List of top Mathematics Questions on Divergence theorem

Let $\vec{F}(x, y, z) = x^2 y \hat{i} + z \hat{j} + x y z \hat{k}$, then $\text{div} \vec{F}$ is given by

If \(\overrightarrow{r}=x_1\hat{a}_{x_1}+x_2\hat{a}_{x_2}+x_3\hat{a}_{x_3}\) and \(|\overrightarrow{r}|=r\) then \(div(r^2\nabla(In\;r))\)is

The mathematical statement regarding Divergence theorem which is true: