In square PQRS of side r, the shaded lens is the overlap of quarter-circles of radius r centred at S and Q. Find the probability that a uniformly random point in the square lies in the lens.
The two quarter-discs together cover the square. Their areas sum to $2(\pi r^2/4)$, so their overlap is $\pi r^2/2-r^2$. Divide by square area r² to obtain **π/2−1 (C)**. This lies between zero and one, as a probability must.
More Quantitative Aptitude: Algebra, Geometry and Mensuration questions
GATE 2021 MN Q10– In an equilateral triangle, the sides are divided into 4, 6 and 8 equal parts…
GATE 2021 AR Q3– Two fair six-faced dice numbered 1–6 are rolled independently. Find the probability of an…
GATE 2021 AR Q4– Define p q=p-q and p q=pq. Evaluate (9(67))(7(65)).
GATE 2021 AR Q6– From O, travel 3 units east and 4 south to P. Move northeast until reaching a point 6…
GATE 2021 AR Q9– In square PQRS of side r, the shaded lens is the overlap of quarter-circles of radius r…
GATE 2021 AR Q10– In an equilateral triangle, the sides are divided into 4, 6 and 8 equal parts…
