Question

If the coefficient of $x^7$ in the expression of ${(a{x}^2+\frac{1}{bx})}^{11}$ is equal to the coefficient of $x^{-7}$ in the expansion of ${(ax-\frac{2}{b{x}^2})}^{11}$, then the relation between $a$ and $b$ is

• A. $ab=64$
• B. $ab=8$
• C. $ab=2$
• D. None of these

Answer 1

The correct option is A $ab=64$

$(a{x}^2+\frac{1}{b^n}{)}^{11}$

coefficient of $x^7$

let nth term

$(a{x}^2{)}^{11-n}\times (\frac{1}{bc}{)}^n$

$=\frac{x^{22-2n}}{x^n}$

$=x^{23-3n}$

$22-3n=7$

$22-7=3n$

$n=\frac{15}{3}=5$

for $(ax-\frac{2}{b{x}^2}{)}^{11}$

mth term.

$(ax{)}^{11-m}\times (-\frac{2}{b{x}^2}{)}^m$

$11-m-2m=-7$

$11+7=3m$

$m=6$