Number of integral terms in the expansion of 7 1 2 + 11 1 6 824 is equal to ______.

We know that,

General term in expansion of ${\left((7{)}^{1/2}+(11{)}^{1/6}\right)}^{824}$ is given by,

$t_{r+1}={}^{824}C_r·7^{\frac{824-r}{2}}·{11}^{\frac{r}{6}}$

For integral term, $r$ must be multiple of $6$ and should be less than $824$

So, the series will be $r=0,6,12, ..... 822$

Now, finding number of terms we get,

$822=0+\left(n-1\right)6$

$\Rightarrow 137=\left(n-1\right)$

$\Rightarrow n=138$

Hence, total integral terms will be $138$