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The area A of the region enclosed between the two unit circles x² + y² = 1 and (x-1)² + y² = 1. Which of the following statements is/are true?

1. (A) A > pi/2
2. (B) A < pi/2
3. (C) A is irrational
4. (D) A is rational

Correct answer: (B) A < pi/2

Solution

A = 2*(pi/3 - sqrt(3)/4) = 2*pi/3 - sqrt(3)/2 ≈ 1.228, which is less than pi/2 ≈ 1.571. Since A involves both pi and sqrt(3), it is irrational. Options B and C are both true.

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