NDA 1 2024 Maths, question 97

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.

Q97

What is the value of $A_{1}$ ?

(a) $\frac{\pi-2}{4}$
(b) $\frac{\pi+2}{4}$
(c) $\frac{3\pi-2}{4}$
(d) $\frac{3\pi+2}{4}$ Correct answer

Solution.

Answer: (d) $\frac{3\pi+2}{4}$

The circle has centre (1, 0) and radius 1.
Its intersections with y = x are (0, 0) and (1, 1), giving a minor central angle π/2.
The minor segment has area π/4 − 1/2 = (π − 2)/4.
Subtracting from the full area π gives the major area A₁ = (3π + 2)/4.