M.A

Yes, you can do M.A. In Psychology after graduation in any field. The course is eligible for the students who have completed graduation in any discipline with a minimum of 50% marks from a recognised university. It may vary for different universities. But there are many Universities that allow you to pursue a master's in psychology without a Bachelor's specifically in the field. Here are some of the good universities you can refer to pursue Psychology course:
Amity University
G D Goenka University
IILM University, Gurugram
Ambedkar University.

MAT exam is only considered for PGDM. For others, you will have to attend CAT, CMAT or KMAT

Hi Tripti. If you want to do M.A. From regular mode then you need to qualify entrance exam organise by respective University in which you are interested to get admission. Or if you want to study from distance mode like from IGNOU then you can get direct admission in IGNOU.