Moment of inertia of thin rod, about an axis passing through at a distance $\frac{\mathrm{L}}{4}$ from centre of rod is (mass - m, length - L)

By parallel axis theorem :

Moment of inertia of thin rod, about an axis passing through at a distance $\frac{\mathrm{L}}{4}$ from centre is

$M.I=\frac{m{L}^2}{12}+m{\left(\frac{L}{4}\right)}^2$

$=\frac{7m{L}^2}{48}$