Dual

Dear Vivek, it does not make any difference whether you have done LL.B. Or not. It is an added feather in your cap. Infact it will help you to do your BBA job with better knowledge of law. You can positively go ahead with it. I hope this would suffice. All the best and God Bless You.

With 50k rank in OBC category, it is highly unlikely.

The minimum age criteria is 20 years and the maximum limit is 25 years.

Yes, these integrated courses are available in India. It is available in:
Sharda University
Goenka University
Regional Institute of Education
Bangalore University
Ranchi University
BU, Bhopal.

AIMS does offer dual specialization but you can opt this in second year only. In first year there is no specialization in first year.

Osmania University, Bangalore University, University of Hyderabad, Pondicherry University, Sharda University, etc. offer integrated B.Sc+M.Sc course of 5-year duration.

To take admission in integrated B.Sc+M.Sc you need to clear your 12th with 55% aggregate. Eligible candidates need to appear for the entrance exam conducted by Tripura University, called TUET.
Admission is based on the score obtained in the entrance exam.