NIMCET 2009 Question Paper with solutions

Question : 40 of 120

Marks: +1, -0

A set contains

(2 n+1)

elements. If the number of subsets which contain at most

n

elements is 4096 , then the value of

n

Solution:

The number of required subsets

= ^{2 n+2} C_{0}+ ^{2 a+2} C_{1}+. . .+ ^{2 n+1} C_{n}

=\;{1}/{2}[2^{2 n+1} ]=2^{2 n}=4^{n}

But

4^{n}=4096=4^{6}

⇒ n=6

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