Moment of Inertia & Radius of Gyration question from JEE Main 2021 (16 Mar, Shift 1)

Answer: (d)

1. Diagonal $BD$ is at distance $\frac{l}{\sqrt{2}}$ (half the diagonal) from $A$, so the axis through $A$ parallel to $BD$ is at $\frac{l}{\sqrt{2}}$ from $B$ and $D$.
2. $C$ is a full diagonal away: distance $\sqrt{2}\,l$. $A$ is on the axis.
3. $I = 0 + 2m\left(\frac{l}{\sqrt{2}}\right)^2 + m(\sqrt{2}l)^2 = ml^2 + 2ml^2 = 3ml^2$
4. So the answer is (d) $3ml^2$.