Question:
The total number of irrational terms in the binomial expansion of $\left(7^{1 / 5}-3^{1 / 10}\right)^{60}$ is :
Correct Option: , 4
Solution:
General term $\mathrm{T}_{\mathrm{r}+1}={ }^{60} \mathrm{C}_{\mathrm{r}} 7^{\frac{60-\mathrm{r}}{5}} 3^{\frac{\mathrm{r}}{10}}$
$\therefore$ for rational term, $\mathrm{r}=0,10,20,30,40,50,60$
$\Rightarrow$ no of rational terms $=7$
$\therefore$ number of irrational terms $=54$
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