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If the coefficients of x^2a n d\ x^3 in ...

If the coefficients of `x^2a n d\ x^3` in the expansion of `(3+a x)^9`are the same, then the value of `a` is

A

`-7/9`

B

`-9/7`

C

`7/9`

D

`9/7`

Text Solution

Verified by Experts

The correct Answer is:
D
Coefficients of `x^{2}=` Coefficients of `x^{3}`
`\ ^{9} C_{2} times 3^{9-2} a^{2}=\ ^{9} C_{3} times 3^{9-3} a^{3} `
`Rightarrow a=frac{\ ^{9} C_{2}}{\ ^{9} C_{3}} times 3 `
`=frac{9 ! times 3 ! times 6 ! times 3}{2 ! times 7 ! times 9 !} `
...
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