PrepRung
Sign inSign up free

NDA 2020 Maths · Mathematics · Sets, Relations and Functions · medium

A set has 64 subsets. How many of its subsets contain an odd number of elements?

Single correct option

A set has 64 subsets. How many of its subsets contain an odd number of elements?
  1. A. 31
  2. B. 63
  3. C. 32
  4. D. 16
Show answer and solution

Answer: (C) 32

2n=642^n=64 gives n=6n=6. Subsets with an odd number of elements equal those with an even number, each being 2n−1=322^{n-1}=32, because ∑(6r)(−1)r=0\sum\binom{6}{r}(-1)^r=0. The 63 counts all non-empty subsets, and 31 would be 25−12^5-1.
Report a mistake

Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake