B.Tech

The order would be -
IIT Bombay - JEE Advanced
NIT Nagpur - JEE Mains
COEP / VJTI - MHCET
Walchand - MHCET
PICT (if it becomes autonomous this year) - MHCET
VIT - MHCET

Check out the link below and click on the link below now college cut-off:
https://www.shiksha.com/b-tech/resources/jee-mains-cut-off-predictor

Check out the link below and click to know college cut-off:.
https://www.shiksha.com/b-tech/resources/jee-mains-cut-off-predictor

Your rank is quite low and without donation its seems little difficult, still you can check out the link below:
https://www.resonance.ac.in/reso/news/JEE-Main-Branch-Predictor.aspx

Check out the link below and click to know college cut-off:
https://www.shiksha.com/b-tech/resources/jee-mains-cut-off-predictor

Yes, you can get the admission in B.Tech engineering colleges if you have qualified in 12th board exams and some other entrance exams for engineering like JEE Mains, Advanced and CET.

Vishwakarma Institute of Technology
College of Engineering Pune
Sinhgad College of Engineering
Bharati Vidyapeeth University College of Engineering
Maharashtra Institute of Technology Academy Of Engineering
Rajarshi Shahu College of Engineering,
And the procedure is LEET entrance exam.

It is a good college approved by Anna University. The average salary package is around 3.20 lacs pa as far as placements are concerned about. Have good reputation in it.

Tuition + Caution deposit = Rs.4,05,000 per annum for 3rd category.