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If the coefficient x^(2) and x^(3) in th...

If the coefficient `x^(2) and x^(3)` in the expansion of `(1 + 8x + bx^(2))(1 - 3x)^(9)` in the power of x are equal , then b is :

A

`(54)/(7)`

B

`(27)/(7)`

C

`(108)/(7)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
`(1 + 8x + bx^(2))(1 - 3x)^(9)`
`(1 + 8x + bx^(2)) sum_(r=0)^(9) 9C_(2)(-3x)^(r)`
`therefore` Coefficient of `x^(2) = 9C_(2) .9 - 8. 9C_(1) 3 + b`
`therefore` Coefficient of `x^(3) = - 9C_(3). 27 + 8. 9C_(1) 9 - b. 9C_(1).3`
Both are equal `rArr b = (54)/(7)`
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