Data Analytics

I think you should go with B.Sc. Statistics, because B.Sc. Data Science students have big competition with B.Tech CSE students and most of the companies prefers to select the B.Tech CSE students in place of B.Sc. Students.

Below is a list of non IIM colleges that provide good placements for the management graduates:
REGENESYS INSTITUTE OF MANAGEMENT, MUMBAI.
FACULTY OF MANAGEMENT STUDIES, DELHI.
XAVIER LABOUR RESEARCH INSTITUTE, JAMSHEDPUR.
MANAGEMENT DEVELOPMENT INSTITUTE, GURGAON.
INDIAN INSTITUTE OF FOREIGN TRADE IIFT NEW DELHI.

You have not mentioned about the course you wants to pursue. However the eligibility criteria of M.Sc. Data Science is given below. M.Sc. Data Analytics eligibility Criteria : Students who wish to pursue M.Sc. Data Analytics must hold a Bachelors degree in relevant discipline or equivalent from a recognised university. For admission to this course, students are required to clear the cutoff percent set by the respective College or University in the entrance examination.

The following are the few colleges that offer M.Sc Data Science course in TamilNadu as under.
1. Amrita Vishwa Vidyapeetham Coimbatore
2. Loyola College Chennai
3. VIT Vellore
4. VIT Chennai.

Hello,
It is very nice to hear from you that you are aiming for admission in Mumbai IIT for CSE. This means you would be almost in top 50 or 100 of JEE advanced. In view of this I do not see any hindrance of you not getting admission 4 years later in IIT Hyderabad for your MTech. But then nobody can predict as to what will be the situation and scheme of things for admission in mtech 4 years down the line. But, normally speaking yes you should get admission.
Best wishes to you.