As you want to get the details of career in government sector after B.Tech (Electronics and Telecommunication) so here it is for you:

Central Government Jobs after B. Tech in Electronics and Communication:
The main employers of these professionals are

Indian Telecom Sector
BSNL
MTNL
Post and Telegraph Department
Defense
All India Radio
Civil Aviation Department
National Physical Laboratory
Bharat Electronics Limited
Oil and Natural Gas Corporation Ltd (ONGC)
Bharath Electricals limited
Steel Authority of India Limited
Banking Sector
Air force etc

Government Sector Jobs after B.Tech in Electronics and Communication:
The fields where they can join are:

Civil services
Defense
Indian Railways
Indian Air Force and many more
BSNL
Doordarshan (Prasarbharthi), etc
VSSC/ISRO

Private Sector Jobs after B.Tech in Electronics and Communication:
It is possible for students to get jobs such as:

ASIC Design Engineer
ASIC Engineer Trainee
Business Analyst, IT
Developer
Jr. Embedded Engineer
Jr. Software Engineer (Trainee)
Network Support Engineer
Programmer
Software Engineer -.Net
Test / Quality Assurance (QA) Engineer (Computer Software)

Some of the areas where graduates of Electronics and Communication can get good jobs are given below:

Hardware Manufacturing
Home Appliance and VLSI design
Power sector
Software Engineering/IT
Telecommunication