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

Q: The term independent of x in $\large (\sqrt{\frac{x}{3}} + \sqrt{\frac{3}{2x^2}} )^{10} $ is

(A) 1

(B) 5/12

(C) ¹⁰C₁

(D) None of these

Sol. General term in the expansion is

$\large = 10_{C_r} (\frac{x}{3})^{r/2} (\frac{3}{2x^2})^{\frac{10-r}{2}}$

$\large = 10_{C_r} x^{\frac{3r}{2}-10} . \frac{3^{5-r}}{2^{(10-r)/2}}$

For constant term, 3r/2 = 10  ⇒ r = 20/3

which is not an integer. Therefore, there will be no constant term.

Hence (D) is the correct answer.