A square plate of mass M and edge L is shown in the figure. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15^o horizontal is :

\(\frac{11 ML^2}{24}\)

From parallel axis theorem : 

\(I_1 = \frac{ML^2}{12}\)

\(I_2 = I_1 + Mx^2\)

\(I_2 = \frac{ML^2}{12} + M(\frac{\sqrt{3}L}{2\sqrt{2}})^2\)

\(I_2 = \frac{11 ML^2}{24}\)