Hi Amit,

I guess you're searching for the government engineering colleges across India. There are several exams that will fulfill your requirements:

1. IIT-JEE (for national level colleges)

2. Several state level government engineering cilleges' exams like: JEECE(Jharkhand), OJEE(Orissa), WBJEE(West Bengal), UPSEE(Uttar Pradesh), etc.

I hope I've answered your query successfully.