Comprehension

Direction : Consider the following for the items that follow :

The area bounded by the parabola y2 = kx and the line x = k, where k > 0, is 4/3 square units.

What is the value of k? 

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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Detailed Solution

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Explanation:

Given:

The area bounded by the parabola y2 = kx and the line x = k, where k > 0, is 4/3 square units

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Area bounded = 4/3 sq. units

\(2 \int_0^kydx\)

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

⇒1 = k2

⇒ k = ±1 (since k>0)

⇒ k = 1

∴ Option (b) is correct.

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