# If the expansion of $(x^2+\large\frac{2}{x})^n$ for positive integer n has $13^{th}$ term independent of $x$ then n is

$\begin{array}{1 1}(A)\;16\\(B)\;18\\(C)\;20\\(D)\;\text{None of these}\end{array}$

Toolbox:
• $T_{r+1}=nC_r a^{n-r}b^r$
$T_{13}=T_{12+1}=nC_{12}(x^2)^{n-12}(\large\frac{2}{x})^{12}$
$\Rightarrow nC_{12} 2^{12} x^{2n-36}$
The term independent of $x$
$2n-36=0$
(i.e) $2n=36$
$n=18$
Hence (B) is the correct answer.