Here I am Giving Some of the Good Core Sectors Companies list which are Offering Good Jobs for EEE Students :

Core Jobs in Private Sector;

Bharat Sanchar Nigam Limited
Bharat Airtel Limited
IBM
Reliance Power
Infosys Technologies Limited
Wipro
Mahindra Satyam
Hewlett Packard India Limited
HCL Info-systems Limited
Reliance Communications
LG Electronics Limited
Videocon Industries Ltd
Panasonic
Siemens
Samsung India Limited
Mahanagar Telecom Nigam Limited
Redington India Limited
Cognizant Technology Solutions
Qualcomm
Accenture , etc

Core jobs in Government Sector;

Bharat Heavy Electricals Limited
Bharat Electronics Limited
National Thermal Power Corporation
Steel Authority of India Limited
Power Grid
ECIL
Indian Space Research Organization

After Completing B. Tech (EEE) you Can Get into These Sectors :-

Power Generation Sector

Product Designing Sector

Industrial Maintenance Sector

You can get in to it Sector by Learning Some Extra Computer Courses.

Electronics Sector