Question

The number of terms in the expansion of $ (\sqrt{5}+\sqrt[4]{11})^{124} $ which are integers, is equal to

• A. 0
• B. 30
• C. 31
• D. 32

Answer 1

Answer: (D)

The general term in the expansion of $(\sqrt{5}+4 \sqrt{11})^{124}$ is
$T_{r+1}={ }^{124} C_{r}(\sqrt{5})^{124-r}(\sqrt[4]{11})^{r}$
$={ }^{124} C_{r} \cdot 5^{(124-r) / 2} \cdot 11^{r / 4}$
For integer terms $r=0,4,8,12, \ldots, 124$
$\therefore $ Number of terms which are integers $=32$