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Question

The coefficient of 1x in the expansion of (1+x)n(1+1x)n is


Your Answer
A
n!(n1)!(n+1)!
Correct Answer
B
(2n)!(n1)!(n+1)!
Your Answer
C
(2n)!(2n1)!(2n+1)!
Your Answer
D
2n!(n2)!(n+2)!

Solution

The correct option is B (2n)!(n1)!(n+1)!
Coefficient of x1 in (1+x)n(1+1x)n
=  Coefficient of x1 in xn(1+x)2n
=  Coefficient of xn1 in (1+x)2n
Now as we know that coefficient of xr in expansion of (1+x)n is nCr
Hence required coefficient is 
= 2nCn1
=(2n)!(n1)!(n+1)!

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