Question:
A ratio of the $5^{\text {th }}$ term from the beginning to the $5^{\text {th }}$ term from the end in the binomial
expansion of $\left(2^{1 / 3}+\frac{1}{2(3)^{1 / 3}}\right)^{10}$ is :
Correct Option: , 4
Solution:
$\frac{\mathrm{T}_{5}}{\mathrm{~T}_{5}^{1}}=\frac{{ }^{10} \mathrm{C}_{4}\left(2^{1 / 3}\right)^{10-4}\left(\frac{1}{2(3)^{1 / 3}}\right)^{4}}{{ }^{10} \mathrm{C}_{4}\left(\frac{1}{2\left(3^{1 / 3}\right)}\right)^{10-4}\left(2^{1 / 3}\right)^{4}}=4 \cdot(36)^{1 / 3}$