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Question
If the coefficients of x2 and x3 in the expansion of (3 + ax)9 are the same, then the value of a is
Options
\[- \frac{7}{9}\]
\[- \frac{9}{7}\]
\[\frac{7}{9}\]
\[\frac{9}{7}\]
Solution
\[\frac{9}{7}\]
Coefficients of x2 = Coefficients of x3
\[^{9}{}{C}_2 \times 3^{9 - 2} a^2 = ^{9}{}{C}_3 \times 3^{9 - 3} a^3 \]
\[ \Rightarrow a = \frac{^{9}{}{C}_2}{^{9}{}{C}_3} \times 3\]
\[ = \frac{9! \times 3! \times 6! \times 3}{2! \times 7! \times 9!}\]
\[ = \frac{9}{7}\]
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