Q75 / 160 · WBJEE 2009 · Mathematics
If the co-efficients of $x^2$ and $x^3$ in the expansion of $(3+a x)^9$ be same, then the value of ' $a$ ' is
- A$\frac{3}{7}$
- B$\frac{7}{3}$
- C$\frac{7}{9}$
- Correct answerD$\frac{9}{7}$
Solution
$$
\begin{aligned}
& \text { Hints : }(3+a x)^9={ }^9 \mathrm{C}_0 3^9+{ }^9 \mathrm{C}_1 3^8(a x)+{ }^9 \mathrm{C}_2 37(a x)^2+{ }^9 \mathrm{C}_3 3{ }^6(a x)^3 \\
& { }^9 \mathrm{C}_2 3^7 a^2={ }^9 \mathrm{C}_3 3{ }^6 \mathrm{a}^3 \\
& \frac{9}{7}=a
\end{aligned}
$$
Hence, the correct answer is option: 'D'.