Mathematics - Binomial Theorem Question with Solution | TestHub

In the expansion of ${\left(x^4+\frac{1}{x^3}\right)}^{15}$, let $T_r$ is the $r^{\text{th }}$ term
$\begin{array}{rl}{T}_r& ={}^{15}{C}_{r-1}{\left(x^4\right)}^{15-r+1}{\left(\frac{1}{x^3}\right)}^{r-1}\\ & ={}^{15}{C}_{r-1}{x}^{64-4r-3r+3}=15_{C_{r-1}}{x}^{67-7r}\end{array}$
${\mathrm{x}}^{18}$ occurs in this term
$\Rightarrow 18=67-7r\Rightarrow 7r=49\Rightarrow r=7.$