Question

If the coefficient of $x^{7}in{(a{x}^2-\frac{1}{bx})}^{11}$ is equal to the coefficient of $x^{-7}in{(ax-\frac{1}{b{x}^2})}^{11}$ then ab =

• A. 0
• B. 1
• C. -1
• D. 2

Answer 1

The correct option is C

-1

For the Coefficient of $x^{7}in{(a{x}^2-\frac{1}{bx})}^{11};r=\frac{22-7}{3}=\frac{15}{3}=5$

$\therefore Coefficientof{x}^{7}is{-}^{11}{C}_5{a}^6\frac{1}{b^5}$

For the coefficient of $x^{7}in{(ax-\frac{1}{b{x}^2})}^{11};r=\frac{11+7}{3}=6\therefore Coefficientof{x}^{-7}is{}^{11}{C}_6{a}^5\frac{1}{b^6}$

The coefficient are equal $\Rightarrow {-}^{11}{C}_5\frac{a^6}{b^5}{=}^{11}{C}_6\frac{a^5}{b^6}\Rightarrow ab=-1$