hi,

yes, it is a major problem to do m.tech after applying in different stream in gate and not eligible to apply for m.tech. some of the iits and nits do not allow b.tech ee to do m.tech on electronics engineering related stream. some of the best private college for m.tech on vlsi design:

vellore institute of technology

thapar institute of engineering and technology

srm institute of science and technology

ramaiah institute of technology

sastra university

amity school of engineering and technology