JEE Advanced 2022 Paper 2, Physics Section 1 Q6: Gauss's Law

The charge $q$ sits on the flat circular disc that forms the common base of the hemisphere and the cone, at its center.

By symmetry, exactly half of the total flux $\frac{q}{{\epsilon }_0}$ from the point charge goes into each side of the plane of the disc.

Therefore the flux through the conical (downward) side is ${\Phi }_{\text{cone}}=\frac{q}{2{\epsilon }_0}=\frac{3q}{6{\epsilon }_0}$.

Matching with $\frac{nq}{6{\epsilon }_0}$ gives $n=3$.