GATE 2021 BM – Question 9

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 2 marks · Multiple choice

PQRS is a square. The shaded region is the intersection of two circular sectors, each of radius equal to the square’s side, with centres at S and Q. What is the probability that a uniformly chosen point in the square lies in the shaded region?

$4-\pi/2$
1/2
$\pi/2-1$
$\pi/4$

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Show answer and explanation

Correct answer: (C) $\pi/2-1$

Explanation

Let side length be r. The two quarter-disc sectors each have area πr²/4, and their union fills the square. By inclusion–exclusion, intersection area=πr²/2−r². Dividing by square area r² gives π/2−1, C. The radius cancels.

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