A B C is right angled triangular plane of uniform thickness. The...

The moment of inertia of a body about an axis depends not only on the mass of the body but also on the distribution of mass about the axis. For a given body mass is same, so it will depend only on the distribution of mass about the axis. The mass is farthest from axis $B C$, so $I_2$ is maximum mass is nearest to axis $A C$, so $I_3$ is minimum. Hence, the correct sequence will be $I_2 \gt I_1 \gt I_3$