The correct options are
A It is the point through which the weight of a body acts.
C The centre of gravity of an object need not always coincide with its geometric centre.
D A body can be balanced at a single point if it coincides with the centre of gravity..
It is the point through which the weight of a body acts. It is unique for every body. For objects having uniform density, centre of gravity coincides with the geometric centre. A body can be balanced at a single point if it coincides with the centre of gravity.