Question

The sum of rational terms in $(\sqrt{2}+\sqrt[3]{3}+\sqrt[6]{5}{)}^{10}$ is

• A. 12632
• B. 1260
• C. 126
• D. 1262

Answer 1

Answer: (A)

General term $=\frac{10!}{\alpha !\beta !\gamma !}{2}^{\alpha /2}{3}^{\alpha /3}{5}^{\gamma /6}$
For rational terms
$\alpha =0,2,4,6,8,10$
$\beta =0,3,6$
$\gamma =0,6$
Hence, possible sets $=(4,6,0),(4,0,6),(10,0,0)$
Hence, there are $3$ rational terms.
$\therefore$ Required sum $=\frac{10!}{4!6!}{2}^2{3}^2+\frac{10!}{4!6!}{2}^{2}5+\frac{10!}{10!}{2}^5$
$=12632$