Chennai

Check the below link for colleges in Chennai. You can sort the list based on fees, placements, student review and infrastructure. Good MBA institutes in and around Chennai are IFMR, Great Lakes and Loyola Institute:
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-chennai/2-2-0-64-0

Please refer to the link provided below for detailed information of Saveetha Institute of Medical and Technical Sciences, Poonamallee, Chennai. Find admission process, eligibility, fees, rankings, placements, infrastructure, courses offered and much more at this link. https://www.shiksha.com/univers

You can do so via the CBSE website.

As per last year statistics, you will get core branches(civil, mechanical or EC) in main KTK campus. But for CSE there are very few chances of getting the main campus. So all the best for your future.

Yes, definitely you deserve a seat in SRM, Chennai with the above-mentioned rank but you have to wait till counselling for this because there is a dilemma of branch and campus.

You should go for regular education for MBA. Do MBA from elite B-Schools then you need to qualify CAT/MAT/XAT with a min of 50% in graduation.
Elite B-Schools are:
Indian School of Business (ISB), Hyderabad (accepts GMAT)
Jamnalal Bajaj Institute of Management Studies, Mumbai (accepts CET)
Xavier's Labo

There are over 51 BBA colleges in Chennai. Please refer to the link provided below for a detailed list of these colleges. You should be able to navigate to the top colleges in this list using the filters on the web page.
Regards.
https://www.shiksha.com/bba/colleges/bba-colleges-tamil-nadu?uaf[]=loc

Hi Arun,
Yes, MIT comes under top colleges list. But you have to be more specific with the course you want to pursue for more information.