Psychology

If the subject in which you have got compartment was a additional one than there is no barrier for you to apply. But if it was your main subject, you need to clear your compartment with good marks. Otherwise, your admission in the college will not be valid and would be canceled.
For more information, you can visit the official website of the college.
All the best for your future.

The syllabus:
Data analysis and interpretation
Mathematics Quantitative aptitude
Numerical ability
Fundamental mathematical operations
Reasoning Critical reasoning
Analogical reasoning
Logical reasoning
General knowledge Current affairs
English Language
Comprehension skills
Verbal reasoning.

Yes, Lady Sriram College offers a degree in BA in Psychology and Human Resource. For more details, please go through the link. https://www.shiksha.com/humanities-social-sciences/psychology/course/b-a-hons-in-psychology-lady-shri-ram-college-for-women-lajpat-Nagar-Delhi-52422?actionType=compare&course=52422
Good luck.

No entrance exam date is been shown here on the website. You better check at the official website of the university.

Yes, you can definitely pursue M.A. in psychology. Already having done MBA which gives scope for many opportunities, you need to have a better clarity as why you want to pursue a career in Psychology. Psychology is one of the interesting field to study and practice as a career.

Yes, Jain University offers M.Sc. Psychology is Integrated with British Association of Counselling & Psychotherapy, UK. The eligibility criteria is given below.
Eligibility : The minimum qualification required to apply is a bachelors degree in the respective discipline from a recognised university.

https://www.shiksha.com/humanities-social-sciences/psychology/colleges/b-a-colleges-india
Here is the college list for distance education available in B.A. Psychology.