# If the seventh terms from the beginning and the end in the expansion of $\big(\sqrt[3]{2} +\large\frac{1}{\sqrt[3]{3}} \big)^n$ are equal then n equals _____

$\begin{array}{1 1}(A)\;10\\(B)\;12\\(C)\;14\\(D)\;18\end{array}$

Toolbox:
• $T_{r+1}=nC_r a^{n-r} b^r$
Seventh term from the beginning =Seventh term from the end
$T_7=T_{n-7+2}$
$nC_6(2^{1/3})^{n-6}.(\large\frac{1}{3^{1/3}})^6$$=nC_{n-6}(2^{1/3})^6(\large\frac{1}{3^{1/3}})^{n-6}$
$\Rightarrow (2^{1/3})^{n-12}=(\large\frac{1}{3^{1/3}})^{n-12}$
When n-12=0
$n=12$
Hence (B) is the correct answer.