Question

Constant term in the expansion of ${(x-\frac{1}{x})}^{10}$ is

• A. 152
• B. -152
• C. -252
• D. 252

Answer 1

The correct option is C

-252

Suppose (r+1)th term is the constant term in the given expansion.

Then, we have:

$T_{r+1}={}^{10}{C}_r(x{)}^{10-r}{\left(\frac{-1}{x}\right)}^r$

$={}^{10}{C}_r(-1{)}^r{x}^{10-r-r}$

For this term to be constant, we must have:

10-2r=0

$\therefore$ Required term $=-{}^{10}{C}_5=-252$