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Find the coefficient of x^7 in the expan...

Find the coefficient of `x^7` in the expansion of `(1 - x -x^2 + x^3)^(6)dot`

A

132

B

144

C

-132

D

-144

Text Solution

Verified by Experts

The correct Answer is:
D
`(1-x-x^(2)+x^(3))^(6)`
` = (1-x)^(6)(1-x^(2))^(6)`
`= (1-.^(6)C_(1)x+.^(6)C_(2)x-.^(6)C_(3)x^(3)+.^(6)C_(4)x^(4)-.^(6)C_(5)x^(5)+.^(6)C_(6)x^(6))(1-.^(6)C_(1)x^(2)+.^(6)C_(2)x^(4)-.^(6)C_(3)x^(6)+"…..")`
`rArr ` coefficient of `x^7)` is `.^(6)C_(1)..^(6)C_(3)-.^(6)C_(3)+.^(6)C_(5)..^(6)C_(1)`
`= 6 xx 20 - 20 xx 15 + 6 xx 6 = -144`
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