Dual

The fee for integrated BBA+MBA (aviation) in IIKM Business School (Chennai) is INR 5 lacs to INR 25 thousand for 5 years.

Yes, there are quite a few universities which provide BCA+MCA integrated course. You can Check on google for the list of colleges and choose accordingly.

Different institutes/universities have different selection criteria for BBA+MBA programme. Some of them conduct their own entrance exam, and some accept centralized entrance exam score. There are many colleges which offer seats on the basis of merit only. Please refer to the link provided below for further details regarding an integrated MBA:
https://www.shiksha.com/bba/articles/integrated-mba-programmes-in-india-blogId-15044.

They take admissions according to CAT exam. Sometimes, they conduct their separate test also and their cut-off range is very high. So, prepare well.

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.