Question

Let I_A and I_B be moments of inertia of a body about two axes A and B respectively. The axis A passes through the centre of mass of the body but B does not

(a) I_A < I_B
(b) If I_A < I_B, the axes are parallel 
(c) If the axes are parallel, I_A< I_B
(d) If the axes are not parallel I_A > I_B

Answer 1

(c) If the axes are parallel, I_A< I_B  

Explanation: 

From the parallel axis theorem I_B = I_A + I_A.r² where r is the distance between the parallel axes. Hence I_A < I_B. 

Others are not necessary conditions.