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CUET · MATHS · PYQ PAPER 2023

The area of the region enclosed between the two circles \(x^2+y^2=1\) and \((x-1)^2+y^2=1\) is

  1. A \(\left(2 \pi / 3-\frac{\sqrt{3}}{4}\right)\) units
  2. B \(\left(\pi / 3-\frac{2 \sqrt{3}}{3}\right)\) units
  3. C \(\left(2 \pi / 3-\frac{\sqrt{3}}{2}\right)\) units
  4. D \(\left(\pi / 6-\frac{\sqrt{3}}{2}\right)\) units
Verified Solution

Answer & Solution

Correct Answer

(C) \(\left(2 \pi / 3-\frac{\sqrt{3}}{2}\right)\) units

Step-by-step Solution

Detailed explanation

Radius \(r=1\), distance between centers \(d=1\). Area \(A = 2r^2 \cos^{-1}\left(\frac{d}{2r}\right) - \frac{d}{2} \sqrt{4r^2 - d^2}\) \(A = 2(1)^2 \cos^{-1}\left(\frac{1}{2(1)}\right) - \frac{1}{2} \sqrt{4(1)^2 - (1)^2}\) \(A = 2(\pi/3) - \frac{1}{2} \sqrt{3}\)…