Can you suggest some AICTE approved colleges to pursue distance B.Tech in automobile engineering?

If you're really interested to do automobile engineering, there is no way about distance. You can choose regular mode for completing your engineering graduation. I can suggest you some better colleges according to your location. Please mention your location.

I am not sure if one can do any engineering through distance learning or not. You need to first check with AICTE whether they allow such a thing or not. I hope you will check with them.