MBA Entrance Exam

You are quiet close to the dark horse. Do not spoil your score by choosing an average B-school in hurry. Probably you are investing last time to choose a right career not just a degree with uncertain job profile of 100% placement.
I will try to give you some colleges based in south. You can chase if seats are remain vacant (SIMSREE government of MH, can apply but check up to final list, as general cut off is 99) PUMBA-Pune (Public sector colleges hence lowest cost, high return), NIBM-Pune, XIME-Bangalore, Great lakes-Chennai, IFMR Chennai, etc.
If unable to get into above all then think XIME Kochi, IIRM-Hyderabad (business analyst or risk management), IPE-Hyderabad (Banking finance), MDI-Murshidabad (budding college but growing rapidly with MDI-Gurgaon brand name, try to check the present picture of placement from LinkedIn alumni chat, do not play the gamble by choosing average college as investment is high in private college.
Make a LinkedIn / Quora profile to chat with alumni of your favorite field of job (Sales, HR, Financial product sales and core finance) to get the exact picture of job stability and salary in hand (do not rush behind CTC annual package as this is not your take home; be clever for difference Google this).