JEE PYQ: Permutation And Combination Question 49
Question 49 - 2019 (12 Jan Shift 2)
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) $2^{50}(2^{50} - 1)$
(3) $2^{50} - 1$
(4) $2^{50} + 1$
Show Answer
Answer: (2)
Solution
Total non-empty subsets $= 2^{100} - 1$. Subsets with all odd elements (product odd): 50 odd numbers, $2^{50} - 1$ non-empty subsets. Required $= 2^{100} - 1 - (2^{50} - 1) = 2^{100} - 2^{50} = 2^{50}(2^{50} - 1)$.
BETA
