Question

A set contains $(2n+1)$ elements. If the number of subsets of this set which contain atmost $n$ elements is 4096, then the value of n is

• A. 6
• B. 15
• C. 21
• D. 20

Answer 1

The correct option is A 6

Number of subsets of this set which contain atmost $n$ elements is

${}^{(2n+1)}{C_0+}^{(2n+1)}{C_1+}^{(2n+1)}{C}_n=4096$

$\Rightarrow 2^{2n}=4096=2^{12}\Rightarrow n=6$