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 :
Solution
<p>$$\begin{aligned}
& \text { General term }={ }^n C_r\left(7^{1 / 3}\right)^{n-r}\left(11^{1 / 12}\right)^r \\
& ={ }^n C_r(7)^{\frac{n-r}{3}}(11)^{r / 12}
\end{aligned}$$</p>
<p>For integral terms, $r$ must be multiple of 12</p>
<p>$\therefore \mathrm{r}=12 \mathrm{k}, \mathrm{k} \in \mathrm{~W}$</p>
<p>Total values of $\mathrm{r}=183$</p>
<p>Hence $\max r=12(182)$</p>
<p>$=2184$</p>
<p>Min value of $n=2184$</p>
About this question
Subject: Mathematics · Chapter: Binomial Theorem · Topic: Binomial Expansion
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