Mathematics - Binomial Theorem Question with Solution | TestHub

$\begin{array}{rl}& \text{ General term }={}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}}{\left\{7^{1/3}\right\}}^{\mathrm{n}-\mathrm{r}}{\left(11^{1/12}\right)}^{\mathrm{r}}\\ & ={}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}}\{7{\}}^{\frac{\mathrm{n}-\mathrm{r}}{3}}(11{)}^{\mathrm{r}/12}\end{array}$

For integral terms, r must be multiple of 12
$\therefore \mathrm{r}=12\mathrm{k},\mathrm{k}\in \mathrm{W}$

Total values of $r=183$
Hence $\max r=12(182)$
$=2184$

Min value of $n=2184$