Question

The number of integral terms in the expansion of ${(\sqrt{3}+\sqrt[5]{55})}^{256}$ is

• A. $25$
• B. $26$
• C. $24$
• D. None of these

Answer 1

Answer: (B)

$26$

Total number of integral terms will be
$\frac{256}{L.C.M(2,5)}+1$
$=\frac{256}{10}+1$
$=25.6+1$
However $25.6$ is not an integer, hence take $\left[25.6\right]=25$ where $\left[x\right]$ is the greatest integer function.
Hence total number of integral term, will be
$25+1$
$=26$