>But here the graph shows that the potential energy is minimum during collision.

But it doesn't. Keep in mind that $r$ becomes *smaller* as the balls get closer together and then becomes *larger* as they move apart. The horizontal axis is not time. 

As for the other points, it makes sense that you want $V$ to increase as $r$ decreases. This is because
$$F=-\frac{\text dV}{\text dt}$$
The inverse relationship between $V$ and $r$ means that the force is pushing the balls in contact towards being farther apart. 

None of the other answer choices give you the correct force behavior (check for yourself).

To answer your title question, this does not always have to be the case. But for your system we don't want any attraction between the balls, so we do want this behavior here.