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The eligibility criteria for MBA in general is passed graduation in any discipline from a recognized  university securing 50% aggregate, there is relaxation of 5% for reserved categories, admission is done through various entrance test conducted at various level such as

• national levels such as CAT, XAT, MAT, ATMA, CMAT, IIFT
• university level entrance tests such as NMAT, CUSAT, SNAP, IPU CET
• state level entrance tests such as MAH CET, OJEE, KMAT, TANCET, APICET

check out at https://bschool.careers360.com/exams to know more details regarding  this,

government colleges offering MBA are listed belows;

• Indian Institute of Management Bangalore
• Indian Institute of Management Ahmedabad,
• Indian Institute of Management Kozhikode,
• Indian Institute of Management Lucknow,
• Faculty of Management Studies University of Delhi
• Department of Management Sciences Savitribai Phule Pune University
• Jamnalal Bajaj Institute of Management Studies, Mumbai
• University Business School Panjab University
• Institute of Management Studies Banaras Hindu University Varanasi,
• Maharaja Sayajirao University of Baroda Vadodara,
• University Business School Panjab University Chandigarh
• Jamia Millia Islamia New Delhi
• National Institute of Technology Warangal, Telangana
• Indian Institute of Social Welfare and Business Management Kolkata,
• School of Management Studies University of Hyderabad
• Department of Management Studies Indian Institute of Science Bangalore,
• Indian Institute of Management Kolkata,
• Sydenham Institute of Management Studies Research and Entrepreneurship Education, Mumbai
• Institute of Management Studies Devi Ahilya University, Indore
• Department of Management Studies Indian Institute of Technology Chennai
• Indian Maritime University, Kochi
• Delhi School of Management Delhi Technological University New Delhi
• Department of Management Studies Indian Institute of Technology, New Delhi
• Department of Business and Industrial Management, Veer Narmad South Gujarat University, Surat
• College of Engineering, Trivandrum Thiruvananthapuram,
• BK School of Business Management, Gujarat University, Ahmedabad
• Department of Business Management, Osmania University, Hyderabad
• Indian Institute of Foreign Trade New Delhi,

check out our page at https://bschool.careers360.com/colleges/list-of-government-mba-colleges-in-india to know more details regarding this.