There are not many good colleges providing BBA+MBA in Delhi/NCR. In case you are interested in Noida then there is Amity University, Galgotia university, Greater Noida Institute of Technology which provide BBA+MBA integrated program.
Gap shall be not a problem if you will be able to justify the reason for the gap. If you meet the eligibility criteria for the course then you will be eligible. The criteria may vary college to college. Like in Amity University for this course you need minimum 70% in your 12th class to apply for the written test.

Good Luck.