Can I get good B-schools through May MAT??? Which are the good colleges where I can apply????????

Yes of course, you can get good B-schools through May MAT, if you have good score in the MAT you are eligible for the top colleges. Here is the list of top colleges under MAT:

SIES College of Management Studies, Navi Mumbai
Institute of Management, Christ University, Bangalore
Thiagarajar School of Management, Madurai
School of Communication and Management Studies, Cochin
Amity Business School, Amity University
Amrita School of Business, Bangalore, Kochi, Amritapuri
Balaji Institute of Modern Management, Pune
IILM Academy of Higher Education, Delhi
Profile based shortlisting/700
SDM Institute of for Management Development, Mysore
PES Institute of Technology and Management, Shimoga
KIIT School of Management, Bhubaneswar
Prin. LN Welingkar Institute of Management Development and Research, Mumbai
Gitam School of International Business, Vishakhapatnam
Jaipuria Institute of Management, Lucknow
GL Bajaj Institute of Management & Research, Greater Noida
Acharya Bangalore Business School (ABBS), Bangalore
FLAME School of Business, Pune
Birla Institute of Management Technology (BIMTECH), Greater Noida
Jaipuria Institute of Management, Noida
M S Ramaiah Institute of Management, Bangalore
Balaji Institute of Telecom & Management, Pune
New Delhi Institute of Management (NDIM), New Delhi
SRM School of Management, SRM University, Chennai
AIMS Bangalore
University of Petroleum & Energy Studies (UPES), Dehradun
Balaji Institute of Human Resource Development, Pune
Asia Pacific Institute of Management, New Delhi
Balaji Institute of International Business, Pune
Delhi Business School
ITM Business School, Navi Mumbai
Jagan Institute of Management Studies, Rohini
Dr. Gaur Hari Singhaniya Institute of Management & Research, Kanpur
Jaypee Business School, Noida
Fortune Institute of International Business, New Delhi
Era Business School, New Delhi
Indus Business Academy, Bangalore
PSG Institute of Management, Coimbatore
Asia Pacific Institute of Management, New Delhi
Vignana Jyothi Institute of Management (VJIM), Hyderabad
IFIM Business School, Bangalore
Siva Sivani Institute of Management, Secunderabad
Institute of Management Studies (IMS), Ghaziabad
T A Pai Management Institute (TAPMI), Manipal
Apeejay School of Management
Bharatiya Vidya Bhavan's Usha & Lakshmi Mittal Institute of Management (BULMIM), New Delhi
Kirloskar Institute of Advanced Management Studies, Harihar
Galgotias School of Business, Greater Noida
Acharya School Management, Bangalore