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# Find the term independent of $x,x\neq 0$ in the expansion of $\big(\large\frac{3x^2}{2}-\frac{1}{3x})^{15}$

$\begin{array}{1 1}(A)\;14C_{10}(\large\frac{1}{6})^5\\(B)\;15C_{10}(\large\frac{1}{6})^5\\(C)\;5C_4(\large\frac{1}{6})^4\\(D)\;14C_{10}(\large\frac{1}{4})^5\end{array}$

Toolbox:
• $T_{r+1}=nC_ra^{n-r}b^r$
Given :
$\big(\large\frac{3x^2}{2}-\frac{1}{3x})^{15}$
$T_{r+1}=15C_r(\large\frac{3x^2}{2})^{15-r}(\large\frac{1}{3x})^r$
$\Rightarrow 15C_r(\large\frac{3}{2})^{15-r}(x)^{30-2r}.(\large\frac{1}{3})^r.(\large\frac{1}{x})^r$