JEE Mains · Maths · STD 11 - 1. set theory
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 \(2^{100} -1\)
- B \(2^{50} (2^{50} -1)\)
- C \(2^{50} -1\)
- D \(2^{50} + 1\)
Answer & Solution
Correct Answer
(B) \(2^{50} (2^{50} -1)\)
Step-by-step Solution
Detailed explanation
Product is even when atleast one element of subset is even Hence required number of subsets = total subsets -number of subsets all whose elements are odd \(= 2^{100} - 2^{50}\)
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