Question

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

• A. $T_3$
• B. $T_4$
• C. $T_5$
• D. None of these

Answer 1

The correct option is B

$T_4$

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

Thus, we have:

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

$=(-1{)}^2{}^9{C}_r{x}^{9-r}{x}^{9-r-2r}$

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

9-3r=0

$\therefore r=3$

Hence, the required term is the 4th term i.e. $T_4.$