Question:
Constant term in the expansion of $\left(x-\frac{1}{x}\right)^{10}$ is
(a) 152
(b) −152
(c) −252
(d) 252
Solution:
(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:
$10-2 r=0$
$\Rightarrow r=5$
$\therefore$ Required term $=-{ }^{10} C_{5}=-252$