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Question

The value of nC0nC2+nC1nC3+nC2nC4+....+nCn−2nCn is equal to

A
2nCn2
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B
2nCn+1
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C
2nCn1
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D
None of these
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Solution

The correct option is A 2nCn2
(1+x)n.(1+x)n=(nC0+nC1x+nC2.x2................+nCn1.xn1+nCn.xn).(nCn+nCn1x+nCn2.x2................+nC2.xn2+nC1.xn1+nC0.xn)
Now if we multiply we get
(.............+xn2(nC0.nC2+nC1.nC3+..................+nCn2.nCn...........................) = coefficient of xn2 in expansion of (1+x)2n = 2nCn2
nC0nC2+nC1nC3+nC2nC4+....+nCn−2nCn


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