JEE 2023 — Mathematics PYQ

Given ${\left(x^4-\frac{1}{x^3}\right)}^{15}$

${\mathrm{T}}_{r+1}{=}^{15}{\mathrm{C}}_r{\left(x^4\right)}^{15-r}{\left(\frac{-1}{x^3}\right)}^r$

$\Rightarrow 60-7r=18$

$\Rightarrow r=6$

Coefficient of $x^{18}{=}^{15}{\mathrm{C}}_6=5005$