B.Sc

Yes, you can get.

It depends on which state you are looking for good college. In Delhi University, shri ventakeshawar is a good college. Miranda House is also a good one.

Yes, you can get admission in DOMS PUMBA. The eligibility criteria is given below.
Eligibility: A student must have passed with a minimum of 50 percent marks or equivalent CGPA (45 percent in case of backward class and persons with disability)in any bachelor's degree awarded by any University.
Admission process : PUMBA strictly follows the DTE rules for its admission process of MBA+.
For Maharashtra candidates, students have to qualify MH-CET exam. For Outside Maharashtra Candidates (OMS), students can apply through CMAT/CAT/MH-CET.
So you have to appear an inappropriate entrance exam for getting admission here in the MBA program.

Few good choice to study B.Sc. Psychology are TISS, Matuonal Institute of Mental Health and Neuro Science, different IFS College, BHU, DU, Ferguson college, DHS IIT, LPU, Christ, JNU, Jamia, Jayprakash Narayan Institute, Gujarat Gorensic University, B. R Ambedkar University Agra, University of Pune, Indian Institute of Psychology and Research.