# In the expansion of

Question:

In the expansion of $\left(x-\frac{1}{3 x^{2}}\right)^{9}$, the term independent of $x$ is

(a) T3

(b) T4

(c) T5

(d) none of these

Solution:

(b) $T_{4}$

Suppose $T_{\mathrm{r}+1}$ is the term in the given expression that is independent of $x$.

Thus, we have :

$T_{r+1}={ }^{9} C_{r} x^{9-r}\left(\frac{-1}{3 x^{2}}\right)^{r}$

$=(-1)^{r}{ }^{9} C_{r} \frac{1}{3^{r}} x^{9-r-2 r}$

For this term to be independent of $x$, we must have

$9-3 r=0$

$\Rightarrow r=3$

Hence, the required term is the 4 th term $i . e . T_{4}$