The total number is irrational terms in the binomial expansion of

Let the general term of the expansion

$T_{r+1}={ }^{60} C_{r}\left(7^{\frac{1}{5}}\right)^{60-r}\left(-3^{\frac{1}{10}}\right)^{r}$

$={ }^{60} C_{r} \cdot(7)^{12-\frac{r}{5}}(-1)^{r} \cdot(3)^{\frac{r}{10}}$

Then, for getting rational terms, $r$ should be multiple of L.C.M. of $(5,10)$

Then, $r$ can be $0,10,20,30,40,50,60$.

Since, total number of terms $=61$

Hence, total irrational terms $=61-7=54$