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Question

The coefficient of x13 in (1x)5(1+x+x2+x3)4 is

A
4
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B
4
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C
0
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D
2
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Solution

The correct option is A 4
(1x)5(1+x+x2(1+x))4
=(1x)5(1+x)4(1+x2)4
=(1x)(1x2)4(1+x2)4
=(1x)(1x4)4=(1x4)4x(1x4)4
For x13,(1x4)4 would have no terms (even power)
In second term, general term is
x×4Cr(x4)r
r=3
coefficient =4C3(1)3=4C3=4
(A)

1124069_1204047_ans_cfb05c87ac344bccbbc6247b53055398.jpg

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