Comprehension

निर्देश : निम्नलिखित प्रश्नों के लिए निम्नलिखित पर विचार करें:

परवलय y2 = kx और रेखा x = k, जहाँ k > 0 है, द्वारा परिबद्ध क्षेत्रफल 4/3 वर्ग इकाई है।

k का मान क्या है?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. 1/2
  2. 1
  3. √2
  4. 2

Answer (Detailed Solution Below)

Option 1 : 1/2
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NDA 01/2025: English Subject Test
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Detailed Solution

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व्याख्या:

दिया गया है:

परवलय y2 = kx और रेखा x = k, जहाँ k > 0, द्वारा परिबद्ध क्षेत्रफल 4/3 वर्ग इकाई है

qImage67ee82e1896ba874ec3494d4

परिबद्ध क्षेत्रफल = 4/3 वर्ग इकाई

= \(2 \int_0^kydx\)

⇒ 4/3 = \(2 \int_0^k\sqrt k \sqrt xdx\)

⇒1 = k2

⇒ k = ±1 (चूँकि k>0)

⇒ k = 1

∴ विकल्प (b) सही है।

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