Coefficient of x^(11) in the expansion o...

Coefficient of `x^(11)` in the expansion of `(1+x^2)(1+x^3)^7(1+x^4)^(12)` is 1051 b. 1106 c. 1113 d. 1120

A

1051

B

1106

C

1113

D

1120

Text Solution

Verified by Experts

The correct Answer is:

C

We have,
`(1 + x^(2))^(4) (1 +x^(3))^(7) (1 + x^(4))^(12)`
`=(""^(4)C_(0) + ""^(4)C_(1)x^(2) + ""^(4)C_(2)x^(6) +""^(4)C_(4) x^(8))`
`xx(""^(7)C_(0) + ""^(7)C_(1)x^(3) + ""^(7)C_(2)x^(6) +""^(7)C_(4) x^(9)+....)`
`xx (""^(12)C_(0) + ""^(12)C_(1) x^(4) + ""^(12)C_(2) x^(8) +....)`
`therefore ` Cefficient of `x^(11) = ""^(4)C_(0) + ""^(7)C_(1) +""^(12)C_(2) +""^(4)C_(1) xx""^(12)C_(0)`
+ ""^(4)C_(2) xx ""^(7)C_(1) xx""^(12)C_(1) +""^(4)C_(4) xx""^(7)C_(1)xx""^(12)C_(0)`
`= 462 + 140 + 504 + 7 = 1113`.

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