Dual

For admission in integrated geology course of 5 year (B.Sc + M.Sc), you must appear in the entrance organised by Andhra University AUCET with the required eligibility.
Register and Apply
Interested candidates can apply online with required information.
Entrance Test
Eligible candidates need to appear for the Andhra University Common Entrance Test (AUCET) conducted by the University.

You can go for Integrated programme in Management of Indian Institute of Management, Indore. It's the best in its class. And apart from that, as you are from Odisha, the best can be from Utkal University and Xavier University.

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.