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Q.
The number of rational terms in the binomial expansion of $(\sqrt{2}+\sqrt[3]{3})^{18}$ is
Binomial Theorem
Solution:
$ T_{r+1}={ }^{18} C_r \cdot 2^{\frac{(18-r)}{2}} \cdot 3^{\frac{r}{3}}$
For rational term $r=0,3,6,9,12,15,18$ ( $r$ should be a multiple of 3 )
Also, $r$ should be even because $\frac{18-r}{2} \in I$
$\Theta r =0,6,12,18$