When an external force is applied at the centre of mass of a system of particles, then it undergoes

• The claim is correct because only a change in the centre of mass requires external force. 
• Moreover, since there won't be any external forces acting on the system, the linear momentum of the system will not change.
• The only translational motion a rigid body at rest will experience is if force is applied to its centre of mass.

Hence the correct answer is Only translatory motion.