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NDA 2 2024 Maths, question 87

Topic: Integral calculus

Passage · Q87 to Q88

The area bounded by the parabola y2=kxy^{2}=kx and the line x=kx=k, where k>0k>0, is 4/3 square units4/3\text{ square units}.

Q87

What is the value of kk?

  1. (a) 1/21/2
  2. (b) 11Correct answer
  3. (c) 2\sqrt{2}
  4. (d) 22

Solution.

Answer: (b) 11

  1. At x=k, y=±k.
  2. Integrate horizontal widths: area=∫ from −k to k of (k−y²/k)dy=4k²/3.
  3. Equating this to 4/3 and using k>0 gives k=1.