Question

The number of irrational terms in the expansion of $(\sqrt[8]{85}+\sqrt[6]{62}{)}^{100}$ is

• A. $97$
• B. $98$
• C. $96$
• D. $99$

Answer 1

Answer: (A)

$97$

$T_{r+1}={}^{100}{C}_r{5}^{\left(\frac{100-r}{8}\right)}{2}^{\left(\frac{r}{6}\right)}$
For rational terms, $100-r$ should be a multiple of $8$ and $r$ should be a multiple of $6$

Hence we get rational terms for
$r=12,36,60$ and $84$
Hence there will be $4$ rational terms.
Therefore, total number of irrational terms will be
$101-4$
$=97$ terms.