Mathematics - Binomial Theorem Question with Solution | TestHub

${\mathrm{T}}_{\mathrm{r}+1}={}^{256}{\mathrm{C}}_{\mathrm{r}}(\sqrt{3}{)}^{256-\mathrm{r}}(\sqrt[8]{5}{)}^{\mathrm{r}}={}^{256}{\mathrm{C}}_{\mathrm{r}}(3{)}^{\frac{256-\mathrm{r}}{2}}(5{)}^{\mathrm{r}/8}$ Terms will be integral if $\frac{256-\mathrm{r}}{2}\&\frac{\mathrm{r}}{8}$ both are +ve integer. As $0\le \mathrm{r}\le 256\therefore \mathrm{r}=0,8,16,24,\dots \dots \dots \dots 256$ For above values of $\mathrm{r},\left(\frac{256-\mathrm{r}}{2}\right)$ is also an integer.