Question

Which term in the expansion of ${\left(\frac{x}{3}-\frac{2}{x^2}\right)}^{10}$ contains $x^4$?

• A. 1
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (B)

3

The general term is as follows
$T_{r+1}$ $=(-1{)}^r{}^{10}{C}_r{x}^{10-3r}{3}^{10-r}{2}^r$
Hence, for the coefficient of $x^4$
$10-3r=4$
$3r=6$
$r=2$.

So, $r+1=3$rd term