for reference, hash function $f(x)$:
$$f(x) = x \text{ mod } 7$$
Statement I is true.
give hash function a number $x$ no matter big or small and it will map it to some fixed value(slot).
Statement III is true.
yes, it happens often that same number are mapped to same slots, giving rise to collisions in some cases.
Statement II maybe true.
we can code such a hash function too.
But since, I and III are given together as separate options then we choose option C as true.