Regarding the centre of mass of a system of particles, which of the following are correct

a) The location of centre of mass is independent of the reference frame used to locate it.

 b) At the location of centre of  mass there must be  a particle of the system

c) If the particles lie in a plane, the centre of mass also must lie in that plane

d) The total moment of mass of system of particles about the centre of mass must always be zero