Colleges in Rajasthan

The list of shortlisted candidates for GD&PI will be out in starting of March (tentative) and the process will be in last week of March or first week of April (tentative).

Yes, you can apply for BITS, Pilani. You will get a GDPI call from them. Also, you can apply for ITM-Mumbai, Balaji Institutes-Pune, BIMTECH-Noida and Christ University, Bangalore.

Welingkar Bangalore and Christ Bangalore are decent college wher eyou may have chances, BITS pilani has higher cutoff, Welingkar Mumbai goes above 80percentile.

If you fulfill the eligibility criteria i.e.B.E./B.Tech in engineering disciplines or a Masters Degree in any discipline from any recognized university or any Integrated first degree of BITS. Candidates should have obtained minimum of 60% aggregate marks in qualifying degree.
The shortlisting is based on CAT scores and overall profile, with such percentile you have a chance of getting a call for GD & PI.

IITs and NITs are the top government engineering colleges India.

Yes, you can get admission in central universities and state universities which are funded by central and state government well.

I think, for the Mumbai Campus, it's around 210.

Please refer to list of MBA colleges in Rajasthan: https://www.shiksha.com/mba/ranking/top-mba-colleges-rajasthan/2-0-121-0-0

BITS is the one of the best colleges in engineering in India amongst all private institutions.