Can the electron configuration of Te be written that way? Normally, the electron configuration of Te is known as: 

$$\begin{aligned}  {[Kr]} 5s^2 \ce{4d^10} 5p^4 \end{aligned}$$

Then, one day I was asked in a exam if this can be written also as: 

$$\begin{aligned}  {[Kr]} 5s^2 \ce{4d^10} 5p^3 6s^1\end{aligned}$$

I answered that it couldn't. But my answer turned out to be wrong.

If this is correct, why is it allowed to be written like this? And what general case can I learn when being asked such tricky questions?
The second configuration allows Te to take advantage of the relative stability of half-full shells. Having the 5p and 6s orbitals both half-populated is more stable than having 4 electrons in the 5p orbital.

Similar behavior is what allows carbon to form 4 bonds. The $\ce{s^1p^3}$ configuration is more stable than the $\ce{s^2p^2}$.

Tellurium shows the behavior while oxygen does not as a result of the overlap between the 5p and 6s orbitals in the larger atoms. The same degree of overlap does not occur with the 2p and 3s orbitals.