JEE Main 12 Jan 2019 Morning Question 28

Question: A ratio of the $ 5^{th} $ term from the beginning to the $ 5^{th} $ term from the end in the binomial is expansion of $ {{( {2^{1/3}}+\frac{1}{2{{(3)}^{1/3}}} )}^{10}} $ is [JEE Main Online Paper Held On 12-Jan-2019 Morning]

Options:

A) $ 4{{(36)}^{1/3}}:1 $

B) $ 1:2{{(6)}^{1/3}} $

C) $ 2{{(36)}^{1/3}}:1 $

D) $ 1:4{{(16)}^{1/3}} $

Show Answer

Answer:

Correct Answer: A

Solution:

  • In the expansion $ {{( {2^{1/3}}+\frac{1}{2{{(3)}^{1/3}}} )}^{10}} $ the ratio of $ 5^{th} $ term from the beginning to the $ 5^{th} $ term from the end = $ \frac{^{10}C _4{{({2^{1/3}})}^{10-4}}{{( \frac{1}{2{{(3)}^{1/3}}} )}^{4}}}{^{10}C _4{{( \frac{1}{2{{(3)}^{1/3}}} )}^{10-4}}{{({2^{1/3}})}^{4}}}=\frac{4.{{(36)}^{1/3}}}{1} $