Embedded Systems/VLSI

Hi,
There would be limited or no degree in VLSI, you must take MS in Electronics Engineering and specialize in VLSI. Whenever you apply you must check the program structure and tracks they offer. These are some of the well known in your desired area -
Stockholm University, Lulea University, Royal Institute of Technology , Linnaeus University and Linkoping University in Sweden
University of Waterloo, University of Toronto, University of British Columbia and McGill University in Canada
Please visit the university websites for more information. Hope this helped.

BEL, CDAC and NIELIT are leading public sector firms. Besides chip manufacturers like Intel, Cypress, Texas Instruments etc recruit VLSI qualifieds. Register yourself with job portals. Read Employment News and leading national dailies. Entrepreunership opportunities do exist in this domain. Membership of professional associations and contacts with alumni will also benefit. You also hae opportunities for pursuing higher education. Opportunities also exist in academic sector.

As we are mechanical we can't expect any placement from campus. There wont be much placements ,but the will come companies. We should try outside only.

Netaji Subhas Institute of Technology (NSIT)
YMCA University of Science and Technology (YMCA UST)
Indian Institute of Technology, Delhi (IITD)
If you are open for other states then many good institutes and colleges are available.

Yes it is a good choice, you can go for it. However if you target an IIT than it is the best thing for you. Start preparation for GATE with your full efficiency if you get a rank within 1500 you have a fair chance to get admission in IITs.