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  4. In the expansion of (3 x+(1/x))13 coefficient of x7 is-

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Q. In the expansion of $\left(3 x+\frac{1}{x}\right)^{13}$ coefficient of $x^7$ is-

Binomial Theorem

Solution:

$T_{r+1}={ }^{13} C_r(3 x)^{13-x}\left(\frac{1}{x}\right)^r={ }^{13} C_r 3^{13-r} x^{-2 r}$
Put $r=3$
$\Rightarrow $ coefficient of $ x^7 \text { is }={ }^{13} C_3(3)^{10}$