As you want to apply for government jobs after completing B. Tech Electronic and Communication Engineering so yeas you can apply for many jobs here I am giving you information about same:

Some Government Companies where you can apply:
BSNL
MTNL
Doordarshan
VSSC
ISRO
All India Radio

Some more Departments for that you can apply:
Civil Service
Defense

Railways:
Indian Railway Service of Signal Engineers
Indian Railway Stores Service
Indian Inspection Service
Indian Naval Armament Service
Indian Ordnance Factories Service (IOFS)
Electrical and Mechanical Engineers, a branch in the Indian Army
Wireless Planning and Co-ordination Wing
Indian Navy
Indian Supply Service
Indian Telecommunication Service
Junior Telecom Officer (Group B)

Another option for candidates is to write exams conducted by various public sector banks.

The candidates can even look for teaching jobs in different government colleges.

Some other Job options for that you can apply:
Indian Engineering Service (IES)
Indian Telephone Industries, BSNL/MTNL
Semiconductor, Chip Design-Industries (Motorola, IBM, HP, STM, Philips, IT etc)
Indian Oil Corporation Ltd. (HPCL/BPCL/IPCL)
Oil and Natural Gas Corporation Limited (ONGC)
Civil Aviation Department
Steel Authority of Indian Limited (SAIL)
Power Sector (NTPC/NHPC Ltd.)
Bharat Electronics Limited
Indian Railways
Indus tan Aeronautics Limited (ISRO)
Software Industries (ALL MNC’S) (HAL)
Teaching/Research
Government Sector