Question

In the expansion of ( $\frac{a}{x}+bx{)}^{12}$, the coefficient of $x^{-10}$ will be

• A. $12a^{11}$
• B. $12b^{11}a$
• C. $12a^{11}b$
• D. $12a^{11}{b}^{11}$

Answer 1

The correct option is C

$12a^{11}b$

$T_{r+1}={12}_{c_r}{\left(\frac{a}{x}\right)}^{12-r}{\left(bx\right)}^r={12}_{c_r}.a^{12-r}.b^r.x^{2r-12}\therefore 2x-12=-10\Rightarrow r=1\therefore \text{coefficient}=12.a^{11}.b$