total momentum of a system of particles does not depend upon the motion of the particles relative to the centre of mass. But this is not true for total kinetic energy right ? So, does it mean that, when the centre of mass is at rest also, there will be a total kinetic energy of the system ? But how can that be possible ? Pls. clarify...Thnx.

The reason is that momentum is a vector quantity and kinetic energy is not. Momentum is linearly proportional to the velocity but the KE is proportional to the square of the velocity.
A simple example.
Two particle of mass m moving with velocity v but in opposite direction.
So total momentum of the system
$mv+m\left(-v\right)=mv-mv=0$
therefore the CoM is at rest. But the KE of the system is
$\frac{1}{2}m{v}^2+\frac{1}{2}m{\left(-v\right)}^2=\frac{1}{2}m{v}^2+\frac{1}{2}m{v}^2=m{v}^2$
So still the system has a KE the CoM does not move.