Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$T_{r+1}={}^{10}{C}_r{\left(\sqrt{\frac{x}{3}}\right)}^{10-r}{\left(\sqrt{\frac{3}{2x^2}}\right)}^r={}^{10}{C}_r{\left(\frac{1}{\sqrt{3}}\right)}^{10-r}{\left(\sqrt{\frac{3}{2}}\right)}^r{x}^{5-\frac{r}{2}-r}Let{T}_{r+1}bethetermindependentofx.\therefore 5-\frac{r}{2}-r=0\Rightarrow \frac{3r}{2}=5\Rightarrow r=\frac{10}{3}\therefore risnotawholenumber.\therefore Givenexpressiondoesnothavetermindependentofx.$