Question

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

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

Answer 1

Answer: (D)

None of these

$T_{r+1}{=}^{10}{C}_r{\left(\frac{x}{3}\right)}^{\frac{10-r}{2}}{\left(\frac{3}{2x^2}\right)}^{\frac{r}{2}}$

${=}^{10}{C}_r{x}^{\frac{10-r}{2}-r}{\left(\frac{1}{2}\right)}^{\frac{r}{2}}{3}^{r-5}$ Put $\frac{10-r}{2}-r=0$

$\Rightarrow r=\frac{10}{3}\text{/}ϵ$ whole number

$\therefore$ No choice match

$\therefore$ (d) is correct answer.