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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
`2x_(1)+3x_(2)+4x_(3)=11`
Possibilites are `(0,1,2),(1,3,0),(2,1,1),(4,1,0)`.
`:.` Required coefficient
`= (.^(4)C_(0)xx.^(7)C_(1)xx.^(12)C_(2))+(.^(4)C_(1)xx.^(7)C_(3)xx.^(12)C_(6))`
`+(.^(4)C_(2)xx.^(7)C_(1)xx .^(12)C_(1)) + (.^(4)C_(4) xx .^(7)C_(1) xx 1)`
`= (1xx7xx66) + (4 xx 35 xx 1) + (6 xx 7 xx 12) + (1xx 7)`
`= 462 + 140 + 504 + 7 = 1113`
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