Hello Rawool

You can definitely do BBA from one college and MBA from another college and this practice is followed by maximum students. People always want a very good MBA college to pass out from as it helps in future endeavors in their corporate life.

There are various competitive exams to apply for MBA colleges like CAT, XAT, SNAP, NMAT, MAT, and CMAT. These are national level exams which are applicable for colleges al over India. There are state specific or college specific exams as well like TANCET, MHTCET, IBSAT and many more. The basic requirement of these exams is minimum 50% in UG level.

Depending on your interest level you can appear in any of the exams or multiple exams after completing your BBA.

Hope this helps.

All the best

Regards