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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) ""^(9)C_r(-3x)^(r ) `
`:.` Coefficient of ` x^(2) = ""^(9)C_2 . 9-8 . ""^(9)C_1 .3 +b`
` :.` Coefficient of ` x^(3) = -""^(9)C_3. 27 + 8. ""^(9)C_(1) . 9- b. ""^(9)C_1 . 3 `
Both are equal `implies b = (54)/(7)`
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