Mathematics - Binomial Theorem Question with Solution | TestHub

General term is ${ }^{60}{C}_r{\left(7^{\frac{1}{5}}\right)}^{60-r}{\left(-3^{\frac{1}{10}}\right)}^r$

We will get rational term when $r$ is multiple of $10$ and $60-r$ is multiple of $5$.

$\therefore r=0, 10, 20, 30, 40 ,50, 60$

$\therefore$Number of irrational term $=$ Total terms $-$ Number of rational terms

$=\left(60+1\right)-7=54$.