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CUET · MATHS · PYQ PAPER 2025

The area of the region \(\left\{(x, y): x^2+y^2 \leq 1 \leq x+y\right\}\) is

  1. A \(\left(\frac{\pi}{2}-1\right)\) sq.unit
  2. B \(\frac{1}{2}(\pi-1)\) sq.unit
  3. C \(\frac{1}{2}\left(\frac{\pi}{2}-1\right)\) sq.unit
  4. D ( \(\pi-1\) ) sq.unit
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{1}{2}\left(\frac{\pi}{2}-1\right)\) sq.unit

Step-by-step Solution

Detailed explanation

The region is a circular segment of the unit circle \(x^2+y^2 \leq 1\) cut by the line \(x+y=1\). Intersection points of \(x^2+y^2=1\) and \(x+y=1\) are \((0,1)\) and \((1,0)\). The angle subtended by the chord at the origin is \(\theta = \frac{\pi}{2}\). Area of the sector:…