A ratio of the 5th term from the beginning to the , 5th term from the end in the binomial expansion of 21/3+12(3)1/310is

A
$4 (36)^{1 / 3} : 1$
B
$1 : 2 (6)^{1 / 3}$
C
$2 (36)^{1 / 3} : 1$
D
$1 : 4 (16)^{1 / 3}$

Solution:

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

$= \frac{^{10} C_{4} {(2^{1 / 3})}^{10 - 4} {(\frac{1}{2 (3)^{1 / 3}})}^{4}}{^{10} C_{4} {(\frac{1}{2 (3)^{1 / 3}})}^{10 - 4} {(2^{1 / 3})}^{4}} \Rightarrow Ratio = {(2^{1 / 3})}^{2} {(2 (3)^{1 / 3})}^{2} \Rightarrow Ratio = \frac{4 \cdot (36)^{1 / 3}}{1}$

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

Solution:

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