To be very honest, core companies are very less in INDIA. So chances of getting into core is very tough. iNTEL, Qualcomn etc are recruiting from Top IITs and NITs only. Mostly they prefer mtech(vlsi).

There are very few core like dxcorr,sankalp semiconductor etc recruits btech students from state level govt engg and top private college. But the no is very less. Competition is very tough and you have to have crystal clear conceps in subject like Analog, Digital, Device,CKT theory.

For IT jobs

There are plenty of oppurtunities. But here ur electronics skill will be of less use. If you have good communication skill and know basics of any programming languaage and computer engg fundamentals , you will get job in TCS,CTS,WIPRO, INFYOSYS etc.

For Telecomm jobs

Companies like ericsonn,cisco,nokia recruits telecomm enhineer. For this you need clear concepts in communication engg and networking.

For PSU jobs

You have to prepare very well for Gate and secure a brilliant rank(below 100). There are some vacancies in PSU like IOCL, ECIL,NTPC,AAI,BSNL etc .

Hope it helps