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If the coefficient of $x^{2} & x^{3}$ in the expansion of $(3 + a x)^{9}$ are same, then the value of $\frac{7 a}{3}$ is

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$2$

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answer is B.

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Detailed Solution

$T_{r + 1} = {}^{9}C_{r} 3^{9 - r} (ax)^{r}$

Coefficient of $x^{2} = {}^{9}C_{2} 3^{7} a^{2} = coefficient of x^{3} = {}^{9}C_{3} \cdot 3^{6} a^{3}$

$\frac{9 \times 8}{2} \times 3 = \frac{9 \times 8 \times 7}{6} \times a$

$∴ 7 a = 9 \Rightarrow \frac{7 a}{3} = 3$

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