Although 5 years course might waste 1 extra, year you can still do another masters i.e. MBA in your case. Also the added year will give more time for you to prepare for CAT while still being in college. I am doing EP from IIT Roorkee and our campus also has this Integrated MSc physics through JEE and I know of people who went onto did MBA after their masters. Here you have engineering duals option in BHU, while you can easily get 5-year MSc physics at any old IIT.
If you are concerned on wanting 4 years course then try the 4yr BS Physics at IIT Kanpur. You might be thought Nuclear Physics course by HC Verma himself.
Infact did you consider the economics programmes at Kanpur and Kharagpur?