As you want to get the details of government jobs after B.Tech in Electronics Engineering so here it is for you:

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

Some of the companies who regularly recruit electrical engineers are listed below.

Power Grid Corporation of India Limited (PGCIL)
Bharat Electronics Limited (BEL)
National Thermal Power Corporation (NTPC)
Bharat Heavy Electricals Limited (BHEL)
Steel Authority of India Limited (SAIL)
Oil and Natural Gas Corporation (ONGC)
Coal India Limited(CIL)

You can give the exam of IES of UPSC

Here are the few details of that exam:

Important Dates:
DATE OF NOTIFICATION:- 22.03.2014 (SATURDAY)
LAST DATE FOR RECEIPT OF APPLICATIONS:- 21.04.2014 (WEDNESDAY)
DATE OF COMMENCEMENT OF EXAM:- 20.06.2014 (FRIDAY)
DURATION OF EXAM:- 03 DAYS

Categories of which recruitment is made through the Examination
i. Civil Engineering
ii. Mechanical Engineering
iii. Electrical Engineering
iv. Electronics & Tele-communication Engineering

Scheme of Examination:
Paper I (Objective type)
General Ability Test
(Part A: General English)
(Part B: General Studies)
200 Marks

Papers II & III (Objective type):
Civil Engineering/Mechanical Engineering/Electrical Engineering/Electronics & Tele-Communication Engineering
200 Marks for each paper

Papers IV & V(Conventional Type):
Civil Engineering/Mechanical Engineering/Electrical Engineering/Electronics & Tele-communication Engineering
200 Marks for each paper

Total marks for written Examination:
1000 Marks

Personality Test:
200 Marks