A) \[{{2}^{50}}({{2}^{50}}-1)\]
B) \[{{2}^{50}}-1\]
C) \[{{2}^{50}}+1\]
D) \[{{2}^{100}}-1\]
Correct Answer: A
Solution :
Here, S = {1, 2, 3, ..... 100} So, the number of non-empty subsets A of S such that the product of elements in A is even = Total non empty subsets-subsets with product of element is odd \[={{2}^{100}}-1-[{{2}^{50}}-1]={{2}^{100}}-{{2}^{50}}={{2}^{50}}({{2}^{50}}-1)\]
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