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If the coefficient of $x^2$ and $x^3$ in the expansion of $(3+ax)^9$ are same, then the value of $a$ is ?

$\begin{array}{1 1} \frac{3}{7} \\ \frac{7}{3} \\ \frac{9}{7} \\ \frac{7}{9} \end{array}$

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General term in the expansion $(3+ax)^9$ is $^9C_r3^{9-r}.(ax)^r$
For coeff. of $x^2,\:\: r=2$ and for coeff. of $x^3,\:\: r=3$
$\therefore\:$coeff. of $x^2=^9C_2.3^7.a^2$ and
coeff. of $x^3=^9C_3.3^6.a^3$
Given: $^9C_2.3^7.a^2= ^9C_3.3^6.a^3$
$\Rightarrow\:36\times 3=84\times a$
answered Sep 24, 2013 by rvidyagovindarajan_1

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