CAT

As the NEET Score Required is about 510+ for RRMC Bangalore it's under R. G. H. U
Rajarajeswari Medical College and Hospital Bangalore (R. G. university. H. S)
General: Rs 1.98 Lacs, Management Quota: 38.12 Lacs. As per the last year NEET Score, and college which you have mentioned by there are chances to secure seat if NEET Marks are 510-530+ then
Karnataka state domicile like MS Ramaiah, Kempegowda Inst, Dr. B. R. Ambedkar Medical College, Bangalore, M. V. J. Medical College and Research Hospital, Channasandra, Bangalore.

You need to check which university accept the CAT basically CAT is for management and common entrance examination
If you go medical line, check the eligibility
There is a possibility if a seat is available in PMCH
You need to score within a rank of 1500 to get into PMCH Patna college based on NEET rank
Patna Medical College and Hospital was established and originally known as Prince of Wales Medical College is a medical college located in Patna the state capital of Bihar India It is located on the southern bank of the river Ganges and is now affiliated with Aryabhatta Knowledge University.

No, you cannot get admission in government college because for SC category, you have to have rank between 137.108, then you are eligible to take admission in government college of MBBS.

Closing cutt off is around 85%. .

This depends totally on you. If you preparing in your college town & your college town is far from your home town you should select college town it saves your time & effort in this crucial time or you should also opt for your home town.

Yes, there are so many IIM colleges that you can get admission, but you have to score very good marks in the CAT exam. There are so many IIMs that haven't been considered or given more weightage to past academics you can check on the IIM website accordingly, you can target them.

In your graduation, you have to score more than 8 CGPA & for getting admission in IIM -A you have to score above 99 percentile (if GEM), if you are OBC or EWS category score 98 percentile above and if you fall in any other category you have to score more than 95percentile.

Your score is excellent in academics however, you have to need to score more on the CAT exam get into NIT Trichy,

You have to be in Top Ranks you kno what I mean by that IIM is easy when the CAT score is crazy.

No you can opt any entrance exam as per your interest and Cutoff criteria if not satisfied in one attempt.