QJEEM25Maf1f2: JEE Main 2025 Mathematics - Class 11 JEEM25Maf1f2 Solution: The least value of n for which the number of integral terms in…

$\begin{aligned}& \text { General term }={ }^n C_r\left(7^{1 / 3}\right)^{n-r}\left(11^{1 / 12}\right)^r \\& ={ }^n C_r(7)^{\frac{n-r}{3}}(11)^{r / 12}\end{aligned}$

For integral terms, $r$ must be multiple of 12

$\therefore \mathrm{r}=12 \mathrm{k}, \mathrm{k} \in \mathrm{~W}$

Total values of $\mathrm{r}=183$

Hence $\max r=12(182)$

$=2184$

Min value of $n=2184$