Q. The coefficient of $x^{- 7}$ in the expansion of $\left\lbrack ax - \frac{1}{bx^{2}} \right\rbrack^{11}$ will be
A) $\frac{462a^{6}}{b^{5}}$
B) $\frac{462a^{5}}{b^{6}}$
C) $- \frac{462a^{5}}{b^{6}}$
D) $- \frac{462a^{6}}{b^{5}}$
Explanation
(b)
$General\ term,\ T_{r + 1} = \ ^{11}C_{r}\frac{a^{11 - r}}{b^{r}}({- 1)}^{r}x^{11 - 3r}$
For the coefficient of $x^{- 7},$ put
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 11 - 3r = - 7 \Longrightarrow r = 6$
$\therefore Coefficient\ of\ x^{- 7} = \ ^{11}C_{6}\ \frac{a^{5}}{b^{6}} = \frac{{462a}^{5}}{b^{6}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.