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

State Government Jobs:
The candidate has to qualify state level competitive exams to get in to employment offered under the same. Those who pass the preliminary written test have to get through an interview.

Government Career:
They can enter into fields like

Civil services
Defense services
Indian Railways
Aviation industry and many more