Question

The number of integral terms in the expansion$\left(\sqrt{3}+\sqrt[8]{5}\right)^{256}$

• A. 32
• B. 44
• C. 34
• D. 35

Answer 1

Answer: (B)

44

Answer 2

$T _{ r +1}={ }^{256} C _{ r }\left(3^{1 / 2}\right)^{256-6}\left(5^{1 / 8}\right)^{ r }$ It is an integer if $\frac{256- r }{2}$ and $\frac{ r }{8}$ are positive integers. $\therefore 256- r \geq 0$ and $r$ is a multiple of $8 \Rightarrow r$ can be $0,8,16,24, \ldots \ldots \ldots, 8 \times 32$ These are 33 .