NDA 1 2024 Maths, question 98

Topic: Integral calculus

Passage · Q97 to Q98

The circle $x^{2}+y^{2}-2x=0$ is partitioned by line $y=x$ in two segments. Let $A_{1},A_{2}$ be the areas of major and minor segments respectively.

Q98

What is the value of $\frac{2(A_{1}+A_{2})}{A_{1}-3A_{2}}$ ?

(a) $\pi$ Correct answer
(b) $1$
(c) $-1$
(d) $-\pi$

Solution.

Answer: (a) $\pi$

Here A₁ = (3π + 2)/4 and A₂ = (π − 2)/4.
Consequently A₁ + A₂ = π and A₁ − 3A₂ = 2.
The requested ratio 2(A₁ + A₂)/(A₁ − 3A₂) is π.