If any college gives you admission on the basis of JEE MAINS in BSc course then it may be a case. But in general the BSc course is offered either by Merit of your class 12 or through the entrance test taken by a particular university.

Now there is a program called INTEGRATED BS-MS in IISc, IIT's etc. For which you have to qualify the JEE ADVANCED exam. Now if you are from the GEN-EWS category then you have good chance to be eligible for JEE ADVANCED.

Here are some NIT's which offers BSc program:

• NIT Rourkela - National Institute of Technology Rourkela
• National Institute of Technology Surat
• National Institute of Technology Patna
• National Institute of Technology Agartala

You can get admission to these institutes through JEE MAINS if you get a decent rank required for this institute.

I hope my answer helps. All the very best for your future endeavors!