Question

Find the term independent of $x$ in the expansion of ${(\sqrt{\frac{x}{3}}+\frac{3}{2x^2})}^{10}$

• A. $T_3$
• B. $T_4$
• C. $T_5$
• D. No term will be independent of x

Answer 1

The correct option is A $T_3$

For the above question $(\sqrt{\frac{x}{3}}+\frac{3}{2x^2}{)}^{10}$
$T_{r+1}={}^{10}{C}_r{x}^{5-\frac{r}{2}-2r}{3}^{\frac{r}{2}-5+r}{2}^{-r}$
For term independent of x
$5-\frac{r}{2}-2r=0$
$10-5r=0$
$r=2$
$T_3={}^{10}{C}_2{3}^{-2}{2}^{-2}$
$=\frac{45}{9\left(4\right)}$
$=\frac{5}{4}$