a
Moment of inertia of system 

\(=M.I. of A + M.I.\, of\, B+M.I \,of\, C\)

\(M.I\) of\( A = M . T\) through center and 

perpendicular to length \(= \) \(\frac{1}{{12}}M{L^2}\)

\(M.I\) of \(C = M.I \,of\, A = \) \(\frac{1}{{12}}M{L^2}\)

\(M.I \,of\, B = 0\)

(moment of mass about an axis passing through its own position is zero)

\(\therefore \,Total\,M.I\, = \frac{1}{{12}}M{L^2} + \frac{1}{{12}}M{L^2} = \frac{1}{6}M{L^2}\)