Colleges in Tamil Nadu

You have a good score in GRE and IELTS keeping that in mind you can do MS from foreign in Data Analytics as you are good in Python and R. You can easily get a scholarship in foreign.

Yes, you can go for a Ph.D. in CS after completing your MBA degree. To be in the safe side, you should have a very good research paper that will ease your application for PhD degree.

Yes, why not. You can get enrolled in BBA. I would suggest Amity University for distance learning as you have very good marks. So, you can get a 10% scholarship also from there. Amity is a brand name university. It's an internationally valid university and UGC approved. So, it's better to go with Am

Check out the link below for question papers of IMUCET
https://www.shiksha.com/university/indian-maritime-university-Chennai/imucet-exam-question-papers.

Hello,
IIM Trichy, Great Lakes, and IIT (both located in Chennai) are the prominent colleges for pursuing MBA in Tamil Nadu. https://www.shiksha.com/mba/ranking/top-mba-colleges-in-tamil-nadu/2-2-123-0-0 kindly visit this link for more details.

This year, VIT seems to not accept UCEED ranks. Check VIT's official website www.vit.ac.in for more details.

No. VIT doesn't have a course as of now (2019) in BBA in Hospital Management.