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} $
