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Question

nr=0r2.(nCr)2 is equal to

A
n2 . 2n2Cn1
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B
n2 . 2nCn
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C
n2 . 2n1(r=1n1 (2r1))(n1)!
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D
2n (nr=1(2r1))n!
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Solution

The correct option is C n2 . 2n1(r=1n1 (2r1))(n1)!
nr=0 r2.(nCr)2=n2 nr=1(n1Cr1)2

=n2×co-efficeint of xn1 in (1x)2n2
=n2 2n2Cn1

n2.(2n2)!((n1)!)2=n2.(n1)!.2n1.(n1r=0(2r1))((n1)!)2

=n2.2n1.(n1r=0(2r1))(n1)!.

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