HYY.

Here are a few Government colleges offering B.A LLB integrated:

• Indian Law Society Law College, Pune
• National Law University, Delhi
• Faculty of Law, Osmania University
• Faculty of Law, University of Calcutta
• NALSAR Law University, Hyderabad
• Army Institute of Law

you can get into these through CLAT, LSAT.

hope this helps!!

all the best.