A rod of length $L$ is placed along the x-axis with one of its ends at the origin O. The mass of the rod increases linearly as $\frac{dm}{dx}=\lambda x$  where  $\lambda$ is a constant
    

The position of the centre of mass C of the rod, coincides with the geometrical centre C of the rod.

The moment of inertia of rod about y-axis is  $\frac{\lambda L^4}{4}$.

The moment of inertia about the perpendicular axis passing through it center of mass is  $\frac{1}{36}\lambda L^4$.

All the above statements are wrong.