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  4. A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of (2(1/3) + (1/2(3)(1)3))10 is :

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

JEE MainJEE Main 2019Binomial Theorem

Solution:

$\frac{T_{5}}{T_{5}^{1}} = \frac{^{10}C_{4}\left(2^{1/3}\right)^{10-4} \left( \frac{1}{2\left(3\right)^{1/3}}\right)^{4}}{^{10}C_{4} \left(\frac{1}{2\left(3\right)^{1/3}}\right)^{10-4}\left(2^{1/3}\right)^{4}} = 4.\left(36\right)^{1/3} $