-the-most-abundant-biomolecules-on-earth-arc-produced-by
slug: carbohydrates-the-most-abundant-biomolecules-on-earth-arc-produced-by-60284
question: <div class="question">Carbohydrates, the most abundant biomolecules on earth, arc produced by</div>
tags: ['Biology', 'Biomolecules (B)', 'NEET', 'NEET 2005']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">some bacteria, algae and green plant cells</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">fungi, algae and green plant cells</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">all bacteria, fungi and algae</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">viruses, fungi and bacteria.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">some bacteria, algae and green plant cells</span> </div>

answer:
<div class="solution">Carbohydrate is the most abundant biomolecule on earth. Carbohydrate is organic compound synthesized in the chlorophyll-containing cells of some bacteria, algae and green plants, during photosynthesis. Certain photoautotrophic bacteria, e.g. Green sulphur bacteria and purple sulphur bacteria contain pigments like Chlorophyll and Bacteriochlorophyll, respectively that helps them in photosynthesis. During photosynthesis, carbon dioxide reduced into carbohydrates by water and oxygen is liberated.</div>


title: carbohydrates-the-most-abundant-biomolecules-on-earth-are-produced-by
slug: carbohydrates-the-most-abundant-biomolecules-on-earth-are-produced-by-94513
tags: ['Biology', 'Biomolecules (B)', 'JIPMER', 'JIPMER 2007']
source_db: MarksBatch1_P2.db
question:
<div class="question">Carbohydrates, the most abundant biomolecules on earth, are produced by:</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">some bacteria, algae and green plant cells</span> </div>

answer:
<div class="solution">Some photosynthetic bacteria such as Rhodopseudomonas can prepare carbohydrates. But during this type of food synthesis $\mathrm{O}_2$ does not evolved because in this case hydrogen donor is other than $\mathrm{H}_2 \mathrm{O}$. Algae (green and blue green) and all green plant cells prepare their food (carbohydrate) through photosynthesis.<br/>Here, hydrogen ions are donated by water molecules by the process of photolysis of water i.e., $\mathrm{O}_2$ is released during this type of food synthesis.</div>


title: carbylamine-reaction-is-given-by-aliphatic
slug: carbylamine-reaction-is-given-by-aliphatic-58934
question: <div class="question">Carbylamine reaction is given by aliphatic</div>
tags: ['Chemistry', 'Amines', 'VITEEE', 'VITEEE 2007']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">primary amine</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">secondary amine</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">tertiary amine</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">quaternary ammonium salt</span> </li> </ul>

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

answer:
<div class="solution">Carbylamine test is given by aliphatic primary amine.<br/>Aliphatic (or aromatic) $1^{\circ}$ amine $+\mathrm{CHCl}_{3}+$ $\mathrm{KOH} \longrightarrow$ Bad smelling isocyanide.</div>


title: carrier-ions-like-na-facilitate-the-absorption-of-substance-like
slug: carrier-ions-like-na-facilitate-the-absorption-of-substance-like-96209
tags: ['Biology', 'Transport in Plants', 'NEET', 'NEET 2010 (Screening)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Carrier ions like $\mathrm{Na}^{+}$facilitate the absorption of substance like</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">amino acids and glucose</span> </div>

answer:
<div class="solution">Active transport occurs with the help of energy, usually against concentration gradient. For this, cell membrane possesses carriers and gated channels. Active transports of one substance is often accompanied by permeation of other substances. The phenomenon is called secondary active transport. It is of two main types-Co-transport (eg, glucose and some amino acids along with inward pushing of excess $\mathrm{Na}^{+}$) and counter transport $\left(\mathrm{Ca}^{2+}\right.$ and $\mathrm{H}^{+}$movement outwardly as excess $\mathrm{Na}^{+}$passes inwardly).</div>


title: catalytic-dehydrogenation-of-a-primary-alcohol-gives-a
slug: catalytic-dehydrogenation-of-a-primary-alcohol-gives-a-73547
question: <div class="question">Catalytic dehydrogenation of a primary alcohol gives a</div>
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'KCET', 'KCET 2008']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">secondary alcohol</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">aldehyde</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">ketone</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">ester</span> </li> </ul>

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

answer:
<div class="solution">Primary alcohols get dehydrogenated with reduced copper at $573 \mathrm{~K}$, to give corresponding aldehydes.<br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/kcet/Snq8RjvfV0QJ-NpVddZiMWo_BZ89wo092WeqMOzOqqo.original.fullsize.png"/><br/></div>


title: catalytic-dehydrogenation-of-a-primary-alcohol-gives-aan-1
slug: catalytic-dehydrogenation-of-a-primary-alcohol-gives-aan-1-41016
question: <div class="question">Catalytic dehydrogenation of a primary alcohol gives a/an</div>
tags: ['Chemistry', 'Aldehydes and Ketones', 'JEE Main']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">secondary alcohol</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">aldehyde</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">ketone</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">ester</span> </li> </ul>

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

answer:
<div class="solution">Catalytic dehydration of a primary alcohol gives aldehyde i.e.,<br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/comedk/4stDGt0lSyvCNdDF5r4tQJX1rO7cUAqUOUCcHPgwTy8.original.fullsize.png"/><br/></div>


title: cell-is-basic-unit-of-life-discuss-in-brief
slug: cell-is-basic-unit-of-life-discuss-in-brief-41031
question: <div class="question">Cell is basic unit of life. Discuss in brief.</div>
tags: ['Biology', 'Cell - The Unit of Life']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
answer:
<div class="solution">Cell : The Basic Unit of life : All the living organism are composed of small, tiny structure or compartments called cells. These cells are called the 'building blocks' of life. The cells in true sense are considered as the basic unit of life because all the life processes i.e., metabolism, responsiveness, reproduction are carried out by the cells. Respiration, nutrition, release of energy for the body are carried out within the cells only. Even the animals and plants reproduce because the cells reproduce individually. Growth occurs because cell grow and multiply.<br/>In Amoeba all the life processes are performed within the boundaries of the single cell. This is true of all other multicellular organisms. The only difference in the multicellular organisms is that the body of these organisms is made up of many cells. In these organisms, the cell do not behave independently, but get organized into tissues. Each tissue is specialized to perform specific functions. Different tissues then get organised into tissues. Each tissue is specialized to perform specific functions. Different tissues then get organised into organs which perform certain specific functions. Different organs are finally organised to form organ systems. Now it must be very clear that the basic structure to tissues, organs and organ system are the cells only. These tissues, organs and organ system of the organisms work because the cells work. Thus "the cells are structural and functional unit of the living beings" hence it is the basic unit of life.</div>


title: cell-wall-of-fungi-is-composed-of
slug: cell-wall-of-fungi-is-composed-of-89382
question: <div class="question">Cell wall of fungi is composed of</div>
tags: ['Biology', 'Biological Classification', 'JIPMER', 'JIPMER 2018']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">chitin</span> </div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">chitin</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">pectin</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">cellulose</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">mannans</span> </li> </ul>

answer:
<div class="solution">The cell wall of fungi is composed of chitin. It is the second most abundant carbohydrate. It is a homopolymer of N -Acetyl Glucosamine (NAG) joined with $\beta$ 1-4 linkages. NAG is a modification of glucose molecule.</div>


title: cellulose-does-not-form-blue-colour-with-iodine-because
slug: cellulose-does-not-form-blue-colour-with-iodine-because-12505
question: <div class="question">Cellulose does not form blue colour with Iodine because</div>
tags: ['Biology', 'Biomolecules (B)', 'NEET', 'NEET 2023 (All India)']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">It breaks down when iodine reacts with it.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">It is a disaccharide.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">It is a helical molecule.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">It does not contain complex helices and hence cannot hold iodine molecules.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">It does not contain complex helices and hence cannot hold iodine molecules.</span> </div>

answer:
<div class="solution"><blockquote><p>Cellulose is a polymeric polysaccharide consisting of only one type of monosaccharide, i.e., glucose. Cellulose is a homopolymer. Starch is a variant of this but is present as a storehouse of energy in plant tissues. Starch forms helical secondary structures, and it can hold iodine molecules in the helical portion. The starch-iodine is blue. Cellulose does not contain complex helices and hence cannot hold iodine.</p></blockquote></div>


title: cellulose-the-most-important-constituent-of-the-plant-cell-wall-is-made-up-of
slug: cellulose-the-most-important-constituent-of-the-plant-cell-wall-is-made-up-of-52927
tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch1_P2.db
question:
<div class="question">Cellulose, the most important constituent of the plant cell wall is made up of</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Branched-chain of glucose molecules linked by <mtext>Î²</mtext>-1, 4 glycosidic bonds in a straight chain and <mtext>Î±</mtext>-1, 6 glycosidic bonds at the site of branching</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Unbranched chain of glucose molecules linked by <mtext>Î²</mtext>-1, 4 glycosidic bond</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Branched-chain of glucose molecules linked by <mtext>Î±</mtext>-1, 6 glycosidic bonds at the site of branching</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Unbranched chain of glucose molecules linked by <mtext>α</mtext>-1, 4 glycosidic bond</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Unbranched chain of glucose molecules linked by <mtext>Î²</mtext>-1, 4 glycosidic bond</span> </div>

answer:
<div class="solution">Cellulose is the most abundant carbohydrate. Cellulose molecule is composed of 1600 to 6000 glucose molecules joined together. Those polymers form long twisting macromolecules of cellulose. The chains are unbranched and linear. The successive glucose residues are joined together by <mtext>Î²</mtext>-1-4, linkages.</div>


tags: ['Chemistry', 'Electrostatics', 'NEET']
source_db: MarksBatch1_P2.db
title:
certainly-heres-a-single-correct-question-with-four-options-question-what-is-the-meaning-of-the-statement-electric-charge-of-a-body-is-quantised

slug:
certainly-heres-a-single-correct-question-with-four-options-question-what-is-the-meaning-of-the-statement-electric-charge-of-a-body-is-quantised-73316

question:
<div class="question">Certainly, here's a single correct question with four options:   Question: What is the meaning of the statement 'electric charge of a body is quantised'?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Electric charge is only found in whole number multiples of elementary charge.</span> </div>

answer:
<div class="solution">Correct Option is : (C)<br/>Electric charge is only found in whole number multiples of elementary charge.</div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'AIIMS', 'AIIMS 2017']
source_db: MarksBatch1_P2.db
title:
ch-3-3-coch-3-and-ch-3-oc-2-h-5-are-treated-with-hydroiodic-acid-the-fragments-obtained-after-reactions-are-respectively

slug:
ch-3-3-coch-3-and-ch-3-oc-2-h-5-are-treated-with-hydroiodic-acid-the-fragments-obtained-after-reactions-are-respectively-56123

question:
<div class="question">$\left(\mathrm{CH}_3\right)_3 \mathrm{COCH}_3$ and $\mathrm{CH}_3 \mathrm{OC}_2 \mathrm{H}_5$ are treated with hydroiodic acid. The fragments obtained after reactions are respectively</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\left(\mathrm{CH}_3\right)_3 \mathrm{CI}+\mathrm{CH}_3 \mathrm{OH} ; \mathrm{CH}_3 \mathrm{I}+\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left(\mathrm{CH}_3\right)_3 \mathrm{CI}+\mathrm{CH}_3 \mathrm{OH} ; \mathrm{CH}_3 \mathrm{OH}+\mathrm{C}_2 \mathrm{H}_5 \mathrm{I}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left(\mathrm{CH}_3\right)_3 \mathrm{COH}+\mathrm{CH}_3 \mathrm{I} ; \mathrm{CH}_3 \mathrm{OH}+\mathrm{C}_2 \mathrm{H}_5 \mathrm{I}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{CH}_3 \mathrm{I}+\left(\mathrm{CH}_3\right)_3 \mathrm{COH} ; \mathrm{CH}_3 \mathrm{I}+\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(\mathrm{CH}_3\right)_3 \mathrm{CI}+\mathrm{CH}_3 \mathrm{OH} ; \mathrm{CH}_3 \mathrm{I}+\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}$</span> </div>

answer:
<div class="solution">When mixed ethersare used, the formation of alkyl iodide depends on the nature of alkyl groups. Methyl iodide is formed when one group is methyl and the other a primary or secondary alkyl group. Here reaction follows $\mathrm{S}_{\mathrm{N}} 2$ mechanism and because of the steric effect of the larger group, $\mathrm{I}^{-}$attacks the smaller (Me) group.<br/>$\mathrm{CH}_3 \mathrm{OC}_2 \mathrm{H}_5+\mathrm{HI} \longrightarrow \mathrm{CH}_3 \mathrm{I}+\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}$<br/>When the substrate is a methyl $t$-alkyl ether, the products are $t-R \mathrm{I}$ and $\mathrm{MeOH}$. Here reaction follows $\mathrm{S}_{\mathrm{N}} 1$ mechanism and formation of products is controlled by the stability of carbocation. Since carbocation stability order is $3^{\circ}&gt;2^{\circ}&gt;1^{\circ}&gt;\stackrel{+}{\mathrm{C}} \mathrm{H}_3$, therefore alkyl halide is always derived from tert-alkyl group.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/aiims/hY9pEZrjzsrMqsT2iJu-yPaiclPYvJ3NNQxAwhi_OFM.original.fullsize.png"/><br/></div>


title: chargaffs-rule-states-that-in-an-organism
slug: chargaffs-rule-states-that-in-an-organism-76294
question: <div class="question">Chargaff's rule states that in an organism</div>
tags: ['Chemistry', 'Biomolecules', 'NEET', 'NEET 2003']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">amount of adenine (A) is equal to that of thymine $(\mathrm{T})$ and the amount of guanine $(\mathrm{G})$ is equal to that of cytosine (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">amount of adenine (A) is equal to that of guanine (G) and the amount of thymine $(T)$ is equal to that of cytosine (C)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">amount of adenine (A) is equal to that of cytosine $(\mathrm{C})$ and the amount of thymine $(T)$ is equal to that of guanine (G)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">amounts of all bases are equal</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">amount of adenine (A) is equal to that of thymine $(\mathrm{T})$ and the amount of guanine $(\mathrm{G})$ is equal to that of cytosine (C)</span> </div>

answer:
<div class="solution">Chargaff rule states that in DNA there is always equality in quantity between the bases $\mathrm{A}$ and $\mathrm{T}$ and between the bases $\mathrm{G}$ and $\mathrm{C}$.<br/>Related Theory<br/>In all the species the molar ratios $[A]=[T]$ and $[C]=[G]$, and that ratio $[C+G] /[A+T]$ was typically less than the unity with $[C+G]$ is less abundant.</div>


title: chemistry-alcohols-phenols-and-ethers-jee-main-66fe8f5081bd456237f43d9b
slug: chemistry-alcohols-phenols-and-ethers-jee-main-66fe8f5081bd456237f43d9b-42835
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Main']
source_db: MarksBatch1_P2.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/neet/be1492a7-ce86-46e5-bb9c-469f24e09caa.png" style="width: 426px; height: 107px;"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/neet/1c3fb7b5-ac66-4dad-a1c6-b268df389928.png" style="width: 248px; height: 149px;"/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/neet/65e52f58-b5c8-4bed-813a-82ed5abc4d2e.png" style="width: 301px; height: 139px;"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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"><msub><mi>CH</mi><mn>3</mn></msub><mo>-</mo><mi>CH</mi><mo>=</mo><mi>CH</mi><mo>-</mo><msub><mi>CH</mi><mn>3</mn></msub></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/neet/c33ee3d0-9946-4b46-bd89-4d2f9429af1a.png" style="width: 363px; height: 101px;"/></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/pyq/neet/65e52f58-b5c8-4bed-813a-82ed5abc4d2e.png" style="width: 301px; height: 139px;"/></span> </div>

answer:
<div class="solution"><p>The reaction between 3-methylbutan-2-ol and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>HBr</mi></math> is explained below.<br/>In the first step, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mi>OH</mi></math> group is protonated. In the second step, a molecule of water is lost to form secondary carbocation. Third step is the rearrangement of less stable secondary carbocation to more stable tertiary carbocation through <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>2</mn><mo>-</mo></math>hydride ion shift. Final step is the nucleophilic attack of bromide ion on tertiary carbocation to form 2-bromo-2-methylbutane as shown below.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/neet/0b7b4794-7745-4657-b472-ece2ec6e2c3b.png" style="width: 402px; height: 264px;"/></p></div>


title: china-rose-has
slug: china-rose-has-83869
question: <div class="question">China rose has</div>
tags: ['Biology', 'Morphology of Flowering Plants', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Parietal placentation, twisted aestivation, monoadelphous, perigynous flower.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Axile placentation, twisted aestivation, monoadelphous, hypogynous flower.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Parietal placentation, valvate aestivation, diadelphous, perigynous flower.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Axile placentation, valvate aestivation, diadelphous, hypogynous flower.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Axile placentation, twisted aestivation, monoadelphous, hypogynous flower.</span> </div>

answer:
<div class="solution">When the placenta is axial and the ovules are attached to it in a multilocular ovary, the placentation is said to be axile, as in china rose, tomato, and lemon. If one margin of the appendage overlaps that of the next one and so on as in china rose, lady's finger and cotton, it is called twisted aestivation. In the hypogynous flower the gynoecium occupies the highest position while the other parts are situated below it. The ovary in such flowers is said to be superior, e.g., mustard, china rose and brinjal. The stamens are united into one bunch or one bundle (monadelphous) as seen in in china rose.</div>


title: chlorenchyma-is-known-to-develop-in-the
slug: chlorenchyma-is-known-to-develop-in-the-95570
question: <div class="question">Chlorenchyma is known to develop in the</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'AIIMS', 'AIIMS 2008']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">cytoplasm of Chlorella</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">mycelium of a green mould such as Aspergillus</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">spore capsule of a moss</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">pollen tube of Pinus.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">spore capsule of a moss</span> </div>

answer:
<div class="solution">Chlorenchyma or assimilatory parenchyma are parenchymatous cells that possess abundant<br/>chloroplasts in them. They are capable of photosynthesis. A spore capsule of moss can perform photosynthesis because of the presence of chlorenchyma cells in them.</div>


tags: ['Chemistry', 'Structure of Atom', 'KVPY', 'KVPY 2017 (5 Nov SB/SX)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$3: 1$</span> </div>
source_db: MarksBatch1_P2.db
title:
chlorine-has-two-naturally-occurring-isotopes-35-cl-and-37-cl-if-the-atomic-mass-of-cl-is-3545-the-ratio-of-natural-abundance-of-35-cl-and-37-cl-is-cl

slug:
chlorine-has-two-naturally-occurring-isotopes-35-cl-and-37-cl-if-the-atomic-mass-of-cl-is-3545-the-ratio-of-natural-abundance-of-35-cl-and-37-cl-is-cl-38130

question:
<div class="question">Chlorine has two naturally occurring isotopes, ${ }^{35} \mathrm{Cl}$ and ${ }^{37} \mathrm{Cl}$. If the atomic mass of $\mathrm{Cl}$ is $35.45$ the ratio of natural abundance of ${ }^{35} \mathrm{Cl}$ and ${ }^{37} \mathrm{Cl}$ is closest to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$3.5: 1$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$3: 1$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2.5: 1$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4: 1$</span> </li> </ul>

answer:
<div class="solution">Mav $=\frac{\mathrm{M}_{1} \mathrm{n}_{1}+\mathrm{M}_{2} \mathrm{n}_{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}}$<br/>$35.45=\frac{35 \mathrm{n}_{1}+37 \mathrm{n}_{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}}$<br/>$\therefore \mathrm{n}_{1}: \mathrm{n}_{2}=3: 1$</div>


title: chlorocyclohexane-is
slug: chlorocyclohexane-is-26904
question: <div class="question">Chlorocyclohexane is</div>
tags: ['Chemistry', 'General Organic Chemistry', 'AP EAMCET', 'AP EAMCET 2023 (17 May Shift 2)']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Primary alkyl halide</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Tertiary alkyl halide</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Allylic halide</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Secondary alkyl halide</span> </li> </ul>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/PjGE8z3fnkDUADs-vslR6iAWsi_wt0zxXQD766jzZ48.original.fullsize.png"/><br/></div>


title: chloromethane-on-treatment-with-excess-of-ammonia-yields-mainly
slug: chloromethane-on-treatment-with-excess-of-ammonia-yields-mainly-29927
question: <div class="question">Chloromethane on treatment with excess of ammonia yields mainly</div>
tags: ['Chemistry', 'Haloalkanes and Haloarenes']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>N, N-dimethylmethanamine <br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/9UWkg9nBRh1R7YslNpZtjxvGvToUxvSr3kTXlhSqApI.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{N}$-methylmethanamine $\left(\mathrm{CH}_3-\mathrm{NH}-\mathrm{CH}_3\right)$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>methanamine $\left(\mathrm{CH}_3 \mathrm{NH}_2\right)$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>mixture containing all these in equal proportion</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>methanamine $\left(\mathrm{CH}_3 \mathrm{NH}_2\right)$<br/></span> </div>

answer:
<div class="solution">$\mathrm{CH}_3 \mathrm{Cl}+\mathrm{NH}_3 \rightarrow \mathrm{CH}_3 \mathrm{NH}_2+\mathrm{HCl}$<br/>Excess Methanamine<br/>However, if the two reactants are present in the same amount, then the mixture of amines(i.e., primary, secondary and tertiary) are obtained.</div>


tags: ['Mathematics', 'Probability', 'KVPY', 'KVPY 2014 (SB/SX)']
answer: <div class="solution">Check for $n=1,2,3, \ldots \ldots$</div>
source_db: MarksBatch1_P2.db
title:
choose-a-number-n-uniformly-at-random-from-the-set-1-2-100-choose-one-of-the-first-seven-days-of-the-year-2014-at-random-and-consider-n-consencutive-d

slug:
choose-a-number-n-uniformly-at-random-from-the-set-1-2-100-choose-one-of-the-first-seven-days-of-the-year-2014-at-random-and-consider-n-consencutive-d-56537

question:
<div class="question">Choose a number n uniformly at random from the set $\{1,2, \ldots 100\}$. Choose one of the first seven days of the year 2014 at random and consider n consencutive days among the chosen $n$ days, the number of Sunday is different from the number of Mondays?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{2}{7}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{12}{49}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{43}{175}$</span> </li> </ul>

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


tags: ['Biology', 'Cell - The Unit of Life', 'NEET']
source_db: MarksBatch1_P2.db
title:
choose-an-option-with-the-correct-statements-from-the-list-below-i-the-telomere-is-heterochromatic-in-nature-ii-the-acrocentric-chromosome-has-centrom

slug:
choose-an-option-with-the-correct-statements-from-the-list-below-i-the-telomere-is-heterochromatic-in-nature-ii-the-acrocentric-chromosome-has-centrom-77424

question:
<div class="question">Choose an option with the correct statements from the list below.<br/> <br/>
i. The telomere is heterochromatic in nature.<br/>
ii. The acrocentric chromosome has centromere close to its end.<br/>
iii. Satellite is located near primary constriction.<br/>
iv. Submetacentric chromosomes are L-shaped.</div>

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

answer:
<div class="solution">The telocentric chromosome has centromere at the end of the chromosome and in the acrocentric chromosome, the centromere is near the end. These centromeres are present in the primary constriction and all chromosomes have primary constriction but some chromosomes during metaphase also show secondary constrictions that are called a satellite. They are present in some chromosome and help to identify the chromosome from others.</div>


tags: ['Biology', 'Molecular Basis of Inheritance', 'JIPMER', 'JIPMER 2008']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch1_P2.db
title:
choose-the-alternative-which-can-be-substituted-for-the-given-wordssentence-a-person-who-enters-without-any-invitation

slug:
choose-the-alternative-which-can-be-substituted-for-the-given-wordssentence-a-person-who-enters-without-any-invitation-73688

question:
<div class="question">choose the alternative which can be substituted for the given words/sentence.<br/>A person who enters without any invitation</div>

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

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


tags: ['Biology', 'Chemical Coordination and Integration', 'NEET']
source_db: MarksBatch1_P2.db
title:
choose-the-correct-combination-of-labelling-that-depicts-the-hormonal-control-of-the-female-reproductive-system

slug:
choose-the-correct-combination-of-labelling-that-depicts-the-hormonal-control-of-the-female-reproductive-system-85053

question:
<div class="question">Choose the correct combination of labelling that depicts the hormonal control of the female reproductive system.<br/> <img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/content_p410q80.png" style="width: 350px; height: 200px;"/></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A - GnRH, B - LH/FSH, C- estrogen or progesterone, D - uterus</span> </div>

answer:
<div class="solution">Oogenesis occurs under the influence of hormones. GnRH is secreted by the hypothalamus which stimulates the anterior lobe of pituitary gland to secrete LH and FSH. FSH stimulates the growth of the ovarian follicles and also increases the development of egg/oocyte within the follicle to complete the meiosis I to form secondary oocyte. FSH also stimulates the formation of estrogens. LH stimulates the corpus luteum to secrete progesterone. Ovulation is induced by LH. Both estrogen and progesterone then act on uterus.</div>


title: choose-the-correct-decreasing-order-of-reactivity-of-alkyl-halides-towards-s-n-1-reaction
slug: choose-the-correct-decreasing-order-of-reactivity-of-alkyl-halides-towards-s-n-1-reaction-18069
tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'TS EAMCET', 'TS EAMCET 2023 (13 May Shift 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Choose the correct decreasing order of reactivity of alkyl halides towards $\mathrm{S}_{\mathrm{N}} 1$ reaction.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Tertiary halide $&gt;$ Secondary halide $&gt;$ Primary halide</span> </div>

answer:
<div class="solution">The reactivity of alkyl halides towards nucleophilic $\mathrm{S}_{\mathrm{N}} 1$ reaction depends on the stability of the intermediate carbocation formed in the first step.<br/>Thus, reactivity follows the order :$3^{\circ}$ halide $&gt;2^{\circ}$ halide $&gt;1^{\circ}$ halide.</div>


title: choose-the-correct-match-bladderwert-sundew-venus-fly-trap
slug: choose-the-correct-match-bladderwert-sundew-venus-fly-trap-29059
question: <div class="question">Choose the correct match.<br/>Bladderwert, sundew, Venus fly trap</div>
tags: ['Biology', 'Morphology of Flowering Plants', 'NEET', 'NEET 2002']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Nepenthese, Dionea, Drosera</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Nepenthese, Utricularia, Vanda</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Utricularia, Drosera, Dionea</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Dionea, Trapa, Vanda</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Utricularia, Drosera, Dionea</span> </div>

answer:
<div class="solution">Utricularia - Bladderwort,<br/>Drosera - Sundew<br/>Dionea - Venus fly trap<br/>They all are insectivorous plants.<br/>Caution<br/>- Insectivorous plants have evolved to develop in places where the soil is thin or poor in nutrients, especially nitrogen. They're found within nitrogen deficient soil. That's why they trap and digest insects to soak up nutrients.</div>


title: choose-the-correct-match-from-the-following-1
slug: choose-the-correct-match-from-the-following-1-40477
question: <div class="question">Choose the correct match from the following.</div>
tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">collagen - most abundant protein in the biosphere</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">GLUT-4 - enables glutamine transport into cells</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">receptor - proteins that receive smell and taste</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">trypsin - hormone used during digestion of food</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">receptor - proteins that receive smell and taste</span> </div>

answer:
<div class="solution">collagen - most abundant protein in the animal world<br/>GLUT-4 - enables glucose transport into cells<br/>receptor - proteins for sensory reception like smell, taste, sound, etc.<br/>trypsin - digestive enzyme</div>


tags: ['Mathematics', 'Matrices', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
choose-the-correct-option-about-the-matrices-given-below-beginaligned-aleftbeginarrayccccos-fracpi4-sin-fracpi4-0-sin-fracpi4-cos-fracpi4-0-0-0-1endar-1

slug:
choose-the-correct-option-about-the-matrices-given-below-beginaligned-aleftbeginarrayccccos-fracpi4-sin-fracpi4-0-sin-fracpi4-cos-fracpi4-0-0-0-1endar-1-34196

question:
<div class="question">Choose the correct option about the matrices given below<br/>\(\begin{aligned} &amp; A=\left[\begin{array}{ccc}\cos \frac{\pi}{4} &amp; \sin \frac{\pi}{4} &amp; 0 \\ -\sin \frac{\pi}{4} &amp; \cos \frac{\pi}{4} &amp; 0 \\ 0 &amp; 0 &amp; 1\end{array}\right] \\ &amp; B=\left[\begin{array}{ccc}1 &amp; 0 &amp; 0 \\ 0 &amp; \cos \frac{\pi}{3} &amp; \sin \frac{\pi}{3} \\ 0 &amp; -\sin \frac{\pi}{3} &amp; \cos \frac{\pi}{3}\end{array}\right] \\ &amp; C=\left[\begin{array}{ccc}\cos \frac{\pi}{6} &amp; 0 &amp; \sin \frac{\pi}{6} \\ 0 &amp; 1 &amp; 0 \\ -\sin \frac{\pi}{6} &amp; \cos \frac{\pi}{6} &amp; 0\end{array}\right]\end{aligned}\)<br/>\(D=\left[\begin{array}{ccc}<br/>\cos \frac{\pi}{2} &amp; \sin \frac{\pi}{2} &amp; 0 \\<br/>-\sin \frac{\pi}{2} &amp; \cos \frac{\pi}{2} &amp; 0 \\<br/>0 &amp; 0 &amp; 1<br/>\end{array}\right]\)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(A^{2020}=1\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(B^{2020}=1\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(D^{2019}=l\)</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">\(B^{2022}=1\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(B^{2022}=1\)</span> </div>

answer:
<div class="solution">Given matrix<br/>\(\begin{aligned}<br/>&amp; A=\left[\begin{array}{ccc}<br/>\cos \frac{\pi}{4} &amp; \sin \frac{\pi}{4} &amp; 0 \\<br/>-\sin \frac{\pi}{4} &amp; \cos \frac{\pi}{4} &amp; 0 \\<br/>0 &amp; 0 &amp; 1<br/>\end{array}\right] \\<br/>&amp; \Rightarrow \quad A^2=\left[\begin{array}{ccc}<br/>\cos \frac{\pi}{2} &amp; \sin \frac{\pi}{2} &amp; 0 \\<br/>-\sin \frac{\pi}{2} &amp; \cos \frac{\pi}{2} &amp; 0 \\<br/>0 &amp; 0 &amp; 1<br/>\end{array}\right] \\<br/>\end{aligned}\)<br/>\(\begin{array}{ll}<br/>\therefore &amp; A^2=D=\left[\begin{array}{ccc}<br/>\cos \frac{\pi}{2} &amp; \sin \frac{\pi}{2} &amp; 0 \\<br/>-\sin \frac{\pi}{2} &amp; \cos \frac{\pi}{2} &amp; 0 \\<br/>0 &amp; 0 &amp; 1<br/>\end{array}\right]=\left[\begin{array}{ccc}<br/>0 &amp; 1 &amp; 0 \\<br/>-1 &amp; 0 &amp; 0 \\<br/>0 &amp; 0 &amp; 1<br/>\end{array}\right] \\<br/>\therefore &amp; A^4=\left[\begin{array}{ccc}<br/>-1 &amp; 0 &amp; 0 \\<br/>0 &amp; -1 &amp; 0 \\<br/>0 &amp; 0 &amp; 1<br/>\end{array}\right]=D^2 \Rightarrow A^8=\left[\begin{array}{lll}<br/>1 &amp; 0 &amp; 0 \\<br/>0 &amp; 1 &amp; 0 \\<br/>0 &amp; 0 &amp; 1<br/>\end{array}\right] \\<br/>\therefore &amp; A^{2020}=\left(A^{505}\right)^4=\left(\left(A^8\right)^{63} \cdot A\right)^4=\left(I^{63} \cdot A\right)^4=A^4 \neq I<br/>\end{array}\)<br/>Similarly, \(D^4=I\), so \(D^{2019} \neq I\)<br/>Now, \(B=\left[\begin{array}{ccc}1 &amp; 0 &amp; 0 \\ 0 &amp; \cos \frac{\pi}{3} &amp; \sin \frac{\pi}{3} \\ 0 &amp; -\sin \frac{\pi}{3} &amp; \cos \frac{\pi}{3}\end{array}\right]\)<br/>\(\Rightarrow \quad B^2=\left[\begin{array}{ccc}<br/>1 &amp; 0 &amp; 0 \\<br/>0 &amp; \cos \frac{2 \pi}{3} &amp; \sin \frac{2 \pi}{3} \\<br/>0 &amp; -\sin \frac{2 \pi}{3} &amp; \cos \frac{2 \pi}{3}<br/>\end{array}\right]\)<br/>\(\begin{aligned}<br/>&amp; \Rightarrow B^4=\left[\begin{array}{ccc}<br/>1 &amp; 0 &amp; 0 \\<br/>0 &amp; \cos \frac{4 \pi}{3} &amp; \sin \frac{4 \pi}{3} \\<br/>0 &amp; -\sin \frac{4 \pi}{3} &amp; \cos \frac{4 \pi}{3}<br/>\end{array}\right] \\<br/>&amp; \Rightarrow B^6=\left[\begin{array}{ccc}<br/>1 &amp; 0 &amp; 0 \\<br/>0 &amp; \cos \frac{6 \pi}{3} &amp; \sin \frac{6 \pi}{3} \\<br/>0 &amp; -\sin \frac{6 \pi}{3} &amp; \cos \frac{6 \pi}{3}<br/>\end{array}\right]=I \\<br/>&amp; \therefore B^{2020} \neq I \text { but } B^{2022}=\left(B^6\right)^{337}=I^{337}=I<br/>\end{aligned}\)</div>


tags: ['Mathematics', 'Matrices', 'AP EAMCET', 'AP EAMCET 2020 (18 Sep Shift 1)']
source_db: MarksBatch1_P2.db
title:
choose-the-correct-option-about-the-matrices-given-below-beginaligned-aleftbeginarrayccccos-fracpi4-sin-fracpi4-0-sin-fracpi4-cos-fracpi4-0-0-0-1endar

slug:
choose-the-correct-option-about-the-matrices-given-below-beginaligned-aleftbeginarrayccccos-fracpi4-sin-fracpi4-0-sin-fracpi4-cos-fracpi4-0-0-0-1endar-85606

question:
<div class="question">Choose the correct option about the matrices given below<br/>\(\begin{aligned} &amp; A=\left[\begin{array}{ccc}\cos \frac{\pi}{4} &amp; \sin \frac{\pi}{4} &amp; 0 \\ -\sin \frac{\pi}{4} &amp; \cos \frac{\pi}{4} &amp; 0 \\ 0 &amp; 0 &amp; 1\end{array}\right] \\ &amp; B=\left[\begin{array}{ccc}1 &amp; 0 &amp; 0 \\ 0 &amp; \cos \frac{\pi}{3} &amp; \sin \frac{\pi}{3} \\ 0 &amp; -\sin \frac{\pi}{3} &amp; \cos \frac{\pi}{3}\end{array}\right] \\ &amp; C=\left[\begin{array}{ccc}\cos \frac{\pi}{6} &amp; 0 &amp; \sin \frac{\pi}{6} \\ 0 &amp; 1 &amp; 0 \\ -\sin \frac{\pi}{6} &amp; \cos \frac{\pi}{6} &amp; 0\end{array}\right]\end{aligned}\)<br/>\(D=\left[\begin{array}{ccc}<br/>\cos \frac{\pi}{2} &amp; \sin \frac{\pi}{2} &amp; 0 \\<br/>-\sin \frac{\pi}{2} &amp; \cos \frac{\pi}{2} &amp; 0 \\<br/>0 &amp; 0 &amp; 1<br/>\end{array}\right]\)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(A^{2020}=1\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(B^{2020}=1\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(D^{2019}=l\)</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">\(B^{2022}=1\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(B^{2022}=1\)</span> </div>

answer:
<div class="solution">Given matrix<br/>\(\begin{aligned}<br/>&amp; A=\left[\begin{array}{ccc}<br/>\cos \frac{\pi}{4} &amp; \sin \frac{\pi}{4} &amp; 0 \\<br/>-\sin \frac{\pi}{4} &amp; \cos \frac{\pi}{4} &amp; 0 \\<br/>0 &amp; 0 &amp; 1<br/>\end{array}\right] \\<br/>&amp; \Rightarrow \quad A^2=\left[\begin{array}{ccc}<br/>\cos \frac{\pi}{2} &amp; \sin \frac{\pi}{2} &amp; 0 \\<br/>-\sin \frac{\pi}{2} &amp; \cos \frac{\pi}{2} &amp; 0 \\<br/>0 &amp; 0 &amp; 1<br/>\end{array}\right] \\<br/>\end{aligned}\)<br/>\(\begin{array}{ll}<br/>\therefore &amp; A^2=D=\left[\begin{array}{ccc}<br/>\cos \frac{\pi}{2} &amp; \sin \frac{\pi}{2} &amp; 0 \\<br/>-\sin \frac{\pi}{2} &amp; \cos \frac{\pi}{2} &amp; 0 \\<br/>0 &amp; 0 &amp; 1<br/>\end{array}\right]=\left[\begin{array}{ccc}<br/>0 &amp; 1 &amp; 0 \\<br/>-1 &amp; 0 &amp; 0 \\<br/>0 &amp; 0 &amp; 1<br/>\end{array}\right] \\<br/>\therefore &amp; A^4=\left[\begin{array}{ccc}<br/>-1 &amp; 0 &amp; 0 \\<br/>0 &amp; -1 &amp; 0 \\<br/>0 &amp; 0 &amp; 1<br/>\end{array}\right]=D^2 \Rightarrow A^8=\left[\begin{array}{lll}<br/>1 &amp; 0 &amp; 0 \\<br/>0 &amp; 1 &amp; 0 \\<br/>0 &amp; 0 &amp; 1<br/>\end{array}\right] \\<br/>\therefore &amp; A^{2020}=\left(A^{505}\right)^4=\left(\left(A^8\right)^{63} \cdot A\right)^4=\left(I^{63} \cdot A\right)^4=A^4 \neq I<br/>\end{array}\)<br/>Similarly, \(D^4=I\), so \(D^{2019} \neq I\)<br/>Now, \(B=\left[\begin{array}{ccc}1 &amp; 0 &amp; 0 \\ 0 &amp; \cos \frac{\pi}{3} &amp; \sin \frac{\pi}{3} \\ 0 &amp; -\sin \frac{\pi}{3} &amp; \cos \frac{\pi}{3}\end{array}\right]\)<br/>\(\Rightarrow \quad B^2=\left[\begin{array}{ccc}<br/>1 &amp; 0 &amp; 0 \\<br/>0 &amp; \cos \frac{2 \pi}{3} &amp; \sin \frac{2 \pi}{3} \\<br/>0 &amp; -\sin \frac{2 \pi}{3} &amp; \cos \frac{2 \pi}{3}<br/>\end{array}\right]\)<br/>\(\begin{aligned}<br/>&amp; \Rightarrow B^4=\left[\begin{array}{ccc}<br/>1 &amp; 0 &amp; 0 \\<br/>0 &amp; \cos \frac{4 \pi}{3} &amp; \sin \frac{4 \pi}{3} \\<br/>0 &amp; -\sin \frac{4 \pi}{3} &amp; \cos \frac{4 \pi}{3}<br/>\end{array}\right] \\<br/>&amp; \Rightarrow B^6=\left[\begin{array}{ccc}<br/>1 &amp; 0 &amp; 0 \\<br/>0 &amp; \cos \frac{6 \pi}{3} &amp; \sin \frac{6 \pi}{3} \\<br/>0 &amp; -\sin \frac{6 \pi}{3} &amp; \cos \frac{6 \pi}{3}<br/>\end{array}\right]=I \\<br/>&amp; \therefore B^{2020} \neq I \text { but } B^{2022}=\left(B^6\right)^{337}=I^{337}=I<br/>\end{aligned}\)</div>


title: choose-the-correct-order-of-electron-gain-enthalpy-2
slug: choose-the-correct-order-of-electron-gain-enthalpy-2-62900
tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'NEET']
source_db: MarksBatch1_P2.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/modules/dbq/cheas77dtry/wxXWUD5q3wvx2802R2y14336Biyd5fAD4CYh71M9gjn9s1kwPS.png"/>Choose the correct order of electron gain enthalpy</div>

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

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

answer:
<div class="solution">Correct Option is : 4 <br/> He<ar> <!-- /Solution --> <!-- Call to Action --> <section class="call-to-action" data-pagefind-ignore=""> <div class="call-to-action-header"> <svg fill="none" height="24" viewbox="0 0 25 24" width="25" xmlns="http://www.w3.org/2000/svg"> <path d="M19.9999 13.5C20.0018 13.8058 19.9089 14.1047 19.734 14.3555C19.559 14.6063 19.3107 14.7968 19.023 14.9006L14.1874 16.6875L12.4062 21.5269C12.3007 21.8134 12.1098 22.0608 11.8594 22.2355C11.6089 22.4101 11.3109 22.5038 11.0055 22.5038C10.7002 22.5038 10.4022 22.4101 10.1517 22.2355C9.90124 22.0608 9.71039 21.8134 9.60491 21.5269L7.8124 16.6875L2.97303 14.9062C2.68646 14.8008 2.43915 14.6099 2.26445 14.3595C2.08976 14.109 1.99609 13.811 1.99609 13.5056C1.99609 13.2003 2.08976 12.9022 2.26445 12.6518C2.43915 12.4013 2.68646 12.2105 2.97303 12.105L7.8124 10.3125L9.59366 5.47313C9.69914 5.18656 9.88998 4.93924 10.1404 4.76455C10.3909 4.58985 10.6889 4.49619 10.9943 4.49619C11.2996 4.49619 11.5977 4.58985 11.8481 4.76455C12.0986 4.93924 12.2894 5.18656 12.3949 5.47313L14.1874 10.3125L19.0268 12.0938C19.3146 12.1986 19.5628 12.3901 19.7371 12.642C19.9114 12.8939 20.0033 13.1937 19.9999 13.5ZM14.7499 4.5H16.2499V6C16.2499 6.19891 16.3289 6.38968 16.4696 6.53033C16.6102 6.67098 16.801 6.75 16.9999 6.75C17.1988 6.75 17.3896 6.67098 17.5302 6.53033C17.6709 6.38968 17.7499 6.19891 17.7499 6V4.5H19.2499C19.4488 4.5 19.6396 4.42098 19.7802 4.28033C19.9209 4.13968 19.9999 3.94891 19.9999 3.75C19.9999 3.55109 19.9209 3.36032 19.7802 3.21967C19.6396 3.07902 19.4488 3 19.2499 3H17.7499V1.5C17.7499 1.30109 17.6709 1.11032 17.5302 0.96967C17.3896 0.829018 17.1988 0.75 16.9999 0.75C16.801 0.75 16.6102 0.829018 16.4696 0.96967C16.3289 1.11032 16.2499 1.30109 16.2499 1.5V3H14.7499C14.551 3 14.3602 3.07902 14.2196 3.21967C14.0789 3.36032 13.9999 3.55109 13.9999 3.75C13.9999 3.94891 14.0789 4.13968 14.2196 4.28033C14.3602 4.42098 14.551 4.5 14.7499 4.5ZM22.9999 7.5H22.2499V6.75C22.2499 6.55109 22.1709 6.36032 22.0302 6.21967C21.8896 6.07902 21.6988 6 21.4999 6C21.301 6 21.1102 6.07902 20.9696 6.21967C20.8289 6.36032 20.7499 6.55109 20.7499 6.75V7.5H19.9999C19.801 7.5 19.6102 7.57902 19.4696 7.71967C19.3289 7.86032 19.2499 8.05109 19.2499 8.25C19.2499 8.44891 19.3289 8.63968 19.4696 8.78033C19.6102 8.92098 19.801 9 19.9999 9H20.7499V9.75C20.7499 9.94891 20.8289 10.1397 20.9696 10.2803C21.1102 10.421 21.301 10.5 21.4999 10.5C21.6988 10.5 21.8896 10.421 22.0302 10.2803C22.1709 10.1397 22.2499 9.94891 22.2499 9.75V9H22.9999C23.1988 9 23.3896 8.92098 23.5302 8.78033C23.6709 8.63968 23.7499 8.44891 23.7499 8.25C23.7499 8.05109 23.6709 7.86032 23.5302 7.71967C23.3896 7.57902 23.1988 7.5 22.9999 7.5Z" fill="#1589EE"></path> </svg> <h3>Looking for more such questions to practice?</h3> </div> <p>
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title: choose-the-correct-order-of-electron-gain-enthalpy-3
slug: choose-the-correct-order-of-electron-gain-enthalpy-3-45462
tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'NEET']
source_db: MarksBatch1_P2.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/modules/dbq/cheas77dtry/wxXWUD5q3wvx2802R2y14336Biyd5fAD4CYh71M9gjn9s1kwPS.png"/>Choose the correct order of electron gain enthalpy</div>

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

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

answer:
<div class="solution">Correct Option is : 3 <br/> Br<f> <!-- /Solution --> <!-- Call to Action --> <section class="call-to-action" data-pagefind-ignore=""> <div class="call-to-action-header"> <svg fill="none" height="24" viewbox="0 0 25 24" width="25" xmlns="http://www.w3.org/2000/svg"> <path d="M19.9999 13.5C20.0018 13.8058 19.9089 14.1047 19.734 14.3555C19.559 14.6063 19.3107 14.7968 19.023 14.9006L14.1874 16.6875L12.4062 21.5269C12.3007 21.8134 12.1098 22.0608 11.8594 22.2355C11.6089 22.4101 11.3109 22.5038 11.0055 22.5038C10.7002 22.5038 10.4022 22.4101 10.1517 22.2355C9.90124 22.0608 9.71039 21.8134 9.60491 21.5269L7.8124 16.6875L2.97303 14.9062C2.68646 14.8008 2.43915 14.6099 2.26445 14.3595C2.08976 14.109 1.99609 13.811 1.99609 13.5056C1.99609 13.2003 2.08976 12.9022 2.26445 12.6518C2.43915 12.4013 2.68646 12.2105 2.97303 12.105L7.8124 10.3125L9.59366 5.47313C9.69914 5.18656 9.88998 4.93924 10.1404 4.76455C10.3909 4.58985 10.6889 4.49619 10.9943 4.49619C11.2996 4.49619 11.5977 4.58985 11.8481 4.76455C12.0986 4.93924 12.2894 5.18656 12.3949 5.47313L14.1874 10.3125L19.0268 12.0938C19.3146 12.1986 19.5628 12.3901 19.7371 12.642C19.9114 12.8939 20.0033 13.1937 19.9999 13.5ZM14.7499 4.5H16.2499V6C16.2499 6.19891 16.3289 6.38968 16.4696 6.53033C16.6102 6.67098 16.801 6.75 16.9999 6.75C17.1988 6.75 17.3896 6.67098 17.5302 6.53033C17.6709 6.38968 17.7499 6.19891 17.7499 6V4.5H19.2499C19.4488 4.5 19.6396 4.42098 19.7802 4.28033C19.9209 4.13968 19.9999 3.94891 19.9999 3.75C19.9999 3.55109 19.9209 3.36032 19.7802 3.21967C19.6396 3.07902 19.4488 3 19.2499 3H17.7499V1.5C17.7499 1.30109 17.6709 1.11032 17.5302 0.96967C17.3896 0.829018 17.1988 0.75 16.9999 0.75C16.801 0.75 16.6102 0.829018 16.4696 0.96967C16.3289 1.11032 16.2499 1.30109 16.2499 1.5V3H14.7499C14.551 3 14.3602 3.07902 14.2196 3.21967C14.0789 3.36032 13.9999 3.55109 13.9999 3.75C13.9999 3.94891 14.0789 4.13968 14.2196 4.28033C14.3602 4.42098 14.551 4.5 14.7499 4.5ZM22.9999 7.5H22.2499V6.75C22.2499 6.55109 22.1709 6.36032 22.0302 6.21967C21.8896 6.07902 21.6988 6 21.4999 6C21.301 6 21.1102 6.07902 20.9696 6.21967C20.8289 6.36032 20.7499 6.55109 20.7499 6.75V7.5H19.9999C19.801 7.5 19.6102 7.57902 19.4696 7.71967C19.3289 7.86032 19.2499 8.05109 19.2499 8.25C19.2499 8.44891 19.3289 8.63968 19.4696 8.78033C19.6102 8.92098 19.801 9 19.9999 9H20.7499V9.75C20.7499 9.94891 20.8289 10.1397 20.9696 10.2803C21.1102 10.421 21.301 10.5 21.4999 10.5C21.6988 10.5 21.8896 10.421 22.0302 10.2803C22.1709 10.1397 22.2499 9.94891 22.2499 9.75V9H22.9999C23.1988 9 23.3896 8.92098 23.5302 8.78033C23.6709 8.63968 23.7499 8.44891 23.7499 8.25C23.7499 8.05109 23.6709 7.86032 23.5302 7.71967C23.3896 7.57902 23.1988 7.5 22.9999 7.5Z" fill="#1589EE"></path> </svg> <h3>Looking for more such questions to practice?</h3> </div> <p>
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title: choose-the-correct-statement-3
slug: choose-the-correct-statement-3-30486
question: <div class="question">Choose the correct statement.</div>
tags: ['Biology', 'Environmental Issues', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0.1% of impurities in sewage water also consist of suspended solids like fecal matter, bacteria, paper fibres, etc.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Mauve-coloured flowers are a characteristic feature of the world's most problematic weed.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Algal blooms cause deterioration of the water quality but do not cause any harm to other aquatic life, like fish.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Biomagnification refers to the decrease in concentration of the toxicant at successive trophic levels.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Mauve-coloured flowers are a characteristic feature of the world's most problematic weed.</span> </div>

answer:
<div class="solution">Beautiful mauve-colored flowers are found on very appealingly-shaped floating plants in water bodies. These plants which were introduced into India for their lovely flowers have caused havoc by their excessive growth by causing blocks in our waterways. They grow faster than our ability to remove them. These are plants of water hyacinth (Eichhornia crassipes), the worldâs most problematic aquatic weed, also called âTerror of Bengalâ. They grow abundantly in eutrophic water bodies, and lead to an imbalance in the ecosystem dynamics of the water body. <br/></div>


title: choose-the-correct-statement-from-following
slug: choose-the-correct-statement-from-following-64591
question: <div class="question">Choose the correct statement from following.</div>
tags: ['Physics', 'Units and Dimensions', 'TS EAMCET', 'TS EAMCET 2022 (18 Jul Shift 1)']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Not all basic laws of physics are universal</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Conservation laws have a deep connection with symmetries of nature</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">There are four to six fundamental forces in nature that govern the diverse phenomena of the world</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Physics can generate new technology but new physics cannot come out from technology</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Conservation laws have a deep connection with symmetries of nature</span> </div>

answer:
<div class="solution"><blockquote><p>Neother's theorem tells that conservation laws have a deep connection with symmetries of nature.</p><p>Fundamental forces are: Strong nuclear force, electromagnetic force, weak nuclear force and gravitational force.</p></blockquote></div>


title: choose-the-correct-statement-regarding-the-formation-of-carbocations-a-and-b-given
slug: choose-the-correct-statement-regarding-the-formation-of-carbocations-a-and-b-given-33962
tags: ['Chemistry', 'Hydrocarbons', 'JEE Main', 'JEE Main 2021 (17 Mar Shift 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question"><p>Choose the correct statement regarding the formation of carbocations A and B given :-</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/ddd634b7-cc82-4b9c-94b1-018b86715a5b-image.png" style="width: 602px; height: 176px;"/></p></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Carbocation B is more stable and formed relatively at faster rate</span> </div>

answer:
<div class="solution"><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/a63692ba-0d1d-4021-b901-2c15f7c092d7-image.png" style="width: 424px; height: 150px;"/></p><p>This is more stable due to secondary cation formation and formed with faster rate due to low activation energy.</p></div>


title: choose-the-mismatched-pair-from-the-following
slug: choose-the-mismatched-pair-from-the-following-27719
question: <div class="question">Choose the mismatched pair from the following.</div>
tags: ['Biology', 'Human Health and Diseases', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">IgG - The most abundant type of serum</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">IgA - Major antibody in secretions such as saliva, tears and breast milk</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">IgD - Plays an important role in protecting against pathogens that invade through the gut or respiratory mucosa</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">IgE - Least abundant and latest isotope which plays an important role in hypersensitivity</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">IgD - Plays an important role in protecting against pathogens that invade through the gut or respiratory mucosa</span> </div>

answer:
<div class="solution">The role of IgD antibodies in immunity is still somewhat unknown, but antibodies that Play an important role in protecting against pathogens invading through the gut or respiratory mucosa is IgA antibodies.</div>


title: choose-the-option-with-the-correct-labels-for-the-diagram-given-below
slug: choose-the-option-with-the-correct-labels-for-the-diagram-given-below-72043
tags: ['Biology', 'Sexual Reproduction in Flowering Plants', 'NEET']
source_db: MarksBatch1_P2.db
question:
<div class="question">Choose the option with the correct labels for the diagram given below.<br/> <img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/micropyle234.jpg" style="max-width:100%; object-fit:contain"/></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A - megaspore dyad, B - nucellus</span> </div>

answer:
<div class="solution">The ovule is a small structure attached to the placenta by means of a stalk called funicle. The body of the ovule fuses with funicle in the region called hilum. Thus, hilum represents the junction between ovule and funicle. Each ovule has one or two protective envelopes called integuments. Integuments encircle the nucellus except at the tip where a small opening called the micropyle is organised. Opposite the micropylar end, is the chalaza, representing the basal part of the ovule.<br/>Enclosed within the integuments is a mass of cells called the nucellus. Cells of the nucellus have abundant reserve food materials. Located in the nucellus is the embryo sac or female gametophyte. An ovule generally has a single embryo sac formed from a megaspore. Meiosis results in the production of four megaspores.<br/><br/>The given diagram is of the micropylar end of the embryo sac.<div style="text-align: center;"><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/micropyle_answer6789.jpg" style="max-width:100%; object-fit:contain"/></div></div>


tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1:3</span> </div>
source_db: MarksBatch1_P2.db
title:
chorine-exists-in-two-isotopic-forms-cl37-and-cl35-but-its-atomic-mass-is-355-this-indicates-the-ratio-of-cl37-and-cl35-is-approximately

slug:
chorine-exists-in-two-isotopic-forms-cl37-and-cl35-but-its-atomic-mass-is-355-this-indicates-the-ratio-of-cl37-and-cl35-is-approximately-35288

question:
<div class="question">Chorine exists in two isotopic forms, Cl-37 and Cl-35 but its atomic mass is 35.5. This indicates the ratio of Cl-37 and Cl-35 is approximately</div>

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

answer:
<div class="solution">Let relative abundance of <math><mi mathvariant="normal">C</mi><mi mathvariant="normal">l</mi><mo>-</mo><mn>37</mn><mo>=</mo><mi mathvariant="normal">x</mi><mi mathvariant="normal">%</mi></math> <br/>then relative abundance of <math><mi mathvariant="normal">C</mi><mi mathvariant="normal">l</mi><mo>-</mo><mn>35</mn><mo>=</mo><mo>(</mo><mn>100</mn><mo>-</mo><mi mathvariant="normal">x</mi><mo>)</mo><mi mathvariant="normal">%</mi></math> <br/>Average atomic mass <math><mo>=</mo><mfrac><mrow><mi mathvariant="normal">x</mi><mo>Ã</mo><mn>37</mn><mo>+</mo><mo>(</mo><mn>100</mn><mo>-</mo><mi mathvariant="normal">x</mi><mo>)</mo><mn>35</mn></mrow><mrow><mn>100</mn></mrow></mfrac><mn>35.5</mn></math> <br/><math><mn>37</mn><mi mathvariant="normal">x</mi><mo>+</mo><mn>3500</mn><mo>-</mo><mn>35</mn><mi mathvariant="normal">x</mi><mo>=</mo><mn>3550</mn></math> <br/><math><mi mathvariant="normal">x</mi><mo>=</mo><mn>25</mn></math> <br/>So <math><mn>100</mn><mo>-</mo><mi mathvariant="normal">x</mi><mo>=</mo><mn>75</mn></math> <br/>Thus, the ratio of Cl-37 and Cl-35 is <math><mi mathvariant="normal">x</mi><mo>:</mo><mo>(</mo><mn>100</mn><mo>-</mo><mi mathvariant="normal">x</mi><mo>)</mo><mo>=</mo><mn>25</mn><mo>:</mo><mn>75</mn></math> <br/>1:3</div>


title: class-crustacea-differs-from-insecta-in-having
slug: class-crustacea-differs-from-insecta-in-having-65422
question: <div class="question">Class Crustacea differs from Insecta in having :</div>
tags: ['Biology', 'Animal Kingdom', 'JIPMER', 'JIPMER 2006']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">two pairs of antennae</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">jointed foot</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">chitinous cuticle</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">two pairs of antennae</span> </div>

answer:
<div class="solution">The main characteristics of class Crustacea and Insecta are as follows :<br/>(1) Class Crustacea : Mostly aquatic with gills, two pairs of antennae and atleast three pairs of jaws, appendages mostly biramous and always more than four in the trunk region.<br/>Example : prawn, crab, lobster etc.<br/>(2) Class Insecta : Hexapod arthropods with a pair of antennae and three pairs of Jaws.<br/>Example : cockroach, grasshopper, bees, housefly etc.</div>


title: class-crustacea-has-following-features
slug: class-crustacea-has-following-features-85132
question: <div class="question">Class Crustacea has following features :</div>
tags: ['Biology', 'Animal Kingdom', 'AIIMS', 'AIIMS 2001']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Cephalothorax, book lungs, chitinous exoskeleton</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Head and thorax, biramous appendages, book lungs</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Head and thorax, book lungs, chitinous exoskeleton</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Cephalothorax, biramous appendages, gills</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Cephalothorax, biramous appendages, gills</span> </div>

answer:
<div class="solution">Crustaceans are mostly marine but a few live in freshwater or moist places. Body consists of cephalothorax and abdomen. Each body segment bears a pair of biramous appendages. Respiration occurs through body surface or gills. Excretion occurs through green glands. They bear two pairs of antennae.</div>


tags: ['Physics', 'Atomic Physics']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
classically-an-electron-can-be-in-any-orbit-around-the-nucleus-of-an-atom-then-what-determines-the-typical-atomic-size-why-is-an-atom-not-say-thousand

slug:
classically-an-electron-can-be-in-any-orbit-around-the-nucleus-of-an-atom-then-what-determines-the-typical-atomic-size-why-is-an-atom-not-say-thousand-24676

question:
<div class="question">Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of nature and see if we can get a quantity with the dimensions of length that isroughly equal totheknown size of an atom $\left(\sim 10^{-}\right.$ 10 m).<br/>(a) Construct a quantity with the dimensions of length from the fundamental constants $e, m_e$, and c. Determine its numerical value.<br/>(b) You will find that the length obtained in (a) is many orders of magnitude smaller than the atomic dimensions. Further, it involves c. But energies of atoms are mostly in non-relativistic domain where c is not expected to play any role. This is what may have suggested Bohr to discard $\mathrm{c}$ and look for 'something else' to get the right atomic size. Now, the Planck's constant h had already made its appearance elsewhere. Bohr's great insight lay in recognising that $h, \mathrm{~m}_{\mathrm{e}}$ and e will yield the right atomic size. Construct a quantity with the dimension of length from $h, m_e$ and e and confirm that its numerical value has indeed the correct order of magnitude.</div>

answer:
<div class="solution">(a) The quantity $\left(\frac{\mathrm{e}^2}{\varepsilon_0 \mathrm{mc}^2}\right)$ has dimensions of length. Its value $\simeq 10^{-15} \mathrm{~m}$ is much smaller than atomic size.<br/>(b) The quantity $\left(\frac{\varepsilon_0(h)^2}{m e^2}\right)$ has dimensions of length. Its value $\approx 10^{-10} \mathrm{~m}$ of the order of atomic size. However constants like $2 \pi$ or $4 \pi$ have to be added to arrive at correct formula.</div>


title: classify-1bromobut2ene-as-primary-secondary-and-tertiary-halides
slug: classify-1bromobut2ene-as-primary-secondary-and-tertiary-halides-26740
question: <div class="question">Classify 1-Bromobut-2-ene as primary, secondary and tertiary halides.</div>
tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'NEET']
answer: <div class="solution">Correct Option is : (A)<br/>Primary halide</div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Primary halide</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Secondary halide</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Tertiary halide</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">Primary halide</span> </div>


title: classify-2bromo2methylpropane-as-primary-secondary-and-tertiary-halides
slug: classify-2bromo2methylpropane-as-primary-secondary-and-tertiary-halides-81381
tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'NEET']
answer: <div class="solution">Correct Option is : (C)<br/>Tertiary halide</div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Classify 2-Bromo-2-methylpropane  as primary, secondary and tertiary halides.</div>

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


title: classify-4bromopent2ene-as-primary-secondary-and-tertiary-halides
slug: classify-4bromopent2ene-as-primary-secondary-and-tertiary-halides-68698
question: <div class="question">Classify 4-Bromopent-2-ene as primary, secondary and tertiary halides.</div>
tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'NEET']
answer: <div class="solution">Correct Option is : (B)<br/>Secondary halide</div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Primary halide</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Secondary halide</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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 halide</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">Secondary halide</span> </div>


tags: ['Chemistry', 'Amines']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
classify-the-following-amines-as-primary-secondary-and-tertiary-i-ii-iii-leftmathrmc2-mathrmh5right2-mathrmchnh2-iv-leftmathrmc2-mathrmh5right2-mathrm

slug:
classify-the-following-amines-as-primary-secondary-and-tertiary-i-ii-iii-leftmathrmc2-mathrmh5right2-mathrmchnh2-iv-leftmathrmc2-mathrmh5right2-mathrm-29981

question:
<div class="question">Classify the following amines as primary, secondary and tertiary :<br/>(i) <img src="https://cdn-question-pool.getmarks.app/modules/cbse/f7RXAHLRufpPxtZTtLFD2LsH0oH2qU-zCk2Y__Gx-sI.original.fullsize.png"/><br/><br/>(ii)<img src="https://cdn-question-pool.getmarks.app/modules/cbse/awwJo5Ytxr2rGyvzCSLMTDrsCH2_WJSLgRk-u7qr2BI.original.fullsize.png"/><br/><br/>(iii) \(\left(\mathrm{C}_2 \mathrm{H}_5\right)_2 \mathrm{CHNH}_2\)<br/>(iv) \(\left(\mathrm{C}_2 \mathrm{H}_5\right)_2 \mathrm{NH}\)</div>

answer:
<div class="solution">(i) \(1^{\circ}\)<br/>(iii) \(1^{\circ}\)<br/>(iii) \(3^{\circ}\)<br/>(iv) \(2^{\circ}\)</div>


title: classify-the-following-amines-as-primary-secondary-or-tertiary-1
slug: classify-the-following-amines-as-primary-secondary-or-tertiary-1-57955
tags: ['Chemistry', 'Amines', 'NEET']
answer: <div class="solution">Correct Option is : (B)<br/>Secondary</div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Classify the following amines as primary, secondary or tertiary:  <br/><img src="https://cdn-question-pool.getmarks.app/modules/ncoq/cheas77dtry/lzP8Q1sZxqHbMnrQzJXWgm1Uxn21zFgnBOpKPtPodiBJJBQCK9..png"/><br/></div>

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

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


title: classify-the-following-amines-as-primary-secondary-or-tertiary-2
slug: classify-the-following-amines-as-primary-secondary-or-tertiary-2-40327
tags: ['Chemistry', 'Amines', 'NEET']
answer: <div class="solution">Correct Option is : (C)<br/>Tertiary</div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Classify the following amines as primary, secondary or tertiary:  <br/><img src="https://cdn-question-pool.getmarks.app/modules/ncoq/cheas77dtry/B6aJYfRlOmZV16xnY2RucGXT5jMSohwdWT3ec4Xe7BBAEe6Hr9..png"/><br/></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="correct"> <span class="option-label">C</span> <span class="option-data">Tertiary</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Quaternary</span> </li> </ul>

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


title: classify-the-following-amines-as-primary-secondary-or-tertiary-3
slug: classify-the-following-amines-as-primary-secondary-or-tertiary-3-85091
tags: ['Chemistry', 'Amines', 'NEET']
answer: <div class="solution">Correct Option is : (A)<br/>Primary</div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Classify the following amines as primary, secondary or tertiary:  <br/><img src="https://cdn-question-pool.getmarks.app/modules/ncoq/cheas77dtry/MlKnWlsiX6B0ETmYDxU8WhdRL5Rb1pzjukmo6o3MjKnhl52nWa..png"/><br/></div>

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

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


title: classify-the-following-amines-as-primary-secondary-or-tertiary
slug: classify-the-following-amines-as-primary-secondary-or-tertiary-28034
tags: ['Chemistry', 'Amines', 'NEET']
answer: <div class="solution">Correct Option is : (A)<br/>Primary</div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Classify the following amines as primary, secondary or tertiary:  <br/><img src="https://cdn-question-pool.getmarks.app/modules/ncoq/cheas77dtry/lQ8YBOX25F3MvWz5uuwapgB14lZBbCZUAh8YipI2ZZMPn39lDj..png"/><br/></div>

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

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


title: classify-the-following-as-primary-secondary-and-tertiary-alcohols-1
slug: classify-the-following-as-primary-secondary-and-tertiary-alcohols-1-89641
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
answer: <div class="solution">Correct Option is : (C)<br/>Secondary alcohol</div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Classify the following as primary, secondary and tertiary alcohols:  <br/><img src="https://cdn-question-pool.getmarks.app/modules/ncoq/cheas77dtry/0EEGK6xWgIQcdUu1cK1cBwIOVRSkCb2RjKjujJnJ0XgQ2njb0s..png"/><br/></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">Tertiary alcohol</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Secondary alcohol</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">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">Secondary alcohol</span> </div>


title: classify-the-following-as-primary-secondary-and-tertiary-alcohols-2
slug: classify-the-following-as-primary-secondary-and-tertiary-alcohols-2-72701
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
answer: <div class="solution">Correct Option is : (C)<br/>Tertiary alcohol</div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Classify the following as primary, secondary and tertiary alcohols: <br/><img src="https://cdn-question-pool.getmarks.app/modules/ncoq/cheas77dtry/r6XccmiIGbuNh1SBGuptSBPxpgu6EsM56nOjqNXJq4GuzqWXQ6..png"/><br/></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">None of the above</span> </li> </ul>

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


title: classify-the-following-as-primary-secondary-and-tertiary-alcohols-3
slug: classify-the-following-as-primary-secondary-and-tertiary-alcohols-3-97454
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
answer: <div class="solution">Correct Option is : (A)<br/>Primary alcohol</div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Classify the following as primary, secondary and tertiary alcohols:  <br/><img src="https://cdn-question-pool.getmarks.app/modules/ncoq/cheas77dtry/XkGdt2a2T7HSG1LByl8gv2XoZoX4qB9OyMyZQIUttoZrP84Gsr..png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Primary 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">B</span> <span class="option-data">Secondary alcohol</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Tertiary alcohol</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above</span> </li> </ul>

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


title: classify-the-following-as-primary-secondary-and-tertiary-alcohols-4
slug: classify-the-following-as-primary-secondary-and-tertiary-alcohols-4-54829
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
answer: <div class="solution">Correct Option is : (B)<br/>Primary alcohol</div>
source_db: MarksBatch1_P2.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/modules/ncoq/cheas77dtry/YR3MN8ijmusos1FAgoSCJegbyVZEhEd7zW4Iew7XANVDELy3SF..png"/><br/>  Classify the following as primary, secondary and tertiary alcohols:</div>

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


title: classify-the-following-as-primary-secondary-and-tertiary-alcohols-5
slug: classify-the-following-as-primary-secondary-and-tertiary-alcohols-5-13221
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
answer: <div class="solution">Correct Option is : (B)<br/>Secondary alcohol</div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Classify the following as primary, secondary and tertiary alcohols:  <br/><img src="https://cdn-question-pool.getmarks.app/modules/ncoq/cheas77dtry/ZEpxZh1hXLekHfPWcLC3tae8WMAp4kX6L7w2aW0wxPJCWJgkiu..png"/><br/></div>

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

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


tags: ['Chemistry', 'Alcohols Phenols and Ethers']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
classify-the-following-as-primary-secondary-and-tertiary-alcohols-i-ii-h-2-c-ch-ch-2-oh-iii-ch-3-ch-2-ch-2-oh-iv-v-vi

slug:
classify-the-following-as-primary-secondary-and-tertiary-alcohols-i-ii-h-2-c-ch-ch-2-oh-iii-ch-3-ch-2-ch-2-oh-iv-v-vi-44346

question:
<div class="question">Classify the following as primary, secondary and tertiary alcohols.<br/>(i)<img src="https://cdn-question-pool.getmarks.app/modules/cbse/4OMwwzYdYJqgtMWeqnXW1aiSXh5Y0PuIY33TliqlgNQ.original.fullsize.png"/><br/><br/>(ii) $\mathrm{H}_2 \mathrm{C}=\mathrm{CH}-\mathrm{CH}_2 \mathrm{OH}$<br/>(iii) $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{OH}$<br/>(iv)<img src="https://cdn-question-pool.getmarks.app/modules/cbse/YcHKg2_dflspYu0253LjzqXOksn6zqZ1wW0Kd1OPaT0.original.fullsize.png"/><br/><br/>(v)<img src="https://cdn-question-pool.getmarks.app/modules/cbse/MqLc2aRMRgr3ntLYxGVpiYUPs-30m0CtNXMWe2XiKZ0.original.fullsize.png"/><br/><br/>(vi)<img src="https://cdn-question-pool.getmarks.app/modules/cbse/c6eFx8poC54wtCCnNz7B-1KF2igihs7Q4ZDq8Ir0AP4.original.fullsize.png"/><br/></div>

answer:
<div class="solution">Primary alcohols: (i), (ii), (iii)<br/>Secondary alcohols : (iv), (v)<br/>Tertiary alcohols : (vi)</div>


title: classify-the-following-as-primary-secondary-and-tertiary-alcohols
slug: classify-the-following-as-primary-secondary-and-tertiary-alcohols-39003
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
answer: <div class="solution">Correct Option is : (A)<br/>Primary alcohol</div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Classify the following as primary, secondary and tertiary alcohols:  <br/><img src="https://cdn-question-pool.getmarks.app/modules/ncoq/cheas77dtry/dMgc59nudnxI4ZSXeBsbUtH59sr602DwLVCnVizTvYFxhBWHY9..png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Primary 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">B</span> <span class="option-data">Secondary alcohol</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Tertiary alcohol</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above</span> </li> </ul>

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


tags: ['Chemistry', 'Haloalkanes and Haloarenes']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
classify-the-following-compounds-as-primary-secondary-and-tertiary-halides-a-1bromobut2ene-b-4bromopent2ene-c-2bromo2methylpropane

slug:
classify-the-following-compounds-as-primary-secondary-and-tertiary-halides-a-1bromobut2ene-b-4bromopent2ene-c-2bromo2methylpropane-79912

question:
<div class="question">Classify the following compounds as primary, secondary and tertiary halides.<br/>(a) 1-bromobut-2-ene<br/>(b) 4-bromopent-2-ene<br/>(c) 2-bromo-2-methylpropane</div>

answer:
<div class="solution">$$<br/>\text { The structural formula of the given compounds are }<br/>$$<br/>(a) <img src="https://cdn-question-pool.getmarks.app/modules/cbse/2Wo10kItjaQj-ZeF0yJbiiqoWdzPclXBs3Nl9fIHQIk.original.fullsize.png"/><br/><br/>(b)<img src="https://cdn-question-pool.getmarks.app/modules/cbse/iQFV4f9GOVgaYKJBawTElgIFs6FBeKq83kz489YORoU.original.fullsize.png"/><br/><br/>(c)<img src="https://cdn-question-pool.getmarks.app/modules/cbse/3s8DXc8t8rUXOz7gPW-xdbX00P7rjKGvLIm06owzLek.original.fullsize.png"/><br/></div>


title: climax-stage-is-achieved-quickly-in-secondary-succession-as-compared-to-primary-succession-why
tags: ['Biology', 'Ecosystem']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
slug:
climax-stage-is-achieved-quickly-in-secondary-succession-as-compared-to-primary-succession-why-25410

question:
<div class="question">Climax stage is achieved quickly in secondary succession as compared to primary succession. Why?</div>

answer:
<div class="solution">The rate of ecological succession is quicker in secondary succession as compared to primary succession as the soil (substratum) is already available for further succession. In primary succession, the succession starts from bare rocks, thus takes time for colonisation by plants first as there are no nutrient holding mechanisms.</div>


title: closed-vascular-bundles-lack-1
slug: closed-vascular-bundles-lack-1-99985
question: <div class="question">Closed vascular bundles lack</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET', 'NEET 2012 (Screening)']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">ground tissue</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">conjunctive tissue</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">cambium</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">pith</span> </li> </ul>

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

answer:
<div class="solution">In dicot stems, cambium is present between phloem and xylem. Such vascular bundles, because of the presence of cambium, posses the ability to form secondary xylem and phloem tissues and hence, are called open vascular bundles. On the contrary, vascular bundles in monocots have no cambium. Hence, they do not form secondary tissues, and are referred to as closed.</div>


title: closed-vascular-bundles-lack
slug: closed-vascular-bundles-lack-21160
question: <div class="question">Closed vascular bundles lack</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Ground tissue</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Conjunctive tissue</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Cambium</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Pith</span> </li> </ul>

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

answer:
<div class="solution">In closed vascular bundle cambium is absent between xylem and phloem. Ground tissue, conjunctive tissue is pith is present in stele. Stele is the arrangement of V.B. If xylem is outside it is exarch &amp; if xylem is inside or below the phloem it is endarch.</div>


title: coagulation-of-egg-on-heating-is-because-of
slug: coagulation-of-egg-on-heating-is-because-of-54706
question: <div class="question">Coagulation of egg, on heating is because of :</div>
tags: ['Chemistry', 'Biomolecules', 'JEE Main', 'JEE Main 2024 (05 Apr Shift 2)']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The secondary structure of protein remains unchanged</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Denaturation of protein occurs</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Biological property of protein remains unchanged</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Breaking of the peptide linkage in the primary structure of protein occurs</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Denaturation of protein occurs</span> </div>

answer:
<div class="solution">Coagulation of egg give primary structure of protein, which is known as denaturation of protein</div>


tags: ['Biology', 'Structural Organisation in Animals', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">I</span> </div>
source_db: MarksBatch1_P2.db
title:
cockroaches-are-a-type-of-insect-belonging-to-the-phylum-arthropoda-and-these-are-dioecious-their-body-is-divided-into-segments-and-further-into-large

slug:
cockroaches-are-a-type-of-insect-belonging-to-the-phylum-arthropoda-and-these-are-dioecious-their-body-is-divided-into-segments-and-further-into-large-10301

question:
<div class="question">Cockroaches are a type of insect belonging to the phylum Arthropoda and these are dioecious. Their body is divided into segments and further into larger parts. Both male cockroach and female cockroach have abdomen that has how many segments?<br/>
 
<table border="1"> <tbody> <tr> <td> </td> <td>Male Cockroach</td> <td>Female Cockroach</td> </tr> <tr> <td>I</td> <td>10</td> <td>10</td> </tr> <tr> <td>II</td> <td>10</td> <td>12</td> </tr> <tr> <td>III</td> <td>12</td> <td>10</td> </tr> <tr> <td>IV</td> <td>06</td> <td>06</td> </tr> </tbody> </table> </div>

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

answer:
<div class="solution">Cockroach, a common insect, shows the features of Arthropoda of been segmented and having appendages. The cockroach body is divisible into three major parts - head, thorax, and abdomen. The head of the cockroach has 6 fused segments and the abdomen is made of 10. Even though, cockroach been dioecious (male and female separate organisms), the segmentation of three parts is the same. Abdomen in both female and male consists of 10 segments each. Thus, making row I the right answer</div>


title: coefficient-of-correlation-is-the-measure-of
slug: coefficient-of-correlation-is-the-measure-of-39996
question: <div class="question">Coefficient of correlation is the measure of $\quad$</div>
tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2013 (Phase 2)']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">central tendency</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">dispersion</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">both central tendency and dispersion</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">neither central tendency nor dispersion</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">neither central tendency nor dispersion</span> </div>


tags: ['Physics', 'Units and Dimensions', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch1_P2.db
title:
coefficient-of-thermal-conductivity-is-the-product-of-heat-distance-and-reciprocal-of-area-difference-in-temperature-time-the-new-value-of-a-unit-of-c-1

slug:
coefficient-of-thermal-conductivity-is-the-product-of-heat-distance-and-reciprocal-of-area-difference-in-temperature-time-the-new-value-of-a-unit-of-c-1-56667

question:
<div class="question">Coefficient of thermal conductivity is the product of heat, distance and reciprocal of (area <math> <mo>Ã</mo> </math> difference in temperature <math><mo>Ã</mo></math> time). The new value of a unit of coefficient of thermal conductivity, if fundamental units are <math><mn>21.6</mn><mtext>kg</mtext></math>, <math> <mrow> <mtext>1 decimetre</mtext></mrow></math>, <math> <mrow> <mtext>4 K</mtext> </mrow> </math> and <math> <mrow> <mtext>1 minute </mtext></mrow></math>will be ______ <math><mo>Ã</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>-</mo><mn>6</mn></mrow></msup></math> new units. If your answer is K, mark 2K as answer after rounding off to nearest integer.</div>

answer:
<div class="solution">Coefficient of thermal conductivity, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">k</mi><mo>=</mo><mfrac><mrow><mi mathvariant="normal">Q</mi><mo>Ã</mo><mi>l</mi></mrow><mrow><mi mathvariant="normal">A</mi><mo>Ã</mo><mi>ÎÎ¸</mi><mo>Ã</mo><mi>t</mi></mrow></mfrac></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>â</mo><mo> </mo><mi mathvariant="normal">K</mi><mo>=</mo><mfrac><mrow><mstyle displaystyle="true"><mfrac><mrow><mi>m</mi><msup><mi>l</mi><mn>2</mn></msup></mrow><msup><mi>t</mi><mn>2</mn></msup></mfrac></mstyle><mo>Ã</mo><mi mathvariant="normal">l</mi></mrow><mrow><msup><mi mathvariant="normal">l</mi><mn>2</mn></msup><mo>Ã</mo><mi mathvariant="normal">Î</mi><mi mathvariant="normal">Î¸</mi><mo>Ã</mo><mi mathvariant="normal">t</mi></mrow></mfrac></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>â</mo><mo> </mo><mi mathvariant="normal">K</mi><mo>=</mo><mfrac><mrow><mi mathvariant="normal">m</mi><mo>Ã</mo><mi mathvariant="normal">l</mi></mrow><mrow><mi mathvariant="normal">Î</mi><mi mathvariant="normal">Î¸</mi><mo>Ã</mo><msup><mi mathvariant="normal">t</mi><mn>3</mn></msup></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>21.6</mn><mo>Ã</mo><mn>0.1</mn></mrow><mrow><mn>4</mn><mo>Ã</mo><msup><mfenced separators="|"><mn>60</mn></mfenced><mn>3</mn></msup></mrow></mfrac></math><br/><math><mo>=</mo><mn>2.5</mn><mo>Ã</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>-</mo><mn>6</mn></mrow></msup></math> new units</div>


tags: ['Physics', 'Units and Dimensions', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">02.50</span> </div>
source_db: MarksBatch1_P2.db
title:
coefficient-of-thermal-conductivity-is-the-product-of-heat-distance-and-reciprocal-of-area-difference-in-temperature-time-the-new-value-of-a-unit-of-c

slug:
coefficient-of-thermal-conductivity-is-the-product-of-heat-distance-and-reciprocal-of-area-difference-in-temperature-time-the-new-value-of-a-unit-of-c-58283

question:
<div class="question">Coefficient of thermal conductivity is the product of heat, distance and reciprocal of (area <math> <mo>Ã</mo> </math> difference in temperature <math><mo>Ã</mo></math> time). The new value of a unit of coefficient of thermal conductivity, if fundamental units are <math><mn>21.6</mn><mtext>kg</mtext></math>, <math> <mrow> <mtext>1 decimetre</mtext></mrow></math>, <math> <mrow> <mtext>4 K</mtext> </mrow> </math> and <math> <mrow> <mtext>1 minute </mtext></mrow></math>will be ______ <math><mo>Ã</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>-</mo><mn>6</mn></mrow></msup></math> new units.</div>

answer:
<div class="solution">Coefficient of thermal conductivity, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">k</mi><mo>=</mo><mfrac><mrow><mi mathvariant="normal">Q</mi><mo>Ã</mo><mi>l</mi></mrow><mrow><mi mathvariant="normal">A</mi><mo>Ã</mo><mi>ÎÎ¸</mi><mo>Ã</mo><mi>t</mi></mrow></mfrac></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>â</mo><mo> </mo><mi mathvariant="normal">K</mi><mo>=</mo><mfrac><mrow><mstyle displaystyle="true"><mfrac><mrow><mi>m</mi><msup><mi>l</mi><mn>2</mn></msup></mrow><msup><mi>t</mi><mn>2</mn></msup></mfrac></mstyle><mo>Ã</mo><mi mathvariant="normal">l</mi></mrow><mrow><msup><mi mathvariant="normal">l</mi><mn>2</mn></msup><mo>Ã</mo><mi mathvariant="normal">Î</mi><mi mathvariant="normal">Î¸</mi><mo>Ã</mo><mi mathvariant="normal">t</mi></mrow></mfrac></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>â</mo><mo> </mo><mi mathvariant="normal">K</mi><mo>=</mo><mfrac><mrow><mi mathvariant="normal">m</mi><mo>Ã</mo><mi mathvariant="normal">l</mi></mrow><mrow><mi mathvariant="normal">Î</mi><mi mathvariant="normal">Î¸</mi><mo>Ã</mo><msup><mi mathvariant="normal">t</mi><mn>3</mn></msup></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>21.6</mn><mo>Ã</mo><mn>0.1</mn></mrow><mrow><mn>4</mn><mo>Ã</mo><msup><mfenced separators="|"><mn>60</mn></mfenced><mn>3</mn></msup></mrow></mfrac></math><br/><br/><math><mo>=</mo><mn>2.5</mn><mo>Ã</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>-</mo><mn>6</mn></mrow></msup></math> new units</div>


tags: ['Mathematics', 'Statistics', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
coefficient-of-variation-of-two-distributions-are-50-and-60-and-their-arithmetic-means-are-30-and-25-respectively-difference-of-their-standard-deviati-1

slug:
coefficient-of-variation-of-two-distributions-are-50-and-60-and-their-arithmetic-means-are-30-and-25-respectively-difference-of-their-standard-deviati-1-88807

question:
<div class="question">Coefficient of variation of two distributions are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math> and their arithmetic means are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math>, respectively. Difference of their standard deviation is</div>

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

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

answer:
<div class="solution"><p>Given, coefficient of variation <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mn>1</mn></msub><mo>=</mo><mn>50</mn></math></p><p>and coefficient of variation <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mn>2</mn></msub><mo>=</mo><mn>60</mn></math>.</p><p>We have, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mover><mi>x</mi><mo>¯</mo></mover><mn>1</mn></msub><mo>=</mo><mn>30</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mover><mi>x</mi><mo>¯</mo></mover><mn>2</mn></msub><mo>=</mo><mn>25</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo><mo> </mo><mi>C</mi><mo>=</mo><mfrac><mi>σ</mi><mover><mi>x</mi><mo>¯</mo></mover></mfrac><mo>×</mo><mn>100</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo>=</mo><mfrac><msub><mi>σ</mi><mn>1</mn></msub><mn>30</mn></mfrac><mo>×</mo><mn>100</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msub><mi>σ</mi><mn>1</mn></msub><mo>=</mo><mn>15</mn></math></p><p>and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo>=</mo><mfrac><msub><mi>σ</mi><mn>2</mn></msub><mn>25</mn></mfrac><mo>×</mo><mn>100</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msub><mi>σ</mi><mn>2</mn></msub><mo>=</mo><mn>15</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Required difference <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>σ</mi><mn>1</mn></msub><mo>-</mo><msub><mi>σ</mi><mn>2</mn></msub><mo>=</mo><mn>15</mn><mo>-</mo><mn>15</mn><mo>=</mo><mn>0</mn></math></p></div>


tags: ['Mathematics', 'Statistics', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P2.db
title:
coefficient-of-variation-of-two-distributions-are-50-and-60-and-their-arithmetic-means-are-30-and-25-respectively-difference-of-their-standard-deviati

slug:
coefficient-of-variation-of-two-distributions-are-50-and-60-and-their-arithmetic-means-are-30-and-25-respectively-difference-of-their-standard-deviati-93330

question:
<div class="question">Coefficient of variation of two distributions are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math> and their arithmetic means are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math>, respectively. Difference of their standard deviation is</div>

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

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

answer:
<div class="solution"><p>Given, coefficient of variation <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mn>1</mn></msub><mo>=</mo><mn>50</mn></math></p><p>and coefficient of variation <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mn>2</mn></msub><mo>=</mo><mn>60</mn></math>.</p><p>We have, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mover><mi>x</mi><mo>¯</mo></mover><mn>1</mn></msub><mo>=</mo><mn>30</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mover><mi>x</mi><mo>¯</mo></mover><mn>2</mn></msub><mo>=</mo><mn>25</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo><mo> </mo><mi>C</mi><mo>=</mo><mfrac><mi>σ</mi><mover><mi>x</mi><mo>¯</mo></mover></mfrac><mo>×</mo><mn>100</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo>=</mo><mfrac><msub><mi>σ</mi><mn>1</mn></msub><mn>30</mn></mfrac><mo>×</mo><mn>100</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msub><mi>σ</mi><mn>1</mn></msub><mo>=</mo><mn>15</mn></math></p><p>and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo>=</mo><mfrac><msub><mi>σ</mi><mn>2</mn></msub><mn>25</mn></mfrac><mo>×</mo><mn>100</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msub><mi>σ</mi><mn>2</mn></msub><mo>=</mo><mn>15</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Required difference <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>σ</mi><mn>1</mn></msub><mo>-</mo><msub><mi>σ</mi><mn>2</mn></msub><mo>=</mo><mn>15</mn><mo>-</mo><mn>15</mn><mo>=</mo><mn>0</mn></math></p></div>


tags: ['Mathematics', 'Statistics']
source_db: MarksBatch1_P2.db
title:
coefficient-of-variation-of-two-distributions-are-50-and-60-and-their-arithmetic-means-are-30-and-25-respectively-then-difference-of-their-standard-de

slug:
coefficient-of-variation-of-two-distributions-are-50-and-60-and-their-arithmetic-means-are-30-and-25-respectively-then-difference-of-their-standard-de-56280

question:
<div class="question">Coefficient of variation of two distributions are 50 and 60 and their arithmetic means are 30 and 25 , respectively. Then, difference of their standard deviations is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>0<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>1<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$1.5$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$2.5$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>0<br/></span> </div>

answer:
<div class="solution">We know that,<br/>$$<br/>\begin{aligned}<br/>&amp;\text { Coefficient of variation }=\frac{\sigma}{\overline{\mathrm{x}}} \times 100 \\<br/>&amp;\therefore \mathrm{CV} \text { of } 1 \text { st distribution }=\frac{\sigma_1}{30} \times 100 \\<br/>&amp;\Rightarrow \quad 50=\frac{\sigma_1}{30} \times 100 \Rightarrow \sigma_1=15 \\<br/>&amp;\qquad[\mathrm{CV} \text { of } 1 \text { st distribution }=50 \text { (given) }] \\<br/>&amp;\text { Also, } \mathrm{CV} \text { of } 2 \text { nd distribution }=\frac{\sigma_2}{25} \times 100 \\<br/>&amp;\Rightarrow 60=\frac{\sigma_2}{25} \times 100 \\<br/>&amp;\Rightarrow \sigma_2=\frac{60 \times 25}{100} \Rightarrow \sigma_2=15 \\<br/>&amp;\text { Thus, } \sigma_1-\sigma_2=15-15=0<br/>\end{aligned}<br/>$$</div>


tags: ['Mathematics', 'Statistics', 'COMEDK', 'COMEDK 2014']
source_db: MarksBatch1_P2.db
title:
coefficient-of-variation-of-two-distributions-are-60-and-70-and-their-standard-deviation-are-21-and-16-respectively-what-are-their-arithmetic-means

slug:
coefficient-of-variation-of-two-distributions-are-60-and-70-and-their-standard-deviation-are-21-and-16-respectively-what-are-their-arithmetic-means-50265

question:
<div class="question">Coefficient of variation of two distributions are 60 and 70 , and their standard deviation are 21 and 16 respectively. What are their arithmetic means?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">35,20</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$35,22.85$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$30,22.85$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">30,20</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$35,22.85$</span> </div>

answer:
<div class="solution">Coefficient of variation $=\frac{\sigma}{\bar{x}} \times 100$<br/>For first distribution, $60=\frac{21}{\bar{x}} \times 100$<br/>$$<br/>\bar{x}=\frac{21 \times 100}{60}=35<br/>$$<br/>For second distribution, $70=\frac{16}{\bar{x}} \times 100$<br/>$$<br/>\bar{x}=\frac{16 \times 100}{70}=2285<br/>$$<br/>Hence, required means are $35,22.85$.</div>


tags: ['Mathematics', 'Statistics', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
coefficient-of-variation-of-two-distributions-are-60-and-75-and-their-standard-deviation-are-18-and-15-respectively-then-their-arithmetic-means-respec

slug:
coefficient-of-variation-of-two-distributions-are-60-and-75-and-their-standard-deviation-are-18-and-15-respectively-then-their-arithmetic-means-respec-77897

question:
<div class="question">Coefficient of variation of two distributions are <math><mn>60</mn><mi>%</mi></math> and <math><mn>75</mn><mi>%</mi><mo>,</mo></math> and their standard deviation are <math><mn>18</mn></math> and <math><mn>15</mn></math> respectively, then their arithmetic means respectively are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mn>30</mn><mo>,</mo><mi></mi><mn>30</mn></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math><mn>30</mn><mo>,</mo><mi></mi><mn>20</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><mn>20</mn><mo>,</mo><mi></mi><mn>30</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mn>20</mn><mo>,</mo><mi></mi><mn>20</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>30</mn><mo>,</mo><mi></mi><mn>20</mn></math></span> </div>

answer:
<div class="solution">Given, <math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">V</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>60</mn><mo>,</mo><mi mathvariant="normal"></mi><msub><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">V</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>75</mn><mo>,</mo><mi mathvariant="normal"></mi><msub><mrow><mi mathvariant="normal">Ï</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>18</mn></math> and <math><msub><mrow><mi>Ï</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>15</mn></math> <br/>Let <math><msub><mrow><mover accent="true"><mrow><mi>x</mi></mrow><mo>-</mo></mover></mrow><mrow><mn>1</mn></mrow></msub></math> and <math><msub><mrow><mover accent="true"><mrow><mi>x</mi></mrow><mo>-</mo></mover></mrow><mrow><mn>2</mn></mrow></msub></math> be the means of <math><msup><mrow><mn>1</mn></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">t</mi></mrow></msup></math> and <math><msup><mrow><mn>2</mn></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi></mrow></msup></math> distribution respectively. <br/>Then, <math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">V</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi mathvariant="normal">Ï</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><msub><mrow><mover accent="true"><mrow><mi mathvariant="normal">x</mi></mrow><mo>-</mo></mover></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac><mo>Ã</mo><mn>100</mn><mi></mi><mo>â</mo><msub><mrow><mover accent="true"><mrow><mi>x</mi></mrow><mo>-</mo></mover></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mn>18</mn><mo>Ã</mo><mn>100</mn></mrow><mrow><mn>60</mn></mrow></mfrac><mo>=</mo><mn>30</mn></math> <br/><math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">V</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi>Ï</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><msub><mrow><mover accent="true"><mrow><mi>x</mi></mrow><mo>-</mo></mover></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac><mo>Ã</mo><mn>100</mn><mo>â</mo><msub><mrow><mover accent="true"><mrow><mi>x</mi></mrow><mo>-</mo></mover></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mn>15</mn><mo>Ã</mo><mn>100</mn></mrow><mrow><mn>75</mn></mrow></mfrac><mo>=</mo><mn>20</mn></math> <br/>Hence, <math><msub><mrow><mover accent="true"><mrow><mi>x</mi></mrow><mo>-</mo></mover></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>30</mn></math> and <math><mi></mi><msub><mrow><mover accent="true"><mrow><mi>x</mi></mrow><mo>-</mo></mover></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>20</mn></math></div>


title: collagen-is-a
slug: collagen-is-a-95553
question: <div class="question">Collagen is a:</div>
tags: ['Biology', 'Biomolecules (B)', 'NEET', 'NEET 2002']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">fibrous protein</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">globular protein</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">lipid</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">carbohydrate</span> </li> </ul>

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

answer:
<div class="solution">Collagen is the major insoluble fibrous protein in the extracellular matrix and in connective tissue. In fact, it is the single most abundant protein in the animal kingdom.<br/>Related Theory<br/>Collagen is protein molecules made up of amino acids (glycine, proline, and hydroxyproline). It provides structural support to the extracellular space of connective tissues. Due to its rigidity and resistance to stretching, it is the perfect matrix for skin, tendons, bones, and ligaments.</div>


title: colloidal-solutions-can-be-purified-by
slug: colloidal-solutions-can-be-purified-by-21885
question: <div class="question">Colloidal solutions can be purified by</div>
tags: ['Chemistry', 'Surface Chemistry', 'JEE Main', 'JEE Main 2012 (26 May Online)']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>emulsification<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>electrodialysis<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/>peptization<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>using Tyndall effect</span> </li> </ul>

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


tags: ['Physics', 'Waves and Sound', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch1_P2.db
title:
column-i-showns-four-systems-each-of-the-same-length-l-for-producing-standing-waves-the-lowest-possible-natural-frequency-of-a-system-is-called-its-fu

slug:
column-i-showns-four-systems-each-of-the-same-length-l-for-producing-standing-waves-the-lowest-possible-natural-frequency-of-a-system-is-called-its-fu-39105

question:
<div class="question">Column I showns four systems, each of the same length $L$, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as $\lambda_f$. Match each system with statements given in Column II describing the nature and wave length of the standing waves.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/EUOQt3ki7T6dLYxfsmw5td75JLfbZKiLRorgXFDB8DU.original.fullsize.png"/><br/></div>

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

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

answer:
<div class="solution">In organ pipes, longitudinal waves are formed. In string, transverse waves are formed. Open end of pipe is displacement antinode and closed end is displacement node. In case of string fixed end of a string is node.<br/>Further, least distance between a node and an antinode is $\frac{\lambda}{4}$ and between two nodes is $\frac{\lambda}{2}$. Keeping these points in mind answer to this question is as under;<br/>$(\mathrm{A}) \rightarrow(\mathrm{p}, \mathrm{t})$<br/>(B) $\rightarrow(\mathrm{p}, \mathrm{s})$<br/>$(\mathrm{C}) \rightarrow(\mathrm{q}, \mathrm{s})$<br/>(D) $\rightarrow$ (q, r)<br/>Analysis of Question<br/>(i) Unlike the previous years's few match the column problems, this question seems to be more logical. If you know the subject, you can select correct matching without confusion.<br/>(ii) In option (d) of column I, string is fixed from centre, therefore at lowest frequency two loops will be formed as shown below.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/rnGnEFAsnZpkoHbpmxp9dlFR16LVSlCab_-rSfbpjs4.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Wave Optics', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
source_db: MarksBatch1_P2.db
title:
column-i-shows-four-situations-of-standard-youngs-double-slit-arrangement-with-the-screen-placed-far-away-from-the-slits-s-1-and-s-2-in-each-of-these-

slug:
column-i-shows-four-situations-of-standard-youngs-double-slit-arrangement-with-the-screen-placed-far-away-from-the-slits-s-1-and-s-2-in-each-of-these-26081

question:
<div class="question">Column I shows four situations of standard Young's double slit arrangement with the screen placed far away from the slits $S_1$ and $S_2$. In each of these cases $S_1 P_0=S_2 P_0$, $S_1 P_1-S_2 P_1=\frac{\lambda}{4}$ and $S_1 P_2-S_2 P_2=\frac{\lambda}{3}$, where $\lambda$ is the wavelength of the light used. In the cases $\mathrm{B}, \mathrm{C}$ and $\mathrm{D}$, a transparent sheet of refractive index $\mu$ and thickness $t$ is pasted on slit $S_2$. The thickness of the sheets are different in different cases. The phase difference between the light waves reaching a point $P$ on the screen from the two slits is denoted by $\delta(P)$ and the intensity by $I(P)$. Match each situation given in Column-I with the statement(s) in Column-II valid for that situation.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/WB06TwRxOzqpnbZ5VrecHzPxESIeLecOdphK0motYWQ.original.fullsize.png"/><br/></div>

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

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

answer:
<div class="solution">(A) $\rightarrow(\mathrm{p}, \mathrm{s}) \rightarrow$ Intensity at $P_0$ is maximum. It will continuously decrease from $P_0$ towards $P_2$.<br/>$(B) \rightarrow(q) \rightarrow$ Path difference due to slap will be compensated by geometrical path difference. Hence, $\delta\left(P_1\right)=0$.<br/>$(\mathrm{C}) \rightarrow(\mathrm{t}) \rightarrow \delta\left(P_0\right)=\frac{\lambda}{2}, \delta\left(P_1\right)=\frac{\lambda}{2}-\frac{\lambda}{4}=\frac{\lambda}{4}$ and $\delta\left(P_2\right)=\frac{\lambda}{2}-\frac{\lambda}{3}=\frac{\lambda}{6}$. When path difference increases from 0 to $\frac{\lambda}{2}$, intensity will decrease from maximum to zero. Hence, in this case,<br/>$$<br/>I\left(P_2\right)&gt;I\left(P_1\right)&gt;I\left(P_0\right)<br/>$$<br/>$(\mathrm{D}) \rightarrow(\mathrm{r}, \mathrm{s}, \mathrm{t})$<br/>$$<br/>\delta\left(P_0\right)=\frac{3 \lambda}{4}, \delta\left(P_1\right)=\frac{3 \lambda}{4}-\frac{\lambda}{4}=\frac{\lambda}{2}<br/>$$<br/>and $\delta\left(P_2\right)=\frac{3 \lambda}{4}-\frac{\lambda}{3}=\frac{5 \lambda}{12}$<br/>In this case $I\left(P_1\right)=0$</div>


title: comment-on-the-following-observation-e-0-for-m-2-aq-2e-m-s-where-m-ca-sr-or-ba-is-nearly-constant
tags: ['Chemistry', 's Block Elements', 'NEET']
source_db: MarksBatch1_P2.db
slug:
comment-on-the-following-observation-e-0-for-m-2-aq-2e-m-s-where-m-ca-sr-or-ba-is-nearly-constant-23587

question:
<div class="question">Comment on the following observation: E<sup>0</sup>for M<sup>2+</sup><sub>(aq)</sub>+ 2e<sup>â</sup>â M<sub>(s)</sub>(where M = Ca, Sr, or Ba) is nearly constant.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">This indicates that the standard reduction potentials of calcium, strontium, and barium are similar.</span> </div>

answer:
<div class="solution">Correct Option is : (A)<br/>This indicates that the standard reduction potentials of calcium, strontium, and barium are similar.</div>


title: comment-upon-the-habitats-and-external-features-of-animals-belonging-to-classamphibia-and-reptilia
tags: ['Biology', 'Animal Kingdom']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
slug:
comment-upon-the-habitats-and-external-features-of-animals-belonging-to-classamphibia-and-reptilia-74340

question:
<div class="question">Comment upon the habitats and external features of animals belonging to class-Amphibia and Reptilia.</div>

answer:
<div class="solution">Amphibians<br/>(i) They can dwell in aquatic as well as terrestrial habitats.<br/>They are ectothermic or (cold blooded).<br/>(ii) They are tetrapods having (4 limbs) which facilitate movement on land.<br/>(iii) Their limbs have evolved from the pectoral and pelvic fins.<br/>(iv) Skin is thin, covered by mucus and remains mostly moist. It also serves as an accessory source of oxygen.<br/>(v) They breathe through gills and lung gills usually appear in the larval stage, replaced by lungs in the adults stage.<br/>(vi) Their heart is three chambered with two atria and one ventricle.<br/>(vii) Females are oviparous and fertilisation is mostly external.<br/>(viii) Larva is a tadpole, which metamorphose into adult e.g., Rana frog, Nectureus (mud puppy), Salamandera (salamander).<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/5WJrlfJpOZoqNZ84-W3JDfQhvEEV9x5biS-fNE_b_Os.original.fullsize.png"/><br/><br/>Reptiles<br/>(i) They are mostly terrestrial animals and their body is covered by dry, and cornified skin, epidermal scales or scutes.<br/>(ii) In reptiles the mode of locomotion is creeping and crawling.<br/>(iii) Lungs are well developed and present in all stages of life.<br/>(iv) Claws are present in toes.<br/>(v) Appendages are well adapted for land movement.<br/>(vi) Heart possesses a partially divided ventricle and 2 atria.<br/>(vii) They lay amniotic eggs which are inclubated on land.<br/>(viii) They are poikilothermic or cold blooded animals.</div>


title: companion-cells-in-plants-are-associated-with
slug: companion-cells-in-plants-are-associated-with-56665
question: <div class="question">Companion cells in plants are associated with</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'AIIMS', 'AIIMS 2004']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">vessels</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">sperms</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">sieve elements</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">guard cells.</span> </li> </ul>

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

answer:
<div class="solution">The companion cells occur only in angiosperms where they accompany most sieve tube elements. Companion cell is a speciliased type of parenchyma cell which is closely associated in origin, position and function with sieve tube elements. These cells are living having abundant granular cytoplasm and a prominent elongated nucleus. Usually, the nuclei of the companion cell serve for the nuclei of the sieve tubes as they lack them. The companion cells do not contain starch. They live only so long as the sieve tube element with which they are associated and they are crushed with those cells. Longitudinal division of the mother cell of the sieve tube element forms the companion cells. One daughter cell becomes a companion cell and other sieve tube element.</div>


title: compare-the-following-on-the-basis-of-acidity
slug: compare-the-following-on-the-basis-of-acidity-52600
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
source_db: MarksBatch1_P2.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/modules/dbq/cheas77dtry/jwZ1vceyK3Y8CVzmXg23iCcUbsxnKGRjm3BZ4DYEIRNI8sgQyJ.png"/>Compare the following on the basis of acidity</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">p-cresol=o-cresol<m-cresol> </m-cresol></span></div>

answer:
<div class="solution">Correct Option is : 4 <br/> p-cresol=o-cresol<m-cresol> <!-- /Solution --> <!-- Call to Action --> <section class="call-to-action" data-pagefind-ignore=""> <div class="call-to-action-header"> <svg fill="none" height="24" viewbox="0 0 25 24" width="25" xmlns="http://www.w3.org/2000/svg"> <path d="M19.9999 13.5C20.0018 13.8058 19.9089 14.1047 19.734 14.3555C19.559 14.6063 19.3107 14.7968 19.023 14.9006L14.1874 16.6875L12.4062 21.5269C12.3007 21.8134 12.1098 22.0608 11.8594 22.2355C11.6089 22.4101 11.3109 22.5038 11.0055 22.5038C10.7002 22.5038 10.4022 22.4101 10.1517 22.2355C9.90124 22.0608 9.71039 21.8134 9.60491 21.5269L7.8124 16.6875L2.97303 14.9062C2.68646 14.8008 2.43915 14.6099 2.26445 14.3595C2.08976 14.109 1.99609 13.811 1.99609 13.5056C1.99609 13.2003 2.08976 12.9022 2.26445 12.6518C2.43915 12.4013 2.68646 12.2105 2.97303 12.105L7.8124 10.3125L9.59366 5.47313C9.69914 5.18656 9.88998 4.93924 10.1404 4.76455C10.3909 4.58985 10.6889 4.49619 10.9943 4.49619C11.2996 4.49619 11.5977 4.58985 11.8481 4.76455C12.0986 4.93924 12.2894 5.18656 12.3949 5.47313L14.1874 10.3125L19.0268 12.0938C19.3146 12.1986 19.5628 12.3901 19.7371 12.642C19.9114 12.8939 20.0033 13.1937 19.9999 13.5ZM14.7499 4.5H16.2499V6C16.2499 6.19891 16.3289 6.38968 16.4696 6.53033C16.6102 6.67098 16.801 6.75 16.9999 6.75C17.1988 6.75 17.3896 6.67098 17.5302 6.53033C17.6709 6.38968 17.7499 6.19891 17.7499 6V4.5H19.2499C19.4488 4.5 19.6396 4.42098 19.7802 4.28033C19.9209 4.13968 19.9999 3.94891 19.9999 3.75C19.9999 3.55109 19.9209 3.36032 19.7802 3.21967C19.6396 3.07902 19.4488 3 19.2499 3H17.7499V1.5C17.7499 1.30109 17.6709 1.11032 17.5302 0.96967C17.3896 0.829018 17.1988 0.75 16.9999 0.75C16.801 0.75 16.6102 0.829018 16.4696 0.96967C16.3289 1.11032 16.2499 1.30109 16.2499 1.5V3H14.7499C14.551 3 14.3602 3.07902 14.2196 3.21967C14.0789 3.36032 13.9999 3.55109 13.9999 3.75C13.9999 3.94891 14.0789 4.13968 14.2196 4.28033C14.3602 4.42098 14.551 4.5 14.7499 4.5ZM22.9999 7.5H22.2499V6.75C22.2499 6.55109 22.1709 6.36032 22.0302 6.21967C21.8896 6.07902 21.6988 6 21.4999 6C21.301 6 21.1102 6.07902 20.9696 6.21967C20.8289 6.36032 20.7499 6.55109 20.7499 6.75V7.5H19.9999C19.801 7.5 19.6102 7.57902 19.4696 7.71967C19.3289 7.86032 19.2499 8.05109 19.2499 8.25C19.2499 8.44891 19.3289 8.63968 19.4696 8.78033C19.6102 8.92098 19.801 9 19.9999 9H20.7499V9.75C20.7499 9.94891 20.8289 10.1397 20.9696 10.2803C21.1102 10.421 21.301 10.5 21.4999 10.5C21.6988 10.5 21.8896 10.421 22.0302 10.2803C22.1709 10.1397 22.2499 9.94891 22.2499 9.75V9H22.9999C23.1988 9 23.3896 8.92098 23.5302 8.78033C23.6709 8.63968 23.7499 8.44891 23.7499 8.25C23.7499 8.05109 23.6709 7.86032 23.5302 7.71967C23.3896 7.57902 23.1988 7.5 22.9999 7.5Z" fill="#1589EE"></path> </svg> <h3>Looking for more such questions to practice?</h3> </div> <p>
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tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
source_db: MarksBatch1_P2.db
title:
compound-a-c-8-h-10-o-is-found-to-react-with-naoi-produced-by-reacting-y-with-naoh-and-yields-a-yellow-precipitate-with-characteristic-smell-a-and-yar

slug:
compound-a-c-8-h-10-o-is-found-to-react-with-naoi-produced-by-reacting-y-with-naoh-and-yields-a-yellow-precipitate-with-characteristic-smell-a-and-yar-57061

question:
<div class="question">Compound A, <math><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>8</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>10</mn></mrow></msub><mi mathvariant="normal">O</mi></math> , is found to react with NaOI (produced by reacting Y with NaOH) and yields a yellow precipitate with characteristic smell. <br/>A and Yare respectively</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/f2b69b82-a7b5-41e9-b6e3-0ad48128c5e4.png" style="width:1.8in;height:0.61319in"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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"><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/2275e51d-fa5b-4bc2-b16b-b172304638bd.png" style="width:2.3in;height:0.45347in"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/001a9bb3-15ef-4dd6-a66a-090f99027eef.png" style="width:2.3in;height:0.45347in"/></span> </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/68d96ea4-7950-4bce-afff-03e1d00ebc5e.png" style="width:1.74653in;height:0.61319in"/></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/f2b69b82-a7b5-41e9-b6e3-0ad48128c5e4.png" style="width:1.8in;height:0.61319in"/></span> </div>

answer:
<div class="solution">Option (a) is secondary alcohol which on oxidation gives phenylmethyl ketone (Acetophenone). This on reaction with <math><msub><mrow><mi mathvariant="normal">I</mi></mrow><mrow><mn>2</mn></mrow></msub></math> and NaOH form iodoform and sodium benzoate. (Iodoform Test). <br/><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/43fda07a-702a-417e-bde4-afe19adbd991.png" style="width:3.56667in;height:1.48681in"/></div>


tags: ['Chemistry', 'Amines', 'JEE Main', 'JEE Main 2021 (20 Jul Shift 1)']
source_db: MarksBatch1_P2.db
title:
compound-a-is-converted-to-b-on-reaction-with-chcl-3-and-koh-the-compound-b-is-toxic-and-can-be-decomposed-by-c-a-b-and-c-respectively-are

slug:
compound-a-is-converted-to-b-on-reaction-with-chcl-3-and-koh-the-compound-b-is-toxic-and-can-be-decomposed-by-c-a-b-and-c-respectively-are-85951

question:
<div class="question">Compound <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi></math> is converted to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi></math> on reaction with <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CHCl</mi><mn>3</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>KOH</mi></math>. The compound <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi></math> is toxic and can be decomposed by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">C</mi><mo>.</mo><mo> </mo><mi mathvariant="normal">A</mi><mo>,</mo><mo> </mo><mi mathvariant="normal">B</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">C</mi></math> respectively are:</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">primary amine, isonitrile compound, conc. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>HCl</mi></math></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/c9773520-ab45-4bd3-aca4-f685124cb6dc-image.png" style="width: 381px; height: 103px;"/></div>


title: compressed-natural-gas-cng-is
slug: compressed-natural-gas-cng-is-51114
question: <div class="question">Compressed Natural Gas (CNG) is</div>
tags: ['Biology', 'Environmental Issues']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>propane <br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/> methane<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/>ethane<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>butane</span> </li> </ul>

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

answer:
<div class="solution">Compressed Natural Gas $(\mathrm{CNG})$ is the best, cheap fuel, that has replaced petrol and diesel fuel and is considered as clean fuel. it consists of around $90 \%$ methane, by compressing it to less than $1 \%$ of volume it occupies at standard atmospheric pressure. Propane and butane together form LPG or liquified petroleum gas while ethane is used in chemical industry to produce ethene.</div>


title: consider-a-cell-given-below-cu-cu-2-cl-cl-2-pt-write-the-reactions-that-occur-at-anode-and-cathode
tags: ['Chemistry', 'Electrochemistry']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
slug:
consider-a-cell-given-below-cu-cu-2-cl-cl-2-pt-write-the-reactions-that-occur-at-anode-and-cathode-75921

question:
<div class="question">Consider a cell given below<br/>$\mathrm{Cu}\left|\mathrm{Cu}^{2+} \| \mathrm{Cl}^{-}\right| \mathrm{Cl}_2, \mathrm{Pt}$<br/>Write the reactions that occur at anode and cathode.</div>

answer:
<div class="solution">Standard Hydrogen Electrode (SHE) is the reference electrode whose electrode potential is taken to be zero. The electrode potential of other electrodes are measured with respect to it.</div>


title: consider-a-circle-of-radius-r-what-is-the-length-of-a-chord-which-subtends-an-angle-at-the-centre
tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2007 (Phase 2)']
source_db: MarksBatch1_P2.db
slug:
consider-a-circle-of-radius-r-what-is-the-length-of-a-chord-which-subtends-an-angle-at-the-centre-92726

question:
<div class="question">Consider a circle of radius $\mathrm{R}$. What is the length of a chord which subtends an angle $\theta$ at the centre?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \mathrm{R} \sin \left(\frac{\theta}{2}\right)$</span> </div>

answer:
<div class="solution">Let there be a circle of radius $\mathrm{R}$ and chord $\mathrm{AB}$.<br/>$\mathrm{OD} \perp \mathrm{AB}$ and $\mathrm{AD}=\mathrm{DB}$.<br/>and $\mathrm{AD}=2 \mathrm{AD}$<br/>$\angle \mathrm{AOB}=\theta$<br/>$\Rightarrow \quad \angle \mathrm{AOD}=\frac{\theta}{2}$<br/>In $\triangle \mathrm{AOD}$,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/nu3rduZh4eGBKOLEIKc8mZtnHlpO2sS5ICgEvyQEML4.original.fullsize.png"/><br/><br/>$\sin \frac{\theta}{2}=\frac{\mathrm{AD}}{\mathrm{OA}}$<br/>$\sin \frac{\theta}{2}=\frac{\mathrm{AD}}{\mathrm{R}}$<br/>$\mathrm{AD}=\mathrm{R} \sin \frac{\theta}{2}$<br/>$\therefore \quad$ Length of chord $\mathrm{AB}=2 \mathrm{~A} \mathrm{D}=2 \mathrm{R} \sin \frac{\theta}{2}$.</div>


tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-a-circle-passing-through-the-origin-and-the-points-a-b-and-b-a-on-which-line-does-the-centre-of-the-circle-lie

slug:
consider-a-circle-passing-through-the-origin-and-the-points-a-b-and-b-a-on-which-line-does-the-centre-of-the-circle-lie-55460

question:
<div class="question">Consider a circle passing through the origin and the points $(\mathrm{a}, \mathrm{b})$ and $(-b,-a)$.<br/>On which line does the centre of the circle lie?</div>

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

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

answer:
<div class="solution">Suppose; $\mathrm{x}^{2}+\mathrm{y}^{2}+2 \mathrm{gx}+2 \mathrm{fy}+\mathrm{c}=0$ is the eq. of the<br/>circle. Since; it passes through $(0,0) ;(a, b) \&amp;(-b,-a)$<br/>$\therefore \mathrm{C}=0$<br/>$a^{2}+b^{2}+2 g a+2 f b=0$<br/>$\therefore \mathrm{a}^{2}+\mathrm{b}^{2}-2 \mathrm{gb}-2 \mathrm{fb}=0$<br/>on solving:<br/>$\mathrm{g}=-\mathrm{f}$<br/>$\therefore$ centre $=(-\mathrm{g},-\mathrm{f})$ or $(+\mathrm{f},-\mathrm{f})$<br/>$\therefore$ from options:<br/>$\mathrm{x}+\mathrm{y}=0$ is the line which passes through $(f,-f)$</div>


tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-a-circle-passing-through-the-origin-and-the-points-a-b-and-b-a-what-is-the-sum-of-the-squares-of-the-intercepts-cut-off-by-the-circle-on-the-

slug:
consider-a-circle-passing-through-the-origin-and-the-points-a-b-and-b-a-what-is-the-sum-of-the-squares-of-the-intercepts-cut-off-by-the-circle-on-the-70117

question:
<div class="question">Consider a circle passing through the origin and the points $(\mathrm{a}, \mathrm{b})$ and $(-b,-a)$. <br/>What is the sum of the squares of the intercepts cut off by the circle on the axes?</div>

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

answer:
<div class="solution">The two intercepts are : $-2 \mathrm{~g} \&amp;-2 \mathrm{f}$ $\therefore$ from eq $(1) \&amp;(2)$ we get;<br/>$\mathrm{g}=\frac{-1}{2}\left(\frac{a^{2}+b^{2}}{a-b}\right) \&amp; f=\frac{1}{2}\left(\frac{a^{2}+b^{2}}{a-b}\right)$<br/>is sum of squares of intercepts<br/>$=\left(\frac{a^{2}+b^{2}}{a-b}\right)^{2}+\left(\frac{a^{2}+b^{2}}{a-b}\right)^{2}$<br/>$=2\left[\frac{a^{2}+b^{2}}{a-b}\right]^{2}$</div>


tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-a-differential-equation-of-order-m-and-degree-n-which-one-of-the-following-pairs-is-not-feasible

slug:
consider-a-differential-equation-of-order-m-and-degree-n-which-one-of-the-following-pairs-is-not-feasible-66346

question:
<div class="question">Consider a differential equation of order $\mathrm{m}$ and degree $\mathrm{n}$. Which one of the following pairs is not feasible?</div>

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

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

answer:
<div class="solution">Degree of differential equation is always a positive integer.<br/>$\therefore \quad\left(2, \frac{3}{2}\right)$ can not be the feasible.</div>


tags: ['Physics', 'Kinetic Theory of Gases', 'TS EAMCET', 'TS EAMCET 2021 (04 Aug Shift 2)']
source_db: MarksBatch1_P2.db
title:
consider-a-gas-with-molar-mass-m-if-the-sound-at-frequency-f-is-introduced-to-a-tube-of-this-gas-at-temperature-t-then-an-internal-acoustic-standing-w

slug:
consider-a-gas-with-molar-mass-m-if-the-sound-at-frequency-f-is-introduced-to-a-tube-of-this-gas-at-temperature-t-then-an-internal-acoustic-standing-w-89878

question:
<div class="question">Consider a gas with molar mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>.</mo></math> If the sound at frequency <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is introduced to a tube of this gas at temperature <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> then an internal acoustic standing wave is set up with nodes separated by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>.</mo></math> The adiabatic constant <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>γ</mi><mo>=</mo><mfrac><msub><mi>C</mi><mi>p</mi></msub><msub><mi>C</mi><mi>v</mi></msub></mfrac></mrow></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"><mfrac><mrow><mi>M</mi><msup><mi>f</mi><mn>2</mn></msup><msup><mi>L</mi><mn>2</mn></msup></mrow><mrow><mi>R</mi><mi>T</mi></mrow></mfrac></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>M</mi><msup><mi>f</mi><mn>2</mn></msup><msup><mi>L</mi><mn>2</mn></msup></mrow><mrow><mn>4</mn><mi>R</mi><mi>T</mi></mrow></mfrac></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"><mfrac><mrow><mn>4</mn><mi>M</mi><msup><mi>f</mi><mn>2</mn></msup><msup><mi>L</mi><mn>2</mn></msup></mrow><mrow><mi>R</mi><mi>T</mi></mrow></mfrac></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mi>M</mi><msup><mi>f</mi><mn>2</mn></msup><msup><mi>L</mi><mn>2</mn></msup></mrow><mrow><mn>2</mn><mi>R</mi><mi>T</mi></mrow></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mi>M</mi><msup><mi>f</mi><mn>2</mn></msup><msup><mi>L</mi><mn>2</mn></msup></mrow><mrow><mi>R</mi><mi>T</mi></mrow></mfrac></math></span> </div>

answer:
<div class="solution"><p>Recall the formula of the fundamental frequency of the standing wave, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mi>v</mi><mrow><mn>2</mn><mi>L</mi></mrow></mfrac></math>, and the formula of sound waves in terms of absolute temperature and molecular mass, </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msqrt><mfrac><mrow><mn>3</mn><mi>R</mi><mi>T</mi></mrow><mi>M</mi></mfrac></msqrt></math>, <br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>f</mi><mo>=</mo><mfrac><msqrt><mfrac><mrow><mi>γ</mi><mi>R</mi><mi>T</mi></mrow><mi>M</mi></mfrac></msqrt><mrow><mn>2</mn><mi>L</mi></mrow></mfrac><mspace linebreak="newline"></mspace><mo>⇒</mo><msup><mi>f</mi><mn>2</mn></msup><mo>×</mo><mn>4</mn><msup><mi>L</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><mi>γ</mi><mi>R</mi><mi>T</mi></mrow><mi>M</mi></mfrac><mspace linebreak="newline"></mspace><mo>⇒</mo><mi>γ</mi><mo>=</mo><mfrac><mrow><msup><mi>f</mi><mn>2</mn></msup><mo>×</mo><mn>4</mn><msup><mi>L</mi><mn>2</mn></msup><mi>M</mi></mrow><mrow><mi>R</mi><mi>T</mi></mrow></mfrac></math><br/> </p></div>


tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-a-matrix-m-3-2-3-4-1-1-0-0-k-and-the-following-statements-statement-a-inverse-of-m-exists-statement-b-k-0-which-one-of-the-following-in-respe

slug:
consider-a-matrix-m-3-2-3-4-1-1-0-0-k-and-the-following-statements-statement-a-inverse-of-m-exists-statement-b-k-0-which-one-of-the-following-in-respe-75594

question:
<div class="question">Consider a matrix $M=\left[\begin{array}{lll}3 &amp; 4 &amp; 0 \\ 2 &amp; 1 &amp; 0 \\ 3 &amp; 1 &amp; k\end{array}\right]$ and the following<br/>statements <br/>Statement $\mathbf{A}:$ Inverse of $\mathrm{M}$ exists.<br/>Statement $\mathbf{B}: k \neq 0$ Which one of the following in respect of the above matrix and statement is correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">A implies $\mathrm{B}$, but B does not imply A</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{B}$ implies $\mathrm{A}$, but A does not imply $\mathrm{B}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Neither A implies B nor B implies A</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">A implies B as well as B implies 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">A implies B as well as B implies A</span> </div>

answer:
<div class="solution">Given $M=\left[\begin{array}{lll}3 &amp; 4 &amp; 0 \\ 2 &amp; 1 &amp; 0 \\ 3 &amp; 1 &amp; k\end{array}\right]$<br/>Now $|M|=\left|\begin{array}{lll}3 &amp; 4 &amp; 0 \\ 2 &amp; 1 &amp; 0 \\ 3 &amp; 1 &amp; k\end{array}\right|=k(3-8)=-5 k$<br/>From statement II, $k \neq 0$ then inverse of $\mathrm{M}$ exist (statement I). Thus, statement Aimplies B as well as B implies A.</div>


tags: ['Physics', 'Thermal Properties of Matter', 'VITEEE', 'VITEEE 2019']
source_db: MarksBatch1_P2.db
title:
consider-a-pair-of-insulating-blocks-with-thermal-resistances-r-1-and-r-2-as-shown-in-the-figure-the-temperature-at-the-boundary-between-the-two-block

slug:
consider-a-pair-of-insulating-blocks-with-thermal-resistances-r-1-and-r-2-as-shown-in-the-figure-the-temperature-at-the-boundary-between-the-two-block-20657

question:
<div class="question">Consider a pair of insulating blocks with thermal resistances $R_{1}$ and $R_{2}$ as shown in the figure. The temperature $\theta$ at the boundary between the two blocks is
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/viteee/5NvsPEDEaatxEXUB9ziZ-1ZdLOTpajGyNPJ-HLvaDJ8.original.fullsize.png"/></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(\theta_{1} R_{2}+\theta_{2} R_{1}\right) /\left(R_{1}+R_{2}\right)$</span> </div>

answer:
<div class="solution">Rate of transmission of heat
<br/>$$
<br/>\begin{array}{l}
<br/>=\frac{\text { Temperature difference }}{\text { Thermal Resistance }} \\
<br/>\therefore \quad \frac{d Q}{d t}=\frac{d \theta}{R}
<br/>\end{array}
<br/>$$
<br/>Here, $$\frac{d Q}{d t}=\frac{\left(\theta-\theta_{2}\right)}{R_{2}}=\frac{\theta_{1}-\theta}{R_{1}}$$
<br/>$$
<br/>\begin{array}{l}
<br/>\Rightarrow \frac{\theta-\theta_{2}}{R_{2}}=\frac{\theta_{1}-\theta}{R_{1}} \\
<br/>\Rightarrow \quad R_{1} \theta-R_{1} \theta_{2}=R_{2} \theta_{1}-R_{2} \theta \\
<br/>\Rightarrow \quad \theta\left(R_{1}+R_{2}\right)=R_{2} \theta_{1}+R_{1} \theta_{2} \\
<br/>\therefore \quad \theta=\frac{\left(R_{2} \theta_{1}+R_{1} \theta_{2}\right)}{\left(R_{1}+R_{2}\right)}
<br/>\end{array}
<br/>$$</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-a-parallelogram-whose-vertices-are-a-1-2-b-4-y-c-x-6-and-d-3-5-taken-in-order-what-is-the-area-of-the-parallelogram

slug:
consider-a-parallelogram-whose-vertices-are-a-1-2-b-4-y-c-x-6-and-d-3-5-taken-in-order-what-is-the-area-of-the-parallelogram-33508

question:
<div class="question">Consider a parallelogram whose vertices are $\mathrm{A}(1,2), \mathrm{B}(4, \mathrm{y}), \mathrm{C}(\mathrm{x}, 6)$ and $\mathrm{D}(3,5)$ taken in order. <br/>What is the area of the parallelogram?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{7}{2}$ square units</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">4 square units</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{11}{2}$ square units</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">7 square 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">7 square units</span> </div>

answer:
<div class="solution">Area of parallelogram $=2$ area of $\Delta \mathrm{ADB}$ $\vec{a}=\overline{\mathrm{AB}}=(4-1) \hat{i}+(3-2) \hat{j}$<br/>$\vec{b}=\overrightarrow{\mathrm{AD}}=(3-1) \hat{i}+(5-2) \hat{j}$<br/>$\therefore$ Area of parallelogram $=2\left[\frac{1}{2}|\vec{a} \times \vec{b}|\right]=|\vec{a} \times \vec{b}|$<br/>Now; $\vec{a} \times \vec{b}=\left|\begin{array}{ccc}\hat{i} &amp; \hat{j} &amp; \hat{k} \\ 3 &amp; 1 &amp; 0 \\ 2 &amp; 3 &amp; 0\end{array}\right|=7 \hat{k}$.<br/>Area $=|\vec{a} \times \vec{b}|=|7 \hat{\mathrm{k}}|=\sqrt{49}=7$ square unit</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2016 (Phase 1)']
answer: <div class="solution">Point of intersection $(a, b)$ is $\left(\frac{7}{2}, 4\right)$.</div>
source_db: MarksBatch1_P2.db
title:
consider-a-parallelogram-whose-vertices-are-a-1-2-b-4-y-c-x-6-and-d-3-5-taken-in-order-what-is-the-point-of-intersection-of-the-diagonals

slug:
consider-a-parallelogram-whose-vertices-are-a-1-2-b-4-y-c-x-6-and-d-3-5-taken-in-order-what-is-the-point-of-intersection-of-the-diagonals-48550

question:
<div class="question">Consider a parallelogram whose vertices are $\mathrm{A}(1,2), \mathrm{B}(4, \mathrm{y}), \mathrm{C}(\mathrm{x}, 6)$ and $\mathrm{D}(3,5)$ taken in order. <br/>What is the point of intersection of the diagonals?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(\frac{7}{2}, 4\right)$</span> </div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2016 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">36</span> </div>
source_db: MarksBatch1_P2.db
title:
consider-a-parallelogram-whose-vertices-are-a-1-2-b-4-y-c-x-6-and-d-3-5-taken-in-order-what-is-the-value-of-ac-2-bd-2

slug:
consider-a-parallelogram-whose-vertices-are-a-1-2-b-4-y-c-x-6-and-d-3-5-taken-in-order-what-is-the-value-of-ac-2-bd-2-25188

question:
<div class="question">Consider a parallelogram whose vertices are $\mathrm{A}(1,2), \mathrm{B}(4, \mathrm{y}), \mathrm{C}(\mathrm{x}, 6)$ and $\mathrm{D}(3,5)$ taken in order. <br/>What is the value of $\mathrm{AC}^{2}-\mathrm{BD}^{2}$ ?</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">30</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">36</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">40</span> </li> </ul>

answer:
<div class="solution">Suppose Mid point of $A C$ and $B D$ is $M(a, b)$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/GkRKsCr4a28WEfiI-NrZnDg41Lqk8pBltkQI60o08do.original.fullsize.png"/><br/><br/>$a=\frac{1+x}{2}=\frac{3+4}{2}$<br/>$\Rightarrow x=6$<br/>$b=\frac{5+y}{2}=\frac{2+6}{2}$<br/>$\Rightarrow y=3$<br/>$a=\frac{7}{2}, b=4$<br/>$A C^{2}=(1-x)^{2}+(2-6)^{2}=(1-6)^{2}+(-4)^{2}=41$<br/>$B D^{2}=(3-4)^{2}+(5-3)^{2}=1+4=5$<br/>$A C^{2}-B D^{2}=41-5$<br/>$A C^{2}-B D^{2}=36$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-a-random-experiment-of-throwing-together-a-die-and-two-coins-the-associated-sample-space-has

slug:
consider-a-random-experiment-of-throwing-together-a-die-and-two-coins-the-associated-sample-space-has-80070

question:
<div class="question">Consider a random experiment of throwing together a die and two coins. The associated sample space has</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">8 points</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">12 points</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">24 points</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">36 points</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">24 points</span> </div>

answer:
<div class="solution">$6 \times 2 \times 2=24$ sample points $(\because$ no. of points in sample space of a die $=6$ and no. of points in sample space of a $\operatorname{coin}=2$ )</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2014 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1 only</span> </div>
source_db: MarksBatch1_P2.db
title:
consider-a-sphere-passing-through-the-origin-and-the-points-2-1-1-1-5-4-2-4-6-consider-the-following-statements-1-the-sphere-passes-through-the-point-

slug:
consider-a-sphere-passing-through-the-origin-and-the-points-2-1-1-1-5-4-2-4-6-consider-the-following-statements-1-the-sphere-passes-through-the-point-54805

question:
<div class="question">Consider a sphere passing through the origin and the points $(2,1,-1),(1,5,-4),(-2,4,-6)$<br/>Consider the following statements:<br/> 1 . The sphere passes through the point $(0,4,0)$.<br/> 2 . The point $(1,1,1)$ is at a distance of 5 unit from the centre of the sphere. Which of the above statements is/are correct?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">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><li class=""> <span class="option-label">B</span> <span class="option-data">2 only</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Both 1 and 2</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Neither 1 nor 2</span> </li> </ul>

answer:
<div class="solution">(1) Equation of sphere is $x^{2}+y^{2}+z^{2}+2 x-4 y+6 z=0$<br/>Put the value $(0,4,0)$, we get $0+16+0+0-16+0=0$<br/>So, the sphere passes through the point $(0,4,0)$. Hence, Statement 1 is correct.<br/> 2 . Distance between the point $(1,1,1)$ and centre of sphere $(-1,2,-3)$<br/>$=\sqrt{(1+1)^{2}+(1-2)^{2}+(1+3)^{2}}$<br/>$=\sqrt{4+1+16}=\sqrt{21} \neq 5$<br/>Hence, statement 2 is not correct.</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-a-sphere-passing-through-the-origin-and-the-points-2-1-1-1-5-4-2-4-6-what-is-the-radius-of-the-sphere

slug:
consider-a-sphere-passing-through-the-origin-and-the-points-2-1-1-1-5-4-2-4-6-what-is-the-radius-of-the-sphere-76078

question:
<div class="question">Consider a sphere passing through the origin and the points $(2,1,-1),(1,5,-4),(-2,4,-6)$<br/>What is the radius of the sphere?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\sqrt{12}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\sqrt{14}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">12</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">14</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\sqrt{14}$</span> </div>

answer:
<div class="solution">Equation of sphere passing through origin is $x^{2}+y^{2}+z^{2}+2 u x+2 v y+2 w z=0$<br/>which passes through the points $(2,1,-1),(1,5,-4)$, and $(-2,4,-6)$<br/>$\therefore 4 u+2 v-2 w=-6$<br/>$2 \mathrm{u}+10 \mathrm{v}-8 \mathrm{w}=-42$<br/>and $-4 u+8 v-12 w=-56$<br/>Erom eqns (i),<br/>(ii) and (iii), we get $\mathrm{u}=1, \mathrm{v}=-2$ and $\mathrm{w}=3$<br/>$\therefore$ Radius of sphere $=\sqrt{u^{2}+v^{2}+w^{2}}$<br/>$=\sqrt{1+4+9}=\sqrt{14}$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-a-sphere-passing-through-the-origin-and-the-points-211154246-what-is-the-centre-of-the-sphere

slug:
consider-a-sphere-passing-through-the-origin-and-the-points-211154246-what-is-the-centre-of-the-sphere-71113

question:
<div class="question">Consider a sphere passing through the origin and the points (2,1,-1),(1,5,-4),(-2,4,-6) What is the centre of the sphere?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad(-1,2,-3)$</span> </div>

answer:
<div class="solution">$\quad$ From explanation 54 Centre of sphere, $(-\mathrm{u},-\mathrm{v},-\mathrm{w})=(-1,2,-3)$</div>


tags: ['Mathematics', 'Properties of Triangles', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-a-tiangle-abc-in-which-cos-a-cos-b-cos-c-3-sin-3-what-is-the-value-of-cos-2-a-b-cos-2-b-c-cos-2-c-a

slug:
consider-a-tiangle-abc-in-which-cos-a-cos-b-cos-c-3-sin-3-what-is-the-value-of-cos-2-a-b-cos-2-b-c-cos-2-c-a-57415

question:
<div class="question">Consider a tiangle $\mathrm{ABC}$ in which<br/>$\cos A+\cos B+\cos C=\sqrt{3} \sin \frac{\pi}{3}$<br/>What is the value of<br/>$$<br/>\cos \left(\frac{\mathrm{A}+\mathrm{B}}{2}\right) \cos \left(\frac{\mathrm{B}+\mathrm{C}}{2}\right) \cos \left(\frac{\mathrm{C}+\mathrm{A}}{2}\right) ?<br/>$$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{4}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{16}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">None of the above</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">None of the above</span> </div>

answer:
<div class="solution">As we know that<br/>$\sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}=\frac{1}{8}$<br/>$\because\left(\frac{A+B}{2}=\frac{\pi}{2}-\frac{C}{2}\right)$<br/>$\therefore \cos \left(\frac{A+B}{2}\right) \cos \left(\frac{B+C}{2}\right) \cos \left(\frac{C+A}{2}\right)=\frac{1}{8}$</div>


tags: ['Mathematics', 'Properties of Triangles', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-a-tiangle-abc-in-which-cos-a-cos-b-cos-c-3-sin-3-what-is-the-value-of-sin-2-a-sin-2-b-sin-2-c

slug:
consider-a-tiangle-abc-in-which-cos-a-cos-b-cos-c-3-sin-3-what-is-the-value-of-sin-2-a-sin-2-b-sin-2-c-40992

question:
<div class="question">Consider a tiangle $\mathrm{ABC}$ in which<br/>$\cos A+\cos B+\cos C=\sqrt{3} \sin \frac{\pi}{3}$<br/>What is the value of $\sin \frac{\mathrm{A}}{2} \sin \frac{\mathrm{B}}{2} \sin \frac{\mathrm{C}}{2}$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{4}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{1}{8}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{16}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{8}$</span> </div>

answer:
<div class="solution">Given $\cos A+\cos B+\cos C=\sqrt{3} \sin \frac{\pi}{3}$<br/>$\cos A+\cos B+\cos C$<br/>$=2 \cos \frac{A+B}{2} \cdot \cos \frac{A-B}{2}+\left(1-2 \sin ^{2} \frac{C}{2}\right)$<br/>$=2 \sin \frac{C}{2} \cos \frac{A-B}{2}+1-2 \sin ^{2} \frac{C}{2}$<br/>$\left(\because \frac{A+B}{2}=90^{\circ}-\frac{C}{2}\right)$<br/>$=1+2 \sin \frac{C}{2}\left[\cos \frac{A-B}{2}-\sin \frac{C}{2}\right]$<br/>$=1+2 \sin \frac{C}{2}\left[\cos \frac{A-B}{2}-\cos \frac{A+B}{2}\right]$<br/>$=1+4 \sin \frac{C}{2} \sin \frac{A}{2} \sin \frac{B}{2}$<br/>$\cos A+\cos B+\cos C=\sqrt{3} \sin \frac{\pi}{3}$<br/>$1+4 \sin \frac{C}{2} \sin \frac{A}{2} \sin \frac{B}{2}=\sqrt{3} \sin \frac{\pi}{3}$<br/>$\Rightarrow 1+4 \sin \frac{C}{2} \sin \frac{A}{2} \sin \frac{B}{2}=\sqrt{3} \times \frac{\sqrt{3}}{2}$<br/>$\Rightarrow 4 \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}=\frac{3}{2}-1$<br/>$\sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}=\frac{1}{8}$</div>


title: consider-a-triangle-abc-satisfying-2-a-sin-2-2-c-2-c-sin-2-2-a-2-a-2-c-3-b-sin-a-sin-b-sin-c-are-in
tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'NDA', 'NDA 2015 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">A.P.</span> </div>
source_db: MarksBatch1_P2.db
slug:
consider-a-triangle-abc-satisfying-2-a-sin-2-2-c-2-c-sin-2-2-a-2-a-2-c-3-b-sin-a-sin-b-sin-c-are-in-70967

question:
<div class="question">Consider a triangle $\mathrm{ABC}$ satisfying $2 a \sin ^{2}\left(\frac{C}{2}\right)+2 c \sin ^{2}\left(\frac{A}{2}\right)=2 a+2 c-3 b$<br/> $\sin \mathrm{A}, \sin \mathrm{B}_{,} \sin \mathrm{C}$ are in</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">G.P.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">A.P.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">HP.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Neither in G.P. nor in A.Pnor in H.P.</span> </li> </ul>

answer:
<div class="solution">As we have already proven $2 \mathrm{~b}=\mathrm{a}+\mathrm{c}$<br/>as-<br/>$\mathrm{a}=\mathrm{RsinA}$<br/>$\mathrm{b}=\mathrm{RsinB}$<br/>$\mathrm{c}=\mathrm{RsinC}$<br/>$\Rightarrow 2(\mathrm{RsinB})=\mathrm{Rsin} \mathrm{A}+\mathrm{RsinC}$<br/>$\Rightarrow 2 \mathrm{R}(\sin \mathrm{B})=\mathrm{R}(\sin \mathrm{A}+\sin \mathrm{C})$<br/>$2 \sin \mathrm{B}=\sin \mathrm{A}+\sin \mathrm{C}$<br/>$\therefore$ Statement (1) is incorrect.<br/>also $\frac{\mathrm{p}}{\mathrm{q}}=\frac{\mathrm{q}}{\mathrm{r}}=\frac{1}{\sqrt{3}}$<br/>So $\mathrm{p}, \mathrm{q}, \mathrm{r}$ are in G.P.<br/>$\therefore$ Statement $(2)$ is correct.<br/>$\begin{array}{lll}\text { 184. (d) } x^{2}+b x+c=0 &amp; b \neq 0\end{array}$<br/>$\because \tan \alpha$ and $\tan \beta$ are roots of equation.<br/>$\therefore \tan \alpha+\tan \beta=\frac{-b}{1}=-\mathrm{b}$</div>


tags: ['Mathematics', 'Trigonometric Equations', 'NDA', 'NDA 2015 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">A.P.</span> </div>
source_db: MarksBatch1_P2.db
title:
consider-a-triangle-abc-satisfying-2-a-sin-2-2-c-2-c-sin-2-2-a-2-a-2-c-3-b-the-sides-of-the-triangle-are-in

slug:
consider-a-triangle-abc-satisfying-2-a-sin-2-2-c-2-c-sin-2-2-a-2-a-2-c-3-b-the-sides-of-the-triangle-are-in-69599

question:
<div class="question">Consider a triangle $\mathrm{ABC}$ satisfying $2 a \sin ^{2}\left(\frac{C}{2}\right)+2 c \sin ^{2}\left(\frac{A}{2}\right)=2 a+2 c-3 b$<br/>The sides of the triangle are in</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">G.P.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">A.P.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">HP.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Neither in G.P. nor in A.Pnor in H.P.</span> </li> </ul>

answer:
<div class="solution">$\quad 2 \mathrm{a} \sin ^{2}\left(\frac{\mathrm{C}}{2}\right)+2 \mathrm{c} \sin ^{2}\left(\frac{\mathrm{A}}{2}\right)=2 \mathrm{a}+2 \mathrm{c}-3 \mathrm{~b}$<br/>$\Rightarrow 2 \mathrm{a} \times \frac{(\mathrm{s}-\mathrm{a})(\mathrm{s}-\mathrm{b})}{\mathrm{ab}}+2 \mathrm{c} \times \frac{(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})}{\mathrm{bc}}=2 \mathrm{a}+2 \mathrm{c}-3 \mathrm{~b}$<br/>$\Rightarrow \frac{2}{\mathrm{~b}}(\mathrm{~s}-\mathrm{b})[\mathrm{s}-\mathrm{a}+\mathrm{s}-\mathrm{c}]=2 \mathrm{a}+2 \mathrm{c}-3 \mathrm{~b}$<br/>$\Rightarrow \frac{2}{\mathrm{~b}}(\mathrm{~s}-\mathrm{b}) \mathrm{b}=2 \mathrm{a}+2 \mathrm{c}-3 \mathrm{~b} \quad[\because 2 \mathrm{~s}-\mathrm{a}-\mathrm{c}=\mathrm{b}]$<br/>$\Rightarrow \mathrm{a}+\mathrm{c}=2 \mathrm{~b}$<br/>So $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in A.P.</div>


tags: ['Mathematics', 'Ellipse', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-an-ellipse-a-2-x-2-b-2-y-2-1-what-is-the-area-included-between-the-ellipseand-the-greatest-rectangle-inscribed-in-the-ellipse

slug:
consider-an-ellipse-a-2-x-2-b-2-y-2-1-what-is-the-area-included-between-the-ellipseand-the-greatest-rectangle-inscribed-in-the-ellipse-63649

question:
<div class="question">Consider an ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ .<br/>What is the area included between the ellipseand the greatest rectangle inscribed in the ellipse?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$a b(\pi-1)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 a b(\pi-1)$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$a b(\pi-2)$</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">None of these</span> </li> </ul>

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

answer:
<div class="solution">$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$<br/>Area of ellipse is $\pi a b$ Area ofshaded region $=$ Area of ellipse- Area of rectangle $=\pi a b-2 a b=a b(\pi-2)$</div>


tags: ['Mathematics', 'Ellipse', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
consider-an-ellipse-a-2-x-2-b-2-y-2-1-what-is-the-area-of-the-greatest-rectangle-that-can-be-inscribed-in-the-ellipse-1

slug:
consider-an-ellipse-a-2-x-2-b-2-y-2-1-what-is-the-area-of-the-greatest-rectangle-that-can-be-inscribed-in-the-ellipse-1-77499

question:
<div class="question">Consider an ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ .<br/>What is the area of the greatest rectangle that can be inscribed in the ellipse?</div>

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

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

answer:
<div class="solution">Given equation of ellipse, $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$<br/>Let $\mathrm{A}(\mathrm{a} \cos \theta, \mathrm{b} \sin \theta)$ be any point on ellipse(1st quadrant)<br/>Coordinate of $\mathrm{B}=[\mathrm{a} \cos (\pi-\theta), \mathrm{b} \sin (\pi-\theta)]$<br/>$=(-a \cos \theta, b \sin \theta)$(2nd quadrant) <br/>Coordinate of $C=[a \cos (\pi+\theta), b \sin (\pi+\theta)]$(3rd quadrant)<br/>Coordinate of $\mathrm{D}=[\mathrm{a} \cos (2 \pi-\theta), \mathrm{b} \sin (2 \pi-\theta)]$<br/>$=(a \cos \theta,-b \sin \theta) \quad$ (4th quadrant)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/U6mjBdsSSBCeaZUrPC2g_bSvRMy47gXK8yFF9QFbLjk.original.fullsize.png"/><br/><br/>Area of the rectangle $\mathrm{ABCD}$ $=(a \cos \theta+a \cos \theta)(b \sin \theta+b \sin \theta)$<br/>$=2 a \cos \theta \times 2 b \sin \theta=2 a b \sin 2 \theta$<br/>$=2 a b \times 1=2 a b$</div>


tags: ['Mathematics', 'Ellipse', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-an-ellipse-a-2-x-2-b-2-y-2-1-what-is-the-area-of-the-greatest-rectangle-that-can-be-inscribed-in-the-ellipse

slug:
consider-an-ellipse-a-2-x-2-b-2-y-2-1-what-is-the-area-of-the-greatest-rectangle-that-can-be-inscribed-in-the-ellipse-65523

question:
<div class="question">Consider an ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ .<br/>What is the area of the greatest rectangle that can be inscribed in the ellipse?</div>

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

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

answer:
<div class="solution">Given equation of ellipse, $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$<br/>Let $\mathrm{A}(\mathrm{a} \cos \theta, \mathrm{b} \sin \theta)$ be any point on ellipse(1st quadrant)<br/>Coordinate of $\mathrm{B}=[\mathrm{a} \cos (\pi-\theta), \mathrm{b} \sin (\pi-\theta)]$<br/>$=(-a \cos \theta, b \sin \theta)$(2nd quadrant) <br/>Coordinate of $C=[a \cos (\pi+\theta), b \sin (\pi+\theta)]$(3rd quadrant)<br/>Coordinate of $\mathrm{D}=[\mathrm{a} \cos (2 \pi-\theta), \mathrm{b} \sin (2 \pi-\theta)]$<br/>$=(a \cos \theta,-b \sin \theta) \quad$ (4th quadrant)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/U6mjBdsSSBCeaZUrPC2g_bSvRMy47gXK8yFF9QFbLjk.original.fullsize.png"/><br/><br/>Area of the rectangle $\mathrm{ABCD}$ $=(a \cos \theta+a \cos \theta)(b \sin \theta+b \sin \theta)$<br/>$=2 a \cos \theta \times 2 b \sin \theta=2 a b \sin 2 \theta$<br/>$=2 a b \times 1=2 a b$</div>


tags: ['Mathematics', 'Ellipse', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-any-point-p-on-the-ellipse-25-x-2-9-y-2-1-in-the-first-quadrant-let-r-and-s-represent-its-distances-from-4-0-and-4-0-respectively-then-r-s-is

slug:
consider-any-point-p-on-the-ellipse-25-x-2-9-y-2-1-in-the-first-quadrant-let-r-and-s-represent-its-distances-from-4-0-and-4-0-respectively-then-r-s-is-18215

question:
<div class="question">Consider any point $P$ on the ellipse $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$ in the first quadrant. Let $\mathrm{r}$ and s represent its distances from $(4,0)$ and<br/>$(-4,0)$ respectively, then $(\mathrm{r}+\mathrm{s})$ is equal to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">10 unit</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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 unit</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">8 unit</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">6 unit</span> </li> </ul>

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

answer:
<div class="solution">$\frac{\mathrm{x}^{2}}{25}+\frac{\mathrm{y}^{2}}{9}=1$<br/>Put $\mathrm{x}=3$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/U-cBT9-x-ASCIi2F-NJJa0LMSI2vJiQ4z59XNFT9S8s.original.fullsize.png"/><br/><br/>$\frac{9}{25}+\frac{y^{2}}{9}=1$<br/>$y=\frac{12}{5}$<br/>$\mathrm{P}=(3,12 / 5)$<br/>$r=P O=\sqrt{(4-3)^{2}+\left(0-\frac{12}{5}\right)^{2}}$<br/>$=13 / 5$<br/>$\mathrm{S}=\mathrm{PO}^{\prime}=\sqrt{(-4-3)^{2}+\left(0-\frac{12}{5}\right)^{2}}$<br/>$=37 / 5$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-events-a-b-c-d-e-of-the-sample-space-s-n-n-is-an-integer-such-that-10-n-20-given-by-a-is-the-set-of-all-even-numbers-b-is-the-set-of-all-prim-1

slug:
consider-events-a-b-c-d-e-of-the-sample-space-s-n-n-is-an-integer-such-that-10-n-20-given-by-a-is-the-set-of-all-even-numbers-b-is-the-set-of-all-prim-1-94010

question:
<div class="question">Consider events $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}$ of the sample space $\mathrm{S}=\{\mathrm{n}: \mathrm{n}$ is an<br/>integer such that $10 \leq \mathrm{n} \leq 20\}$ given by: <br/>A is the set of all even numbers. <br/>B is the set of all prime numbers. <br/>$\mathrm{C}=(15)$<br/>$\mathrm{D}$ is the set of all integers $\leq 16$. <br/>E is the set of all double digit numbers expressible as a power of 2.<br/><br/>$\mathrm{B}$ and $\mathrm{C}$ are</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Mutually exclusive events but not exhaustive events</span> </div>

answer:
<div class="solution">$\mathrm{B}$ and $\mathrm{C}$ are mutually exclusive events but not exhaustive events.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2014 (Phase 2)']
answer: <div class="solution">A, B and C are exhaustive events and mutually exclusive events.</div>
source_db: MarksBatch1_P2.db
title:
consider-events-a-b-c-d-e-of-the-sample-space-s-n-n-is-an-integer-such-that-10-n-20-given-by-a-is-the-set-of-all-even-numbers-b-is-the-set-of-all-prim-2

slug:
consider-events-a-b-c-d-e-of-the-sample-space-s-n-n-is-an-integer-such-that-10-n-20-given-by-a-is-the-set-of-all-even-numbers-b-is-the-set-of-all-prim-2-17167

question:
<div class="question">Consider events $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}$ of the sample space $\mathrm{S}=\{\mathrm{n}: \mathrm{n}$ is an<br/>integer such that $10 \leq \mathrm{n} \leq 20\}$ given by: <br/>A is the set of all even numbers. <br/>B is the set of all prime numbers. <br/>$\mathrm{C}=(15)$<br/>$\mathrm{D}$ is the set of all integers $\leq 16$. <br/>E is the set of all double digit numbers expressible as a power of 2.<br/><br/>A, B and $C$ are</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Mutually exclusive and exhaustive events</span> </div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2014 (Phase 2)']
answer: <div class="solution">A, B and D are exhaustive events but not mutually<br/>exclusive events.</div>
source_db: MarksBatch1_P2.db
title:
consider-events-a-b-c-d-e-of-the-sample-space-s-n-n-is-an-integer-such-that-10-n-20-given-by-a-is-the-set-of-all-even-numbers-b-is-the-set-of-all-prim-3

slug:
consider-events-a-b-c-d-e-of-the-sample-space-s-n-n-is-an-integer-such-that-10-n-20-given-by-a-is-the-set-of-all-even-numbers-b-is-the-set-of-all-prim-3-76632

question:
<div class="question">Consider events $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}$ of the sample space $\mathrm{S}=\{\mathrm{n}: \mathrm{n}$ is an<br/>integer such that $10 \leq \mathrm{n} \leq 20\}$ given by: <br/>A is the set of all even numbers. <br/>B is the set of all prime numbers. <br/>$\mathrm{C}=(15)$<br/>$\mathrm{D}$ is the set of all integers $\leq 16$. <br/>E is the set of all double digit numbers expressible as a power of 2.<br/><br/>A, $\mathrm{B}$ and $\mathrm{D}$ are</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Exhaustive events but not mutually exclusive events</span> </div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-events-a-b-c-d-e-of-the-sample-space-s-n-n-is-an-integer-such-that-10-n-20-given-by-a-is-the-set-of-all-even-numbers-b-is-the-set-of-all-prim

slug:
consider-events-a-b-c-d-e-of-the-sample-space-s-n-n-is-an-integer-such-that-10-n-20-given-by-a-is-the-set-of-all-even-numbers-b-is-the-set-of-all-prim-24627

question:
<div class="question">Consider events $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}$ of the sample space $\mathrm{S}=\{\mathrm{n}: \mathrm{n}$ is an<br/>integer such that $10 \leq \mathrm{n} \leq 20\}$ given by: <br/>A is the set of all even numbers. <br/>B is the set of all prime numbers. <br/>$\mathrm{C}=(15)$<br/>$\mathrm{D}$ is the set of all integers $\leq 16$. <br/>E is the set of all double digit numbers expressible as a power of 2.<br/><br/>$\mathrm{C}$ and $\mathrm{E}$ are</div>

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

answer:
<div class="solution">$\mathrm{C}$ and $\mathrm{E}$ are mutually exclusive and elementary events.</div>


tags: ['Biology', 'Animal Kingdom', 'NEET', 'NEET 2019 (All India)']
source_db: MarksBatch1_P2.db
title:
consider-following-features-organ-system-level-of-organisation-bilateral-symmetry-true-coelomates-with-segmentation-of-body-select-the-correct-option-

slug:
consider-following-features-organ-system-level-of-organisation-bilateral-symmetry-true-coelomates-with-segmentation-of-body-select-the-correct-option-46777

question:
<div class="question"><p>Consider following features:</p><ul> <li>Organ system level of organisation</li> <li>Bilateral symmetry</li> <li>True coelomates with segmentation of body.</li></ul><p>Select the correct option of animal group which possess all the above characteristics:</p></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Annelida, Arthropoda and Chordata</span> </div>

answer:
<div class="solution"><p style="text-align: justify;">Organ system level organization, bilateral symmetry, true coelomates with the segmentation of body are seen in Annelida, Arthropoda, and Chordata.</p><p style="text-align: justify;">Annelids possess metameric segmentation.</p><p style="text-align: justify;">Arthropods have segmented bodies, like the annelids. These segments have become specialized, however, with one pair of jointed appendages added to each segment. Among living arthropods, the millipedes most closely suggest what the ancestral arthropod might have looked like.</p><p style="text-align: justify;">Chordates use heteromeric segmentation in which the link between segmented parts appears more subtly.</p></div>


title: consider-i-0-1-s-i-n-x-x-d-x-what-is-0-1-s-i-n-x-d-x-equal-to
slug: consider-i-0-1-s-i-n-x-x-d-x-what-is-0-1-s-i-n-x-d-x-equal-to-91062
tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2014 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider $I=\int_{0}^{\pi} \frac{x d x}{1+\sin x}$<br/>What is $\int_{0}^{\pi} \frac{d x}{1+\sin x}$ equal to ?</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">4</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-2$</span> </li> </ul>

answer:
<div class="solution">From eq. (iii).<br/>$2 \mathrm{I}=\pi \int_{0}^{\pi} \frac{\mathrm{d} \mathrm{x}}{1+\sin \mathrm{x}}$<br/>$\Rightarrow \int_{0}^{\pi} \frac{\mathrm{dx}}{1+\sin x}=\frac{2}{\pi} \mathrm{I}$<br/>$\Rightarrow \int_{0}^{\pi} \frac{\mathrm{d} \mathrm{x}}{1+\sin \mathrm{x}}=\frac{2}{\pi} \times \pi=2 \quad(\therefore \mathrm{I}=\pi)$<br/>Given, $\mathrm{I}=\int_{0}^{\pi} \frac{\mathrm{x} \mathrm{dx}}{1+\sin \mathrm{x}}$<br/>$=\int_{0}^{\pi} \frac{(\pi-\mathrm{x})}{1+\sin (\pi-\mathrm{x})} \mathrm{dx}$<br/>$\left[\because \int_{0}^{\mathrm{a}} \mathrm{f}(\mathrm{x}) \mathrm{d} \mathrm{x}=\int_{0}^{\mathrm{a}} \mathrm{f}(\mathrm{a}-\mathrm{x}) \mathrm{d} \mathrm{x}\right]$<br/>$=\int_{0}^{\pi} \frac{(\pi-\mathrm{x})}{1+\sin \mathrm{x}} \mathrm{dx}$<br/>$[\because \sin (\pi-\mathrm{x})=\sin \mathrm{x}]$<br/>Adding eqs. (i) and (ii), we get<br/>$2 \mathrm{I}=\pi \int_{0}^{\pi} \frac{\mathrm{d} \mathrm{x}}{1+\sin \mathrm{x}}$<br/>$\begin{aligned} \Rightarrow 2 \mathrm{I}=2 \pi \int_{0}^{\frac{\pi}{2}} \frac{\mathrm{dx}}{1+\sin \mathrm{x}} \\ &amp;\left[\because \int_{0}^{2 \mathrm{a}} \mathrm{f}(\mathrm{x}) \mathrm{d} \mathrm{x}=2 \int_{0}^{\mathrm{a}} \mathrm{f}(\mathrm{x}) \mathrm{dx}, \text { if } \mathrm{f}(2 \mathrm{a}-\mathrm{x})=\mathrm{f}(\mathrm{x})\right] \end{aligned}$<br/>$\Rightarrow \mathrm{I}=\pi \int_{0}^{\frac{\pi}{2}} \frac{\mathrm{d} \mathrm{x}}{1+\left(\frac{2 \tan \frac{\mathrm{x}}{2}}{1+\tan ^{2} \frac{\mathrm{x}}{2}}\right)}$<br/>$\Rightarrow \mathrm{I}=\pi \int_{0}^{\frac{\pi}{2}} \frac{\sec ^{2} \frac{\mathrm{x}}{2} \mathrm{dx}}{\tan ^{2} \frac{\mathrm{x}}{2}+1+2 \tan \frac{\mathrm{x}}{2}}$<br/>$\Rightarrow \mathrm{I}=\pi \int_{0}^{\frac{\pi}{2}} \frac{\left(\sec ^{2} \frac{\mathrm{x}}{2}\right) \mathrm{dx}}{\left(\tan \frac{\mathrm{x}}{2}+1\right)^{2}}$<br/>Let $\tan \frac{x}{2}+1=t$<br/>$\Rightarrow \sec ^{2} \frac{x}{2} \cdot \frac{1}{2} \mathrm{~d} x=\mathrm{dt}$<br/>$\Rightarrow \sec ^{2} \frac{x}{2} \mathrm{dx}=2 \mathrm{dt}$<br/>When $\mathrm{x}=0$, then $\mathrm{t}=1$ and when $\mathrm{x}=\frac{\pi}{2}$, then $\mathrm{t}=2$<br/>$\therefore \mathrm{I}=2 \pi \int_{1}^{2} \frac{\mathrm{dt}}{\mathrm{t}^{2}}=2 \pi\left[\frac{\mathrm{t}^{-2+1}}{-2+1}\right]_{1}^{2}=-2 \pi\left[\frac{1}{\mathrm{t}}\right]_{1}^{2}$<br/>$=-2 \pi\left[\frac{1}{2}-1\right]$<br/>$=-2 \pi\left(-\frac{1}{2}\right)=\pi$</div>


title: consider-i-0-1-s-i-n-x-x-d-x-what-is-0-1-s-i-n-x-x-d-x-equal-to
slug: consider-i-0-1-s-i-n-x-x-d-x-what-is-0-1-s-i-n-x-x-d-x-equal-to-63366
tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2014 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider $I=\int_{0}^{\pi} \frac{x d x}{1+\sin x}$<br/>What is $\int_{0}^{\pi} \frac{(\pi-x) d x}{1+\sin x}$ equal to?</div>

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

answer:
<div class="solution">Let $\mathrm{I}_{1}=\int_{0}^{\pi} \frac{(\pi-\mathrm{x}) \mathrm{d} \mathrm{x}}{1+\sin \mathrm{x}}$<br/>$=\int_{0}^{\pi} \frac{[\pi-(\pi-\mathrm{x})] \mathrm{d} \mathrm{x}}{1+\sin (\pi-\mathrm{x})}$<br/>$\left[\because \int_{0}^{a} \mathrm{f}(\mathrm{x}) \mathrm{d} \mathrm{x}=\int_{0}^{\mathrm{a}} \mathrm{f}(\mathrm{a}-\mathrm{x}) \mathrm{d} \mathrm{x}\right]$<br/>$\mathrm{I}_{1}=\int_{0}^{\pi} \frac{\mathrm{x} \mathrm{dx}}{1+\sin \mathrm{x}}=\pi \quad[\because \sin (\pi-\mathrm{x})=\sin \mathrm{x}]$<br/>Given, $\mathrm{I}=\int_{0}^{\pi} \frac{\mathrm{x} \mathrm{dx}}{1+\sin \mathrm{x}}$<br/>$=\int_{0}^{\pi} \frac{(\pi-\mathrm{x})}{1+\sin (\pi-\mathrm{x})} \mathrm{dx}$<br/>$\left[\because \int_{0}^{\mathrm{a}} \mathrm{f}(\mathrm{x}) \mathrm{d} \mathrm{x}=\int_{0}^{\mathrm{a}} \mathrm{f}(\mathrm{a}-\mathrm{x}) \mathrm{d} \mathrm{x}\right]$<br/>$=\int_{0}^{\pi} \frac{(\pi-\mathrm{x})}{1+\sin \mathrm{x}} \mathrm{dx}$<br/>$[\because \sin (\pi-\mathrm{x})=\sin \mathrm{x}]$<br/>Adding eqs. (i) and (ii), we get<br/>$2 \mathrm{I}=\pi \int_{0}^{\pi} \frac{\mathrm{d} \mathrm{x}}{1+\sin \mathrm{x}}$<br/>$\begin{aligned} \Rightarrow 2 \mathrm{I}=2 \pi \int_{0}^{\frac{\pi}{2}} \frac{\mathrm{dx}}{1+\sin \mathrm{x}} \\ &amp;\left[\because \int_{0}^{2 \mathrm{a}} \mathrm{f}(\mathrm{x}) \mathrm{d} \mathrm{x}=2 \int_{0}^{\mathrm{a}} \mathrm{f}(\mathrm{x}) \mathrm{dx}, \text { if } \mathrm{f}(2 \mathrm{a}-\mathrm{x})=\mathrm{f}(\mathrm{x})\right] \end{aligned}$<br/>$\Rightarrow \mathrm{I}=\pi \int_{0}^{\frac{\pi}{2}} \frac{\mathrm{d} \mathrm{x}}{1+\left(\frac{2 \tan \frac{\mathrm{x}}{2}}{1+\tan ^{2} \frac{\mathrm{x}}{2}}\right)}$<br/>$\Rightarrow \mathrm{I}=\pi \int_{0}^{\frac{\pi}{2}} \frac{\sec ^{2} \frac{\mathrm{x}}{2} \mathrm{dx}}{\tan ^{2} \frac{\mathrm{x}}{2}+1+2 \tan \frac{\mathrm{x}}{2}}$<br/>$\Rightarrow \mathrm{I}=\pi \int_{0}^{\frac{\pi}{2}} \frac{\left(\sec ^{2} \frac{\mathrm{x}}{2}\right) \mathrm{dx}}{\left(\tan \frac{\mathrm{x}}{2}+1\right)^{2}}$<br/>Let $\tan \frac{x}{2}+1=t$<br/>$\Rightarrow \sec ^{2} \frac{x}{2} \cdot \frac{1}{2} \mathrm{~d} x=\mathrm{dt}$<br/>$\Rightarrow \sec ^{2} \frac{x}{2} \mathrm{dx}=2 \mathrm{dt}$<br/>When $\mathrm{x}=0$, then $\mathrm{t}=1$ and when $\mathrm{x}=\frac{\pi}{2}$, then $\mathrm{t}=2$<br/>$\therefore \mathrm{I}=2 \pi \int_{1}^{2} \frac{\mathrm{dt}}{\mathrm{t}^{2}}=2 \pi\left[\frac{\mathrm{t}^{-2+1}}{-2+1}\right]_{1}^{2}=-2 \pi\left[\frac{1}{\mathrm{t}}\right]_{1}^{2}$<br/>$=-2 \pi\left[\frac{1}{2}-1\right]$<br/>$=-2 \pi\left(-\frac{1}{2}\right)=\pi$</div>


title: consider-i-0-1-s-i-n-x-x-d-x-what-is-i-equal-to
slug: consider-i-0-1-s-i-n-x-x-d-x-what-is-i-equal-to-88837
tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2014 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$\pi$</span> </div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider $I=\int_{0}^{\pi} \frac{x d x}{1+\sin x}$<br/>What is $I$ equal to ?</div>

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

answer:
<div class="solution">According to the explanation, $\mathrm{I}=\pi$<br/>Given, $\mathrm{I}=\int_{0}^{\pi} \frac{\mathrm{x} \mathrm{dx}}{1+\sin \mathrm{x}}$<br/>$=\int_{0}^{\pi} \frac{(\pi-\mathrm{x})}{1+\sin (\pi-\mathrm{x})} \mathrm{dx}$<br/>$\left[\because \int_{0}^{\mathrm{a}} \mathrm{f}(\mathrm{x}) \mathrm{d} \mathrm{x}=\int_{0}^{\mathrm{a}} \mathrm{f}(\mathrm{a}-\mathrm{x}) \mathrm{d} \mathrm{x}\right]$<br/>$=\int_{0}^{\pi} \frac{(\pi-\mathrm{x})}{1+\sin \mathrm{x}} \mathrm{dx}$<br/>$[\because \sin (\pi-\mathrm{x})=\sin \mathrm{x}]$<br/>Adding eqs. (i) and (ii), we get<br/>$2 \mathrm{I}=\pi \int_{0}^{\pi} \frac{\mathrm{d} \mathrm{x}}{1+\sin \mathrm{x}}$<br/>$\begin{aligned} \Rightarrow 2 \mathrm{I}=2 \pi \int_{0}^{\frac{\pi}{2}} \frac{\mathrm{dx}}{1+\sin \mathrm{x}} \\ &amp;\left[\because \int_{0}^{2 \mathrm{a}} \mathrm{f}(\mathrm{x}) \mathrm{d} \mathrm{x}=2 \int_{0}^{\mathrm{a}} \mathrm{f}(\mathrm{x}) \mathrm{dx}, \text { if } \mathrm{f}(2 \mathrm{a}-\mathrm{x})=\mathrm{f}(\mathrm{x})\right] \end{aligned}$<br/>$\Rightarrow \mathrm{I}=\pi \int_{0}^{\frac{\pi}{2}} \frac{\mathrm{d} \mathrm{x}}{1+\left(\frac{2 \tan \frac{\mathrm{x}}{2}}{1+\tan ^{2} \frac{\mathrm{x}}{2}}\right)}$<br/>$\Rightarrow \mathrm{I}=\pi \int_{0}^{\frac{\pi}{2}} \frac{\sec ^{2} \frac{\mathrm{x}}{2} \mathrm{dx}}{\tan ^{2} \frac{\mathrm{x}}{2}+1+2 \tan \frac{\mathrm{x}}{2}}$<br/>$\Rightarrow \mathrm{I}=\pi \int_{0}^{\frac{\pi}{2}} \frac{\left(\sec ^{2} \frac{\mathrm{x}}{2}\right) \mathrm{dx}}{\left(\tan \frac{\mathrm{x}}{2}+1\right)^{2}}$<br/>Let $\tan \frac{x}{2}+1=t$<br/>$\Rightarrow \sec ^{2} \frac{x}{2} \cdot \frac{1}{2} \mathrm{~d} x=\mathrm{dt}$<br/>$\Rightarrow \sec ^{2} \frac{x}{2} \mathrm{dx}=2 \mathrm{dt}$<br/>When $\mathrm{x}=0$, then $\mathrm{t}=1$ and when $\mathrm{x}=\frac{\pi}{2}$, then $\mathrm{t}=2$<br/>$\therefore \mathrm{I}=2 \pi \int_{1}^{2} \frac{\mathrm{dt}}{\mathrm{t}^{2}}=2 \pi\left[\frac{\mathrm{t}^{-2+1}}{-2+1}\right]_{1}^{2}=-2 \pi\left[\frac{1}{\mathrm{t}}\right]_{1}^{2}$<br/>$=-2 \pi\left[\frac{1}{2}-1\right]$<br/>$=-2 \pi\left(-\frac{1}{2}\right)=\pi$</div>


tags: ['Physics', 'Oscillations', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
consider-one-dimensional-motion-of-a-particle-of-mass-m-it-has-potential-energy-u-a-b-x-2-where-a-and-b-are-positive-constants-at-origin-x-0-it-has-in

slug:
consider-one-dimensional-motion-of-a-particle-of-mass-m-it-has-potential-energy-u-a-b-x-2-where-a-and-b-are-positive-constants-at-origin-x-0-it-has-in-54007

question:
<div class="question">Consider one dimensional motion of a particle of mass <math> <mi>m</mi> </math>. It has potential energy <math><mi>U</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></math>, where <math> <mi>a</mi> </math> and <math> <mi>b</mi> </math> are positive constants. At origin <math><mo>(</mo><mi>x</mi><mo>=</mo><mn>0</mn><mo>)</mo></math> it has initial velocity <math> <mrow> <msub> <mi>V</mi> <mn>0 </mn> </msub> </mrow> </math>. It performs simple harmonic oscillations. The frequency of the simple harmonic motion depends on</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mi>b</mi></math> and <math><mi>m</mi></math> alone</span> </div>

answer:
<div class="solution">Given,<br/><br/>Potential energy, <math><mi>U</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></math><br/><br/>Force, <math><mi>F</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mi>d</mi><mi>U</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac></math><br/><br/><math><mo>=</mo><mo>-</mo><mfrac><mrow><mi>d</mi><mo>.</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac></math><br/><br/><math><mo>=</mo><mo>-</mo><mfenced close="]" open="[" separators="|"><mrow><mfrac><mrow><mi>d</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac><mfenced separators="|"><mrow><mi>a</mi></mrow></mfenced><mo>+</mo><mfrac><mrow><mi>d</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac><mo>(</mo><mi>b</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mfenced></math><br/><br/><math><mo>â</mo><mi> </mi><mi> </mi><mi> </mi><mi> </mi><mi>F</mi><mo>=</mo><mn>0</mn><mo>-</mo><mi>b</mi><mo>.</mo><mfrac><mrow><mi>d</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math><br/><br/><math><mo>â</mo><mi> </mi><mi> </mi><mi> </mi><mi> </mi><mi>F</mi><mo>=</mo><mn>0</mn><mo>-</mo><mi>b</mi><mo>.</mo><mn>2</mn><mi>x</mi><mo>=</mo><mo>-</mo><mn>2</mn><mi>b</mi><mi>x</mi></math><br/><br/><math><mo>â</mo><mi> </mi><mi> </mi><mi> </mi><mi> </mi><mi>a</mi><mo>=</mo><mfrac><mrow><mi>F</mi></mrow><mrow><mi>m</mi></mrow></mfrac><mo>=</mo><mo>-</mo><mfrac><mrow><mn>2</mn><mi>b</mi></mrow><mrow><mi>m</mi></mrow></mfrac><mi>x</mi></math> .......(i)<br/><br/>Compare equation. (i) with the standard relation of displacement in case of simple harmonic motion.<br/><br/>i.e., <math><mi>a</mi><mo>=</mo><mfrac><mrow><mi>F</mi></mrow><mrow><mn>2</mn><mi>m</mi></mrow></mfrac><mo>=</mo><mo>-</mo><msup><mrow><mi>Ï</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>x</mi></math><br/><br/>i.e., <math><msup><mrow><mi>Ï</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mfrac><mrow><mn>2</mn><mi>b</mi></mrow><mrow><mi>m</mi></mrow></mfrac></math><br/><br/><math><mi>Ï</mi><mo>=</mo><msqrt><mfrac><mrow><mn>2</mn><mi>b</mi></mrow><mrow><mi>m</mi></mrow></mfrac></msqrt></math><br/><br/>i.e., the frequency of the simple harmonic motion depends on <math><mi>b</mi></math> and <math><mi>m</mi></math> alone.</div>


tags: ['Chemistry', 'Chemical Equilibrium', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
consider-the-atomization-of-br-2-g-according-to-the-reaction-br-2-g-2-br-g-given-antiloge7029x104-if-the-heat-of-atomization-of-bromine-gas-is-82-kjmo

slug:
consider-the-atomization-of-br-2-g-according-to-the-reaction-br-2-g-2-br-g-given-antiloge7029x104-if-the-heat-of-atomization-of-bromine-gas-is-82-kjmo-79862

question:
<div class="question">Consider the atomization of Br<sub>2</sub>(g) according to the reaction :<br/> <math><mrow><msub><mtext>Br</mtext> <mn>2</mn> </msub> <mfenced close=")" open="(" separators=","> <mrow> <mtext>g</mtext> </mrow> </mfenced> <mo>â</mo> <mn>2</mn> <mtext>Br</mtext> <mfenced close=")" open="(" separators=","> <mrow> <mtext>g</mtext></mrow></mfenced></mrow></math>       {Given antiloge(-7.02)=9x10-4}<br/>
If the heat of atomization of bromine gas is 82 KJ/mol ; standard molar entropies of Br(g) and Br<sub>2</sub>(g) are 175 and 245.4 JK<sup>-1</sup>  respectively, calculate degree of dissociation when the total pressure is 40 atm at 500 K.<br/>
(assume <math> <mi>Î±</mi></math>&lt;&lt;1 in your calculation)</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math> <mrow> <mn>2.37</mn> </mrow> <mo>Ã</mo> <mn>1</mn> <msup> <mn>0</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math> <mrow> <mn>3.20</mn> </mrow> <mo>×</mo> <mn>1</mn> <msup> <mn>0</mn> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </msup> </math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math> <mrow> <mn>4.30</mn> </mrow> <mo>×</mo> <mn>1</mn> <msup> <mn>0</mn> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </msup> </math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math> <mrow> <mn>3.60</mn> </mrow> <mo>×</mo> <mn>1</mn> <msup> <mn>0</mn> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math> <mrow> <mn>2.37</mn> </mrow> <mo>Ã</mo> <mn>1</mn> <msup> <mn>0</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </math></span> </div>

answer:
<div class="solution">For <math> <mrow> <msub> <mtext>Br</mtext> <mn>2</mn> </msub> <mfenced close=")" open="(" separators=","> <mrow> <mtext>g</mtext> </mrow> </mfenced> <mo>â</mo> <mn>2</mn> <mtext>Br</mtext> <mfenced close=")" open="(" separators=","> <mrow> <mtext>g</mtext> </mrow> </mfenced> </mrow> </math><br/><math> <mrow> <mo>Î</mo> <msubsup> <mtext>S</mtext> <mtext>reac</mtext> <mo>â</mo> </msubsup> <mo>=</mo> <mn>2</mn> <mo>Ã</mo> <mn>1</mn> <mn>7</mn> <mn>5</mn> <mo>-</mo> <mn>2</mn> <mn>4</mn> <mn>4</mn> <mo>Â·</mo> <mn>4</mn> <mo>=</mo> <mn>105.6</mn> <mtext> J</mtext> <msup> <mtext> K</mtext> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </math><br/><math> <mrow> <mo>Î</mo> <msubsup> <mtext>H</mtext> <mtext>reac</mtext> <mo>â</mo> </msubsup> <mo>=</mo> <mn>8</mn> <mn>2</mn> <mtext> KJ</mtext> <msup> <mtext> m</mtext> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </math><br/><math> <mrow> <mo>Î</mo> <msubsup> <mtext>G</mtext> <mtext>reac</mtext> <mo>â</mo> </msubsup> <mo>=</mo> <mo>Î</mo> <msubsup> <mtext>H</mtext> <mtext>reac</mtext> <mo>â</mo> </msubsup> <mo>-</mo> <mtext>T</mtext> <mo>Î</mo> <msup> <mtext>S</mtext> <mo>â</mo> </msup> <mo>=</mo> <mn>8</mn> <mn>2</mn> <mn>0</mn> <mn>0</mn> <mn>0</mn> <mo>-</mo> <mn>5</mn> <mn>0</mn> <mn>0</mn> <mo>Ã</mo> <mn>105.6</mn> </mrow> </math><br/><math> <mrow> <mo>=</mo> <mn>2</mn> <mn>9</mn> <mo>Â·</mo> <mn>2</mn> <mo>Ã</mo> <mn>1</mn> <msup> <mn>0</mn> <mn>3</mn> </msup> <mtext>J</mtext> <mo>=</mo> <mo>-</mo> <mtext>RT </mtext> <mtext>ln </mtext> <msub> <mtext>K</mtext> <mtext>P</mtext> </msub> </mrow> </math><br/><math> <mrow> <mtext>ln </mtext> <msub> <mtext>K</mtext> <mtext>P</mtext> </msub> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <mn>2</mn> <mn>9</mn> <mn>7</mn> <mn>0</mn> <mn>0</mn> </mrow> <mrow> <mn>8</mn> <mo>Â·</mo> <mn>3</mn> <mn>1</mn> <mn>4</mn> <mo>Ã</mo> <mn>5</mn> <mn>0</mn> <mn>0</mn> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mn>7.02</mn> </mrow> </math><br/><math> <mrow> <mo>â´</mo><mtext>â</mtext><msub> <mtext>K</mtext> <mtext>P</mtext> </msub> <mo>=</mo><mn>9</mn><mo>Ã</mo><msup> <mrow> <mn>10</mn></mrow> <mrow> <mo>â</mo><mn>4</mn></mrow> </msup> </mrow> </math><br/><math> <mrow> <msub> <mtext>K</mtext> <mtext>P</mtext> </msub> <mo>=</mo><mfrac> <mrow> <mn>4</mn><msup> <mtext>Î±</mtext> <mtext>2</mtext> </msup> <mtext>P</mtext></mrow> <mrow> <mn>1</mn><mo>â</mo><msup> <mtext>Î±</mtext> <mtext>2</mtext> </msup> </mrow> </mfrac> </mrow> </math><br/>as <math> <mrow> <mtext>Î±</mtext><mo>&lt;</mo><mo>&lt;</mo><mn>1</mn><mtext>â</mtext><mtext>â</mtext><mo>â´</mo><mtext>â</mtext><mn>1</mn><mo>â</mo><msup> <mtext>Î±</mtext> <mtext>2</mtext> </msup> <mo>=</mo><mn>1</mn></mrow> </math><br/><math> <mrow> <mo>â´</mo><mtext>â</mtext><msub> <mtext>K</mtext> <mtext>P</mtext> </msub> <mo>=</mo><mn>4</mn><mo>Ã</mo><msup> <mtext>Î±</mtext> <mtext>2</mtext> </msup> <mtext>P</mtext></mrow> </math><br/><math> <mrow> <mo>âµ</mo><mtext>â</mtext><mtext>P</mtext><mtext>â</mtext><mtext>=</mtext><mtext>â</mtext><mtext>40</mtext></mrow> </math><br/><math> <mrow> <mo>â´</mo><mtext>â</mtext><mn>9</mn><mo>Ã</mo><msup> <mrow> <mn>10</mn></mrow> <mrow> <mo>â</mo><mn>4</mn></mrow> </msup> <mo>=</mo><mn>4</mn><mo>â</mo><msup> <mi>Î±</mi> <mn>2</mn> </msup> <mo>â</mo><mn>40</mn></mrow> </math><br/><math> <mrow> <mo>â´</mo><mtext>â</mtext><msup> <mtext>Î±</mtext> <mtext>2</mtext> </msup> <mo>=</mo><mfrac> <mn>9</mn> <mrow> <mn>160</mn></mrow> </mfrac> <mo>Ã</mo><msup> <mrow> <mn>10</mn></mrow> <mrow> <mo>â</mo><mn>4</mn></mrow> </msup> </mrow> </math><br/><math> <mrow> <mo>=</mo><mfrac> <mn>9</mn> <mrow> <mn>16</mn></mrow> </mfrac> <mo>Ã</mo><msup> <mrow> <mn>10</mn></mrow> <mrow> <mo>â</mo><mn>5</mn></mrow> </msup> </mrow> </math><br/><math> <mrow> <mo>=</mo><mtext>â</mtext><mn>2.37</mn><mo>Ã</mo><msup> <mrow> <mn>10</mn></mrow> <mrow> <mo>â</mo><mn>3</mn></mrow> </msup> </mrow> </math></div>


title: consider-the-circles-x-2-y-2-2-a-x-c-0-and-x-2-y-2-2-b-y-c-0-the-two-circles-touch-each-other-if
tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
slug:
consider-the-circles-x-2-y-2-2-a-x-c-0-and-x-2-y-2-2-b-y-c-0-the-two-circles-touch-each-other-if-73709

question:
<div class="question">Consider the circles $x^{2}+y^{2}+2 a x+c=0$ and $x^{2}+y^{2}+2 b y+c=0$<br/>The two circles touch each other if</div>

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

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

answer:
<div class="solution">Two circles touch each other, iff distance between two centres $=$ Sum of radius of two circles<br/>$\sqrt{a^{2}+b^{2}}=\sqrt{a^{2}-c}+\sqrt{b^{2}-c}$<br/>On squaring both sides, we get<br/>$a^{2}+b^{2}=a^{2}-c+b^{2}-c+2 \sqrt{\left(a^{2}-c\right)\left(b^{2}-c\right)}$<br/>$\Rightarrow \mathrm{c}=\sqrt{\left(\mathrm{a}^{2}-\mathrm{c}\right)\left(\mathrm{b}^{2}-\mathrm{c}\right)}$<br/>Again, squaring both sides, we get<br/>$$<br/>\mathrm{c}^{2}=\mathrm{a}^{2} \mathrm{~b}^{2}-\mathrm{a}^{2} \mathrm{c}-\mathrm{b}^{2} \mathrm{c}+\mathrm{c}^{2}<br/>$$<br/>$\Rightarrow a^{2} b^{2}=\left(a^{2}+b^{2}\right) c \Rightarrow \frac{1}{c}=\frac{1}{a^{2}}+\frac{1}{b^{2}}$</div>


tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-the-circles-x-2-y-2-2-a-x-c-0-and-x-2-y-2-2-b-y-c-0-what-is-the-distance-between-the-centres-of-the-two-circles

slug:
consider-the-circles-x-2-y-2-2-a-x-c-0-and-x-2-y-2-2-b-y-c-0-what-is-the-distance-between-the-centres-of-the-two-circles-65169

question:
<div class="question">Consider the circles $x^{2}+y^{2}+2 a x+c=0$ and $x^{2}+y^{2}+2 b y+c=0$<br/>What is the distance between the centres of the two circles?</div>

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

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

answer:
<div class="solution">Equations of circles are $x^{2}+y^{2}+2 a x+c=0$<br/>and $x^{2}+y^{2}+2 b y+c=0$<br/>Since, the centres of two circles are $(-a, 0)$ and $(0,-b)$<br/>- Distance between two centres $=\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}}$</div>


title: consider-the-curve-x-a-cos-sin-and-y-a-sin-cos-what-is-d-x-2-d-2-y-equal-to
slug: consider-the-curve-x-a-cos-sin-and-y-a-sin-cos-what-is-d-x-2-d-2-y-equal-to-69058
tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the curve $x=a(\cos \theta+\theta \sin \theta)$ and $y=a(\sin \theta-\theta \cos \theta)$.<br/>What is $\frac{d^{2} y}{d x^{2}}$ equal to?</div>

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

answer:
<div class="solution">Given $\mathrm{x}=\mathrm{a}(\cos \theta+\theta \sin \theta)$<br/>$\mathrm{y}=\mathrm{a}(\sin \theta-\theta \cos \theta)$ and we have $\frac{\mathrm{dy}}{\mathrm{dx}}=\tan \theta$<br/>According to question $\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{d} \mathrm{x}^{2}}=\sec ^{2} \theta \frac{\mathrm{d} \theta}{\mathrm{dx}}$<br/>$=\sec ^{2} \theta\left(\frac{1}{a \theta \cos \theta}\right)$ $\quad \left[\because \frac{\mathrm{dx}}{\mathrm{d} \theta}=\mathrm{a} \theta \cos \theta\right]$<br/>Hence, $\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}=\frac{\sec ^{3} \theta}{\mathrm{a} \theta}$</div>


title: consider-the-curve-x-a-cos-sin-and-y-a-sin-cos-what-is-d-x-d-y-equal-to
slug: consider-the-curve-x-a-cos-sin-and-y-a-sin-cos-what-is-d-x-d-y-equal-to-99030
tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the curve $x=a(\cos \theta+\theta \sin \theta)$ and $y=a(\sin \theta-\theta \cos \theta)$.<br/>What is $\frac{d y}{d x}$ equal to?</div>

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

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

answer:
<div class="solution">Given, $\mathrm{x}=\mathrm{a}(\cos \theta+\theta \sin \theta)$ and<br/>$y=a(\sin \theta-\theta \cos \theta)$<br/>$\frac{\mathrm{dx}}{\mathrm{d} \theta}=\mathrm{a}(-\sin \theta+\theta \cos \theta+\sin \theta)=\mathrm{a} \theta \cos \theta$<br/>$\frac{\mathrm{dy}}{\mathrm{d} \theta}=\mathrm{a}(\cos \theta+\theta \sin \theta-\cos \theta)=\mathrm{a} \theta \sin \theta$<br/>Now $\frac{\mathrm{dy}}{\mathrm{dx}}-\frac{\mathrm{a} \theta \sin \theta}{\mathrm{a} \theta \cos \theta}=\tan \theta$</div>


tags: ['Mathematics', 'Area Under Curves', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-curves-y-sin-x-and-y-cos-x-what-is-the-area-of-the-region-bounded-by-the-above-two-curves-and-the-lines-x-0-and-x-4

slug:
consider-the-curves-y-sin-x-and-y-cos-x-what-is-the-area-of-the-region-bounded-by-the-above-two-curves-and-the-lines-x-0-and-x-4-57038

question:
<div class="question">Consider the curves $y=\sin x$ and $y=\cos x$<br/>What is the area of the region bounded by the above two<br/>curves and the lines $\mathrm{x}=0$ and $x=\frac{\pi}{4}$ ?</div>

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

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/XBxW6K1Pr383ZTVCOQgdV7bzC7Wa3JQt7RfY8iEsyhM.original.fullsize.png"/></div>


tags: ['Mathematics', 'Area Under Curves', 'NDA', 'NDA 2015 (Phase 1)']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch1_P2.db
title:
consider-the-curves-y-sin-x-and-y-cos-x-what-is-the-area-of-the-region-bounded-by-the-above-two-curves-and-the-lines-x-4-and-x-2

slug:
consider-the-curves-y-sin-x-and-y-cos-x-what-is-the-area-of-the-region-bounded-by-the-above-two-curves-and-the-lines-x-4-and-x-2-45174

question:
<div class="question">Consider the curves $y=\sin x$ and $y=\cos x$<br/>What is the area of the region bounded by the above two<br/>curves and the lines $x=\frac{\pi}{4}$ and $x=\frac{\pi}{2} ?$</div>

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

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


title: consider-the-curves-y-x-1-and-x-2-what-is-the-area-of-the-region-bounded-by-the-curves-and-x-axis
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P2.db
slug:
consider-the-curves-y-x-1-and-x-2-what-is-the-area-of-the-region-bounded-by-the-curves-and-x-axis-82854

question:
<div class="question">Consider the curves $\mathrm{y}=|\mathrm{x}-1|$ and $|\mathrm{x}|=2$<br/>What is the area of the region bounded by the curves and $\mathrm{x}-$ axis?</div>

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

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

answer:
<div class="solution">Bounded region is shaded So area of bounded region has two triangles $A C B$ and $B D E$<br/>Area of $\Delta A C B=\frac{1}{2} \times 3 \times 3=\frac{9}{2}$<br/>Area of $\Delta B D E=\frac{1}{2} \times 1 \times 1=\frac{1}{2}$<br/>Area of region bounded by curves and $\mathrm{x}$ -axis is<br/>Area $=\Delta A C B+\Delta B D E=\frac{9}{2}+\frac{1}{2}=5$ square units</div>


title: consider-the-curves-y-x-1-and-x-2-what-isare-the-points-of-intersection-of-the-curves
slug: consider-the-curves-y-x-1-and-x-2-what-isare-the-points-of-intersection-of-the-curves-56299
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the curves $\mathrm{y}=|\mathrm{x}-1|$ and $|\mathrm{x}|=2$<br/>What is/are the point(s) of intersection of the curves?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(-2,3)$ only</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(2,1)$ only</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$(-2,3)$ and $(2,1)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Neither $(-2,3)$ nor $(2,1)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(-2,3)$ and $(2,1)$</span> </div>

answer:
<div class="solution">$y=|x-1|$ and $|x|=2$<br/>$y=\left\{\begin{array}{ll}x-1 &amp; x \geq 1 \\ 1-x &amp; x   &lt; 1\end{array}\right.$<img src="https://cdn-question-pool.getmarks.app/pyq/nda/ZwRvmThY5sInMpQnoHZNZXYmQI0SvMnAN5_6jYgJ_Y4.original.fullsize.png"/><br/><br/>and $x=2$ $x=-2$<br/>Hence curves intersect at $(-2,3)$ and $(2,1)$.</div>


tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2009 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-the-diagonals-of-a-quadrilateral-formed-by-the-vectors-3-i-6-j-2-k-and-4-i-j-3-k-the-quadrilateral-must-be-a

slug:
consider-the-diagonals-of-a-quadrilateral-formed-by-the-vectors-3-i-6-j-2-k-and-4-i-j-3-k-the-quadrilateral-must-be-a-81233

question:
<div class="question">Consider the diagonals of a quadrilateral formed by the vectors $3 \hat{i}+6 \hat{j}-2 \hat{k}$ and $4 \hat{i}-\hat{j}+3 \hat{k}$. The quadrilateral must be a</div>

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

answer:
<div class="solution">Let $\vec{d}_{1}$ and $\vec{d}_{2}$ be the two diagonals of a quadrilateral such that<br/>$\vec{d}_{1}=3 \hat{i}+6 \hat{j}-2 \hat{k}$<br/>and $\vec{d}_{2}=4 \hat{i}-\hat{j}+3 \hat{k}$<br/>Now, Dot product of $\vec{d}_{1}$ and $\vec{d}_{2}$ is<br/>$\vec{d}_{1} \cdot \vec{d}_{2}=3(4)+6(-1)-2(3)=0$<br/>Now, $\left|\vec{d}_{1}\right|=\sqrt{3^{2}+6^{2}+2^{2}}=7$<br/>$\left|\vec{d}_{2}\right|=\sqrt{4^{2}+1^{2}+3^{2}}=\sqrt{26}$<br/>Since, $\left|\vec{d}_{1}\right| \neq\left|\vec{d}_{2}\right|$<br/>Hence, given quadrilateral is a rhombus,</div>


title: consider-the-ellipse-a-2-x-2-b-2-y-2-1-b-a-then-which-one-ofthe-following-is-correct
slug: consider-the-ellipse-a-2-x-2-b-2-y-2-1-b-a-then-which-one-ofthe-following-is-correct-17472
tags: ['Mathematics', 'Ellipse', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(b&gt;a)$. Then, which one ofthe following is correct?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Foci are $(0, \pm b e)$</span> </div>

answer:
<div class="solution">Given equation $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$<br/>Since, $b&gt;a$<br/>Foci $=(0, \pm \mathrm{b})$</div>


tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2010 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4 or 8</span> </div>
source_db: MarksBatch1_P2.db
title:
consider-the-equation-x-p-x-6-1-0-having-integral-coefficients-if-the-equation-has-integral-roots-then-what-values-can-p-have

slug:
consider-the-equation-x-p-x-6-1-0-having-integral-coefficients-if-the-equation-has-integral-roots-then-what-values-can-p-have-63671

question:
<div class="question">Consider the equation $(x-p)(x-6)+1=0$ having integral coefficients. If the equation has integral roots, then what values can p have?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">4 or 8</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">5 or 10</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">6 or 12</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">3 or 6</span> </li> </ul>

answer:
<div class="solution">Given equation is $(x-p)(x-6)+1=0$ $\Rightarrow x^{2}-6 x-p x+6 p+1=0$<br/>$\Rightarrow x^{2}-(p+6) x+(6 p+1)=0$<br/>Now, $b^{2}-4 a c=0$<br/>$a=\mathrm{L}, b=-(p+6), c=6 p+1$<br/>$\Rightarrow(p+6)^{2}-4(6 p+1)=0$<br/>$\Rightarrow p^{2}+36+12 p-24 p-4=0$<br/>$\Rightarrow p^{2}-12 p+32=0$<br/>$\Rightarrow(p-4)(p-8)=0$<br/>$\Rightarrow p=4,8$<br/>Hence, $p$ can have 4 or 8 .</div>


