As we can see, for $\theta =30°$, the ray will incident normally and hence will retrace its path, hence the ray will come out for $\theta =30°$ and $0<l<L$.

$\Rightarrow \left(A\right)$ is correct

Considering the symmetry of the situation, we can have:

Thus, for $\theta =60°$ and $l=\frac{L}{2}$, ray will come out from the setup after two reflections.

$\Rightarrow \left(B\right)$ is correct

Now, when $\theta =60°$ and $l=\frac{L}{3}$, the ray on entering the setup will suffer five reflections and eventually will come out.

As is clear from the above diagram, ray comes out.

$\Rightarrow \left(C\right)$ is not correct

Also, as is clear from the above diagram, total number of reflections $=5$.

$\Rightarrow \left(D\right)$ is not correct.