The centre of mas of a system

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

Statement-1 : The centre of mass of a system of n particles is the weighted average of the position vector of the n particles making up the system . Statement-2 : The position of the centre of mass of a system is independent of coordinate system

The centre of mass of a system of particles is at the origin. It follows that:

The centre of mass of a system of particles is at the origin. It follows that

The coordinate of the centre of mass of a system as shown in figure : -

The centre of mass of a system of particles does not depend upon

Write an expression for the velocity of the centre of mass of a system of particles.