Mechanical Engineering

try for bit mesra

Yes there are universities which offers engineering course without JEE. Universities like JNU, BHU, Lovely Professional University etc conducts their own entrance exam and gives admission on the basis of marks scored in that test. So, you can give entrance exam of these universities and can get admission and scholarship too if you score well in the exam.

You can do M.Tech or MBA or can hunt for a suitable job. You can also appear for Govt Admin exams like that of State PSC and/or UPSC .

Autonomous is would be a much better option I guess. Because there many advantages of being an autonomous college. Moreover the colleges had to pass through many cheks regularly to maintain their autonomous status.