Question

A ratio of the $5^{th}$ term from the beginning to the $5^{th}$ term from the end in the binomial expansion of ${(2^{1/3}+\frac{1}{2(3{)}^{1/3}})}^{10}$ is :

• A. $1:4(16{)}^{\frac{1}{3}}$
• B. $1:2(6{)}^{\frac{1}{3}}$
• C. $2(36{)}^{\frac{1}{3}}:1$
• D. $4(36{)}^{\frac{1}{3}}:1$

Answer 1

The correct option is D $4(36{)}^{\frac{1}{3}}:1$

$\frac{T_5}{T_5^1}=\frac{{}^{10}{C}_4{\left(2^{1/3}\right)}^{10-4}{\left(\frac{1}{2(3{)}^{1/3}}\right)}^4}{{}^{10}{C}_4{\left(\frac{1}{2\left(3^{1/3}\right)}\right)}^{10-4}{\left(2^{1/3}\right)}^4}=4.(36{)}^{1/3}$