Hii,i am here to help you according to your query.Yess,there is an entreance exam which held every year to get a seat in government college.List of some Entrance Exam:

-National Institute of Science Education and Research (NISER) Bhubaneswar and University of Mumbai

-IIT JAM

-Orissa University of Agriculture and Technology (OUAT)

-JEST

-Pant Nagar University Entrance Exam

--UPCATET

-GSAT

-CG PAT

-IISER Entrance Exam

-TIFR GS

-Rajasthan JET

-CIT MSc CET

-IGKV PAT

Hope,this information will helpful for you.Goodluck.