Question

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

• A. $3/2$
• B. $5/4$
• C. $5/2$
• D. None of these

Answer 1

Answer: (B)

$T_{r+1}={}^{10}{C}_r{\left(\sqrt{\frac{x}{3}}\right)}^{10-r}{\left(\frac{3}{2x^2}\right)}^r$
$\frac{10-r}{2}-2r=0$
$10-r-4r=0$
$r=2$
hence term $={}^{10}{C}_2\times \frac{1}{3^4}\times \frac{3^2}{2^2}=\frac{5}{4}$