M.Tech Embedded Systems/VLSI

First of all, BITS Pilani offers M.E, not M.Tech and the course goes by the name of M.E Microelectronics. Placements in any college are very dynamic and changes every year. It depends on the industry a lot. Still most of the times M.E Microelectronics has fantastic placements. You can expect to get a job in core companies like QUALCOMM, INTEL, TI, CYPRESS etc. The packages offered by these companies are very good and most of the times they prefer M.E students over B.E.

It's not possible to get it in category 1 with this rank. You will either get it in category 3 or 4.

IITs, NITs and other state level colleges for M.Tech in VLSI are:
-IIT Kharagpur (KGP)
-IIT Kanpur
-Indian Institute of Technology, [IIT] Delhi
-IIT Roorkee
-IIT Guwahati
-GITAM Institute of Technology
-National Institute of Technology, [NIT] Surathkal
-Punjab Engineering College University of Technology, [PEC] Chandigarh
-Visvesvaraya National Institute of Technology, [VNIT] Nagpur
-Malaviya National Institute of Technology, [MNIT] Jaipur
-Dr. BR Ambedkar National Institute of Technology, [NIT] Jalandhar
-SRM University, Chennai
-National Institute of Technology, Hamirpur [NIT Hamirpur]. .

You can get some help on this link:
https://iitism.ac.in/index.php/placement#phomem.

Programme offered by Rashtrasant Tukadoji Maharaj Nagpur is M.Tech and M.Tech in Geotechnology. To know about the fees you need to contact the college officials.