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MAT score is used by 600+ B-Schools to shortlist candidate for their selection process which may include GDPI and other tests. You may refer to all India ranking of top B-Schools which use MAT score as the selection criteria: https://www.shiksha.com/mba/ranking/top-mba-colleges-in-india-accepting-mat/2-2-0-0-306.
You may choose a few colleges in which you are likely to get GDPI call based on your MAT score. You may apply for admission in your chosen B-Schools. You may refer to your targeted B-Schools with its detailed admission process at its website. You are advised to look at every target B-School's eligibility criteria before applying because it may vary in different B-School.

Saurabh,
Your rank is going to be between 27,000 to 46,000. Use the link below to know the type of college you will get with these marks:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
Going for a newly opened IIIT won't be a good idea, as it will take time for the new place to establish it properly.
With this JEE score, you can get you a seat in some of the best private universities like Lovely, Galgotias, Goenka, etc. Most of these universities are offering admissions on the basis of JEE score, their own tests and 12th marks. Some of them are also offering good scholarships on the basis of above mentioned criteria.
Private universities these days are at par with government ones only, in fact better when it comes to infrastructure, faculty and placements.
Check the websites of some of these universities too for more details.

They have various features:
1. Qualified and experienced faculty from National law schools
2. Guest lecturers by lawyers, Judges and legal luminaries.
3. Meaningful experiential legal education through MOOT Court
4. Legal Aid Clinic for the villages in the vicinity.
5. Well equipped library with 4297 books, 22 Print Journals, 668 Reports and Manupatra E- Journals.
6. Frequent court visits as a part of pragmatic learning.
7. Institutional support to students for participating in National and International Competitions.
8. Entrepreneurship Development Cell, Toastmasters International Club, Theatre Club, Sports Club and Social Service Club for the overall development of the students.

Which University is better It all depends upon the prospect of university/college that you are looking forward to like the curriculum and study, recruitment and placement rate and campus infrastructure and life. Best hotel management colleges are mentioned below:-
Viva College, Virar
Geeta University, Panipat
AIMS Institutes, Bangalore
Christ University, Bangalore
Punjabi University, Patiala
NSHM Knowledge Campus, Kolkata
Gautam College, Hamirpur
MS Ramaiah College of Hotel Management, Bangalore
Jamia Hamdard, New Delhi
Manipal University, Jaipur
SHEDS College of Hospitality Management, Solan
I will be advise you to do your degree from Geeta University which is a well known university and that provides prime placement opportunity, outstanding exposure and professional enhancement training.