Question

The sum of the rational terms in the binomial expansion of ${\left(2^{\frac{1}{2}}+3^{\frac{1}{5}}\right)}^{10}$ is :

• A. 25
• B. 32
• C. 9
• D. 41

Answer 1

Answer: (D)

${\left(2^{1/2}+3^{1/5}\right)}^{10}{=}^{10}{C}_0{\left(2^{1/2}\right)}^{10}{+}^{10}{C}_1{\left(2^{1/2}\right)}^9\left(3^{1/5}\right)+.....{+}^{10}{C}_{10}{\left(3^{1/5}\right)}^{10}$
There are only two rational terms - first term and last term.
Now sum of two rational terms
$={\left(2\right)}^5+{\left(3\right)}^2$
= 32 + 9 = 41