Pune

Try referring cut off of last year which are available in DTE Maharashtra website from there you will get an idea.

Amity Institute of Education
Army Institute of Education
AURA Institutions
B. K. Institute of Education & Technology
C E S College of Educational Research and Training
Central Institute of Education Delhi University
College Of Education, Delhi University S
Department of Education Shri Lal Bahadur Shastri Rashtriya Sanskrit Vidyapeetha
Excel Institute of Management & Technology
Faculty of Education - University of Delhi
Guru Gobind Singh Indraprastha University
Guru Nanak College of Education
Guru Ram Dass College of Education
Indira Gandhi National Open University
International Women Polytechnic
Jamia Millia Islamia

Dear Rahul,
There is hardly any institute or college which gives you admission without any entrance score, I'm talking about a good or average college because if you want to go for MBA then doing it from a below average college just because you don't want to give any entrance make no sense, in fact that don't carry same value.
So it is advisable to appear for entrance test and then go for admissions.this way you will make it to good college which will offer you good placements as well.
All the very best.

It has decent brand reputation but placement and learning opportunity is average, not the preferred choice among recruiters. Better colleges are recommended for great paying jobs Like VJTI, BIMTECH, DJ Sanghvi, SPCE.

D.Y. Patil and ICRI are the best. Check other colleges which are mediocre.
https://www.shiksha.com/mba/colleges/mba-in-hospital-health-care-management-colleges-in-mumbai-all

You should try for MITSOB, FLAME, Balaji Institutes, these are some of the best Institutes you can try for with Your MAT score. All the best for the GDPIs.