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In which of the following cases the centre of mass of a system is certainly not at its centre ?

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Important Questions on Centre of Mass, Momentum and Collisions

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Alpha Question Bank for Engineering: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise - 2>Q 56
If the net external force acting on a system is zero, then the centre of mass
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Alpha Question Bank for Engineering: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise - 2>Q 57
In an elastic collision in absence of external force, which of the following is/are correct?
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Alpha Question Bank for Engineering: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise - 2>Q 58
A small ball collides with a heavy ball initially at rest. In the absence of any external impulsive force, 
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Alpha Question Bank for Engineering: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise - 2>Q 59
A block moving in air explodes in two parts. Then, just after the explosion (neglect change in momentum due to gravity)
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Alpha Question Bank for Engineering: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise - 2>Q 60
Two bodies of the same masses collide head-on elastically, then
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Alpha Question Bank for Engineering: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise - 2>Q 61
External force F→(F→ ≠ 0) acts on a system of particles. The velocity and the acceleration of the centre of mass are found to be vcm and acm at an instant, then it is possible that
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Alpha Question Bank for Engineering: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise - 2>Q 62
A bag of mass M hangs by a long thread, and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined system (bag and bullet) is
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Alpha Question Bank for Engineering: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise - 2>Q 63
A set of n-identical cubical blocks lie at rest along a line on a smooth horizontal surface. The separation between any two adjacent blocks is L. The block at one end is given a speed V towards the next one at time t = 0. All collisions are completely inelastic, Then