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Question

nC0+nC2+nC4++nC2[n/2], where [ ] denotes greatest integer

A
22n1
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B
22n11
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C
2n1
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D
2n11
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Solution

The correct option is C 2n1
The real sol. is taking a binomial = (1+x)n=nC0+nC1x+nC2x2+......
and now taking (1x)n=nC0nC1x+nC2x2......
Now adding both and putting x=1, we get 2n=2(nC0+nC2+nC4+....)
=> 2n1 = required expression

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