Question

Find the coefficient of $x^6$ in the expansion of ${(2x^2-\frac{3}{x})}^{11}$:

• A. $42$
• B. $59$
• C. $44$
• D. $0$

Answer 1

The correct option is D $0$

$T_{r+1}{=}^{11}{C}_r(2x^2{)}^{11-r}{\frac{(-3)}{\left(x\right)}}^r$

${=}^{11}{C}_r{x}^{22-2r}{2}^{11-r}{(-3)}^r$

As coefficient of $x$ is $6$

$⟹22-3r=6$

$r=\frac{16}{3}$ which is not possible.

Therefore , coefficient is $0$