I want to do CA but the institute is not providing B.Com so, I prefer doing B.Com with government college via private mode. Is it possible?

You can go for Open University, which is IGNOU. It is connected with the ICAI (Institute of chartered accountants of India). Here, you can give your graduations exam along with CA, as a private student without interruption by the college. All the best.

You can apply in Delhi University.