Q1
Mathematics
2025
Binomial Theorem
mcq
QP
JEE Main
The least value of n for which the number of integral terms in the Binomial expansion of $(\sqrt[3]{7}+\sqrt[12]{11})^n$ is 183, is :
Answer: A
Explanation:
$\begin{aligned} & \text { General term }={ }^n C_r\left(7^{1 / 3}\right)^{n-r}\left(11^{1 / 12}\right)^r \\ & ={ }^n C_r(7)^{\frac{n-r}{3}}(11)^{r / 12} \end{aligned}$
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 $n=2184$