A) \[4{{(36)}^{1/3}}:1\]
B) \[1:2{{(6)}^{1/3}}\]
C) \[2{{(36)}^{1/3}}:1\]
D) \[1:4{{(16)}^{1/3}}\]
Correct Answer: A
Solution :
In the expansion\[{{\left( {{2}^{1/3}}+\frac{1}{2{{(3)}^{1/3}}} \right)}^{10}}\]the ratio of \[{{5}^{th}}\] term from the beginning to the \[{{5}^{th}}\] term from the end =\[\frac{^{10}{{C}_{4}}{{({{2}^{1/3}})}^{10-4}}{{\left( \frac{1}{2{{(3)}^{1/3}}} \right)}^{4}}}{^{10}{{C}_{4}}{{\left( \frac{1}{2{{(3)}^{1/3}}} \right)}^{10-4}}{{({{2}^{1/3}})}^{4}}}=\frac{4.{{(36)}^{1/3}}}{1}\]
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