D

Step 1: Analyze the motion of the two-block system.
The total mass of the system is 1 kg + 2 kg = 3 kg. The velocity of the center of mass (CM) will depend on the individual motions and masses of the blocks.
Step 2: For block 1 (1 kg) on top and block 2 (2 kg) below, if the motion is horizontal and there are no external forces acting in the horizontal direction, the velocity of the center of mass is constant, meaning it's not changing. Thus, it's effectively constant if no external net force is applied to the system.
Step 3: The momentum of the center of mass will also remain constant if there are no external forces acting on the system.
Step 4: The momentum of the 1 kg block will be zero if it remains stationary or is not in motion relative to the lower block before any external force is applied.
Step 5: The kinetic energy of the 2 kg block is constant if the system is in equilibrium and not subjected to any external forces.
Conclusion: Thus, matching the items from Column I to Column II, we find:
(i) Velocity of center of mass - [D] Constant
(ii) Momentum of center mass - [D] Constant
(iii) Momentum of 1 kg block - [C] Zero
(iv) Kinetic energy of 2 kg block - [D] Constant
Therefore the correct answer is D.