For getting a good college you'll definitely have to sit for the management entrance exams like CAT which is for IIMs and most of the colleges. Even if you score a 60 percentile there you can get a decent college. 

Apart from that for colleges like XLRI you'll have to write XAT exam and for NMIMS and SIBM, NMAT and SNAP respectively. 

Other than that you can sit for IBSAT to get admission in different campuses of ICFAI Business school. 

But you can focus on CAT and CMAT, they'll will be sufficient to get you into most of the colleges. 

Though without exams you can get admission in few colleges through donation but those colleges but those won't be a good colleges. 

Good luck