jee-main 2019 Q63

jee-main · India · session1_12jan_shift1 Combinations & Selection Subset Counting with Set-Theoretic Conditions

Let $S = \{ 1,2,3 , \ldots , 100 \}$, then number of non-empty subsets $A$ of $S$ such that the product of elements in $A$ is even is :
(1) $2 ^ { 100 } - 1$
(2) $2 ^ { 50 } + 1$
(3) $2 ^ { 50 } \left( 2 ^ { 50 } - 1 \right)$
(4) $2 ^ { 50 } - 1$

Let $S = \{ 1,2,3 , \ldots , 100 \}$, then number of non-empty subsets $A$ of $S$ such that the product of elements in $A$ is even is :\\
(1) $2 ^ { 100 } - 1$\\
(2) $2 ^ { 50 } + 1$\\
(3) $2 ^ { 50 } \left( 2 ^ { 50 } - 1 \right)$\\
(4) $2 ^ { 50 } - 1$

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