Yes all IIM’s are Government Institutes .The Indian Institutes of Management (IIMs) are institutes of management education and research in India.

IIMs List:
• Indian Institute of Management Calcutta
• Indian Institute of Management Ahmedabad
• Indian Institute of Management Bangalore
• Indian Institute of Management Lucknow
• Indian Institute of Management Kozhikode
• Indian Institute of Management Indore
• Indian Institute of Management Shillong
• Indian Institute of Management Rohtak
• Indian Institute of Management Ranchi
• Indian Institute of Management Raipur
• Indian Institute of Management Tiruchirappalli
• Indian Institute of Management Udaipur
• Indian Institute of Management Kashipur