IITs and NITs dont offer B.Tech in Automobile Engineering but you can apply in private universities or colleges like Manipal, SRM, Chandigarh University, University of Petroleum and Energy Studies etc and as per my view better to get admission in B.Tech in Mechanical Engineering from IITs/NITs and once you clear it give Gate exam and get required score so that you can get admission in top IITs in M.Tech in ME program but before you make any decision consider your interest, potential and convenience.

Good Luck!!!