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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
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Verified Answer
The correct answer is:
$\frac{9}{7}$
$$
\begin{aligned}
& \text { Hints : }(3+a x)^9={ }^9 \mathrm{C}_0 3^9+{ }^9 \mathrm{C}_1 3^8(a x)+{ }^9 \mathrm{C}_2 37(a x)^2+{ }^9 \mathrm{C}_3 3{ }^6(a x)^3 \\
& { }^9 \mathrm{C}_2 3^7 a^2={ }^9 \mathrm{C}_3 3{ }^6 \mathrm{a}^3 \\
& \frac{9}{7}=a
\end{aligned}
$$
\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}
$$
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