As you want to get the list of some of the best MBA entrance exams which can be given apart from CAT, XAT, XLRI and MAT so here is the information of the same for you:

IRMA Institute of Rural Management Anand

IIFT Indian Institute of Foreign Trade

SNAP Symbiosis International University

IBSAT ICFAI

NMAT NMIMS

TISS Tata Institute of Social Sciences

ATMA Association of Indian Management Studies

MAH-CET Directorate of Technical Education, Maharashtra State

CUSAT Cochin University of Science and Technology

PAM-CAT GNDU, Amritsar / PTU, Jalandhar / Punjbai University, Patiala

MET-MP MADHYA PRADESH PROFESSIONAL EXAMINATION BOARD

TANCET Anna University, Chennai

OCET Punjab University, Chandigarh

UP-SEE UP Technical University

Orissa JEE Orissa JEE

GCET Gujarat Secondary and Higher Secondary Education Board

KMAT KARNATAKA PRIVATE POST-GRADUATE COLLEGES' ASSOCIATION

RMAT Rajasthan Technical University

UPMCAT Uttar Pradesh Technical University