Question

A set contains $(2n+1)$ elements. The number of subsets of the set which contains at most $n$ elements is

• A. $2^n$
• B. $2^{n+1}$
• C. $2^{2n-1}$
• D. $2^{2n}$

Answer 1

The correct option is D $2^{2n}$

Number of subsets$={{}^{2n+1}C}_0+{{}^{2n+1}C}_1+{{}^{2n+1}C}_2+....+{{}^{2n+1}C}_n=N$

$N=2^{2n+1}-N\Rightarrow 2N=2^{2n+1}\Rightarrow N=\frac{2^{2n+1}}{2}=2^{2n}$