Hi Afsar,

What do you mean by non eligible students, every Indian students who passed 12th class with science stream are eligible for engineering in anywhere in India.

Here are some of the best private engineering college in Mumbai who gave admission for students who are not participate in any exam like JEE

1. Usha mittal institute of technology,

2. S.S P.M college of engineering

3. Xavier institute of technology

4. Jaykumar rawal institute of technology

5. Atharva college of engineering 

Hope this Information help you.