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Q.

A point P moves inside a square with vertices A(1,1),B(−1,1),C(−1,−1) and D(1,−1) such that minimum {PA, PB, PC, PD} ≤1. If the area of the region ‘S’ traced out by moving point P is λ, then which of the following is/are correct? 

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a

λ is an irrational number 

b

λ = 3 (where [.] represents greatest integral function)

c

λ is a rational number 

d

Probability that a randomly chosen point inside square ABCD lies in the region S is sec−1(2)

answer is B, C, D.

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Detailed Solution

Question Image

Required area = 4 area in quadrant 1=4×(π4)=π

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A point P moves inside a square with vertices A(1,1),B(−1,1),C(−1,−1) and D(1,−1) such that minimum {PA, PB, PC, PD} ≤1. If the area of the region ‘S’ traced out by moving point P is λ, then which of the following is/are correct?