Correct Answer - A::B::C::D
Since the system of two blocks and a spring is placed on as smooth horizontal floor, therefore no external horizontal force acts on the system.
Since the system is initially at rest, therefore centre of mass of the system will remain stationary and the block will oscillate with the same frequency. it means option d is correct.
Since the system is initially ast rest and centre of mass stationary, therefore centre of mas cannot move or the momentum of the system remains equal to zero. it means, moment of two blocks are numerically equal but they are in opposite directions. therefore, ratio of magnitude of velocity of the two blocks will be in inverse ratio of their masses. Hence, option a is correct.
Since ratio of mass is constant. therefore the ratio of their velocity remain constant. it means that option b is also correct.
Since the system is on smooth horizontal floor, therefore no energy loss takes place. hence, linear momentum and energy of the system remain conserved. therefore, option c is also correct.