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  4. The number of rational terms in the binomial expansion of (4(1/4)+5(1/6))120 is

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

JEE MainJEE Main 2021Binomial Theorem

Solution:

$\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 $r=6 \lambda \,\,0 \leq r \leq 120$
so total no of forms are $21$ .