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Question

The coefficient of xn in the expansion of (1x)ex is

A
1n!
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B
1(n+1)!
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C
1nn!
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D
n1n!
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Solution

The correct option is C 1nn!
(1x)ex=exxex=[1+x1!+x22!+]x[1+x1!+x22!+]
Coefficient of xn will be
=1n!1(n1)!=1n×(n1)!1(n1)!=1nn!

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