The total number of irrational terms in the binomial

Question:

The total number of irrational terms in the binomial expansion of $\left(7^{1 / 5}-3^{1 / 10}\right)^{60}$ is :

  1. 55

  2. 49

  3. 48

  4. 54


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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