Most of the states conduct state level entrance exam and otherwise also institutes which take through their own exam are:
TANCET (Tamil Nadu Common Entrance Test) :TANCET is conducted by Anna University, based in Chennai

MAH CET (Maharashtra MBA Common Entrance Test) :MAH CET is online exam conducted by the Directorate of Technical Education (DTE) for the admission in the MBA.

IIFT (INDIAN INSTITUTE OF FOREIGN TRADE) :The Indian Institute of Foreign Trade (IIFT) conducts a written test for students seeking admission to International Business at the institute.

XAT (Xavier Aptitude Test) : XAT exam is conducted every year by Xavier School of Management, Xavier Labour Relations Institute (XLRI) Jamshedpur.

SNAP (SYMBIOSIS NATIONAL APTITUDE TEST) : Symbiosis National Aptitude Test (SNAP) is a combined Written Test for students seeking admission the Postgraduate Institutes under Symbiosis International University.

NMIMS conducts NMAT.

These are some of the good MBA  entrances.

Good Luck.