JEE Main 12 Jan 2019 Morning Question 13
Question: 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 [JEE Main Online Paper Held On 12-Jan-2019 Morning]
Options:
A) $ 2^{50}(2^{50}-1) $
B) $ 2^{50}-1 $
C) $ 2^{50}+1 $
D) $ 2^{100}-1 $
Show Answer
Answer:
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) $
