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Q.

A positive integer n not exceeding 100 is chosen at random in such a way that, p is the probability of choosing n≤50 and 3p is the probability of choosing n>50. If λ is probability that a perfect square is chosen, then the value of [100λ] ([.] → GIF)

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Detailed Solution

Since the probability is p for choosing n≤50 and 3p for choosing n≥50 , then 50p+50(3p)=1⇒p=0.05⇒50p+150p=1⇒200p=1⇒p=1200=0.05∴ Required probability is 7p+3(3p)=16p=0.08∴ 100λ=8

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