Question

The term independent of $x$ in ${\left[\sqrt{\frac{x}{3}}+\sqrt{\left(\frac{3}{2x^2}\right)}\right]}^{10}$ is

• A. $1$
• B. $\frac{5}{12}$
• C. ${}^{10}{C}_1$
• D. none

Answer 1

The correct option is D none

Writing the general term, we get
$T_{r+1}={}^{10}{C}_r{x}^{5-\frac{3r}{2}}{.3}^{r-5}{.2}^{-\frac{r}{2}}$
For term independent of x,
$5-\frac{3r}{2}=0$
Or
$r=\frac{10}{3}$
Hence $r$ is not a positive integer.
Hence there is no term independent of x.