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 :

Question:

Let $S=\{1,2,3, \ldots, 100\}$. The number of non-empty subsets A of $S$ such that the product of elements in $A$ is even is :

  1. $2^{100}-1$

  2. $2^{50}\left(2^{50}-1\right)$

  3. $2^{50}-1$

  4. $2^{50}+1$

Correct Option: 2

JEE Main Previous Year 1 Question of JEE Main from Mathematics Sets and Relations chapter.
JEE Main Previous Year Jan. 12, 2019 (I)

Solution:

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