Question

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

• A. ${}^{13}{C}_5(3{)}^8$
• B. ${}^{13}{C}_4{3}^9$
• C. ${}^{13}{C}_3{3}^{10}$
• D. ${}^{13}{C}_{10}{3}^3$

Answer 1

Answer: (C)

$T_{r+1}={}^{13}{C}_r(3x{)}^{13-x}{\left(\frac{1}{x}\right)}^r={}^{13}{C}_r{3}^{13-r}{x}^{-2r}$
Put $r=3$
$\Rightarrow$ coefficient of $x^7\text{ is }={}^{13}{C}_3(3{)}^{10}$