Class JEE Mathematics Sets, Relations, and Functions Q #1063
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4 Marks 2019 JEE Main 2019 (Online) 12th January Morning Slot MCQ SINGLE
Let $S = {1, 2, 3, … , 100}$. The number of non-empty subsets A of S such that the product of elements in A is even is :
(A) $2^{50} – 1$
(B) $2^{50} (2^{50} – 1)$
(C) $2^{100} – 1$
(D) $2^{50} + 1$
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Correct Answer: B
Explanation
Let $S = {1, 2, 3, ..., 100}$. The total number of non-empty subsets is $2^{100} - 1$. The number of subsets with an odd product consists only of odd numbers. There are 50 odd numbers in the set $S$. So, the number of such subsets is $2^{50} - 1$. Therefore, the number of subsets with an even product is $(2^{100} - 1) - (2^{50} - 1) = 2^{100} - 2^{50} = 2^{50}(2^{50} - 1)$.

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