Question

Find the coefficient of $x^{-7}$ in the expansion of ${(ax-\frac{1}{b{x}^2})}^{11}$

• A. ${{}^{11}C}_5$
• B. ${{}^{10}C}_4$
• C. ${{}^{11}C}_4$
• D. ${{}^{10}C}_5$

Answer 1

Answer: (A)

${{}^{11}C}_5$

The expansion of${(ax-\frac{1}{b{x}^2})}^{11}$

The general term is: $T_{r+1}={{}^{11}C}_r{\left(ax\right)}^{11-r}{(-\frac{1}{b{x}^2})}^r={(-1)}^r{{}^{11}C}_r.\frac{a^{11-r}}{b^r}.x^{11-3r}$

Substituting $11-3r=-7\therefore 3r=18\Rightarrow r=6\therefore T_7={(-1)}^6.{{}^{11}C}_6\frac{a^5}{b^6}.x^{-7}$

hence answer is${{}^{11}C}_5$