Question:
The number of rational terms in the binomial expansion of $\left(4^{\frac{1}{4}}+5^{\frac{1}{6}}\right)^{120}$ is
Solution:
$\left(4^{1 / 4}+5^{1 / 6}\right)^{120}$
$\mathrm{T}_{\mathrm{r}+1}={ }^{120} \mathrm{C}_{\mathrm{r}}\left(2^{1 / 2}\right)^{120-\mathrm{r}}(5)^{\mathrm{r} / 6}$
for rational terms $\mathrm{r}=6 \lambda \quad 0 \leq \mathrm{r} \leq 120$ so total no of forms are 21 .