Question

A set contains $2n+1$ elements .The number of subsets of this set containing more than $n$ elements is equal to?

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

Answer 1

The correct option is D

$2^{2n}$

Explanation for the correct option:

Find the number of subset:

Let the number of subset be $N$

Number of subsets $={}^{2n+1}C_0+{}^{2n+1}C_1+{}^{2n+1}C_2+....+{}^{2n+1}C_n$

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

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

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

$\Rightarrow$ $N={\mathbf{2}}^{\mathbf{2}\mathbf{n}}$

Hence, Option ‘D’ is Correct.