Question

The number of rational terms in the binomial expansion of ${\left(4^{\frac{1}{4}}+5^{\frac{1}{6}}\right)}^{120}$ is ______

Answer 1

Answer: 21

${\left(4^{\frac{1}{4}}+5^{\frac{1}{6}}\right)}^{120}$
$T_{r+1}={}^{120}{C}_r{\left(2^{1/2}\right)}^{120-r}(5{)}^{r/6}$
for rational terms $r=6\lambda 0\le r\le 120$
so total no of forms are $21$ .