Question

The coefficient of $x^{-3}$ in the expansion of ${(x-\frac{m}{x})}^{11}$ is

• A. $-924m^7$
• B. $-792m^5$
• C. $-792m^6$
• D. $-330m^7$

Answer 1

The correct option is C

$-792m^6$

Let $x^{-3}$ occur at (r+1)th term in the given expansion.

Then, we have:

$T_{r+1}={}^{11}{C}_r{x}^{11-r}{\left(\frac{-m}{x}\right)}^r$

$=(-1{)}^r\times {}^{11}{C}_r{m}^r{x}^{11-r-r}$

For this term to contain $x^{-3}$, we must have:

11-2r =-3

$\Rightarrow r=7$

$\therefore$ Required coefficient

$=(-1{)}^7{}^{11}{C}_7{m}^7$

$=-\frac{11\times 10\times 9\times 8}{4\times 3\times 2}{m}^7$

$=-330m^7$