A body is placed on a horizontal frictionless surface. When a horizontal force F is applied on the body, it is observed that the body makes only translational motion. The which of the following points may be the positions of its centre of mass? 

Since the body does not perform any rotational motion, moment of the applied force about the centre of mass must be zero. In that case the centre of mass must lie on the line of action of the applied force. From the diagram it is evident that B may be the position of centre of mass.