Distance/Correspondence

Hey,
Here is the complete procedure for joining this university:
https://www.shiksha.com/university/andhra-university-visakhapatnam-2948/admission

Yes, distance degree is acceptable for MBA.

There is no such correspondence course for two months.

Yes, you can look up to universities like:
Dr. BR Ambedkar Open University
IGNOU.

BA in Psychology is an undergraduate level Bachelor's Degree program. Students who have passed 12th standard (any stream) are eligible to pursue this course. In simple terms, Psychology is the science of behavior and mind. This domain has decent scope and potential in India and abroad.
Good luck.

No and on the bases of ranking hostel is allotted.

Technically you can pursue a Ph.D programme with a valid distance mode MBA degree. I will suggest that you give UGC NET (also known as CBSE NET) exam as most of the universities has this as eligibility criteria. Although, MBAs will vehemently dismiss the need for PHDs in a teaching Job, most professors in top Business Schools have a Ph.D. So, if your goal is to be part of a prestigious institute like Harvard, Wharton or any other Ivey league schools, doing a Ph.D after Executive or Full-time MBA would be a good move. Thank you.

Eligibility for Admissions in M.Sc (Mathematics) - Two Years Duration Course - Through Distance Learning Mode from any university in Gujarat is B.Sc (Mathematics).

Dear Ankita Ramteke,
You can pursue "Post Graduate Diploma in Applied Statistics" - One Year Duration Post Graduate programme Offered by Distance Learning Mode by IGNOU. You can take up the exam in Maharashtra.