CAT

You can consider the below mentioned colleges:
1. Jaipuria.
2. Sydenham – Pune.
3. ABV – Gwalior.
4. Welingkar.
5. KJ Somaiya.
6. BIT – Mesra.
7. XIME.
8. Alliance.
9. Kirloskar.
If you will apply at XIMB, then you will get RM.

CAT is the only way to get in here.

Then, you have no chance to get in. Try some other institutes.

Nirma gives admission purely based on merit and not on category so minimum required percentile is 75 to get shortlisted for interviews.

80 percentile keeping in mind last year cutoff.

No, it does not matter.

Sir,
Yes, you are eligible to get admission in this college for IB with this much aggregate but you also need to clear interview for the selection because as you have only got 45 percentile in CAT. So, in that case, you can apply for the selection exam which amity university takes before interview which carries basic questions as you get in your CAT exams. I would suggest you to go for that exam as it would become more easier for you to get seat in this course.

Quite good chances keeping in mind last year cutoff unless and until you don't screw the interview.

No, you cannot get admission unless and until you are filling form for NRI Quota.

I guess very less chance to get shortlisted for interview even but you can take a risk and fill the form.