Question

If the coefficient of $x^7$ in ${[a{x}^2+\left(\frac{1}{bx}\right)]}^{11}$ equals the coefficient of $x^{-7}$ in ${[a{x}^2-\left(\frac{1}{bx}\right)]}^{11}$, then 'a' and 'b' satisfy the relation

• A. a - b =1
• B. a +b =1
• C. a/b = 1
• D. ab = 1

Answer 1

The correct option is D

ab = 1

Coefficient of $x^7$ in ${(a{x}^2+\frac{1}{bx})}^{11}$ is ${}^{11}{C}_5$$a^6$ $\frac{1}{b^5}$

Coefficient of $x^{-7}$ in ${[a{x}^2-\left(\frac{1}{bx}\right)]}^{11}$ is ${}^{11}{C}_6$$a^5$ $\frac{1}{b^6}$

${}^{11}{C}_6$$a^5$ $\frac{1}{b^6}$ = ${}^{11}{C}_5$$a^6$ - $\frac{1}{b^5}$ ⇒ ab = $\frac{{}^{11}{C}_6}{{}^{11}{C}_5}$ = $\frac{6}{6}$ = 1