Electrical and Electronics Engineering

First, you need to decide in which field you want to make a career.
Academic:
To become a professor, you need to first qualify Master's degree and later Ph.D degree.
Research:
There are a vast number of research jobs available for different engineering. scholars. If one has interest to build a career in it then one can start a career with Jr/Sr. Research Fellow at well-known institute like CSIR, DRDO, different. IITs, NITs, etc. ISRO, DRDO, etc. recruits young scholar as scientists also. There is a written test followed by series of interview.
Engineer job:
There are many jobs available in PSUs like Maharatna, Navaratna and Miniratna companies like GAIL, SAIL, NTPC, ONGC, etc. Notifications generally come in Nov. or Feb. month. Many of them require GATE score.
IES, Indian Engineering exam is considered one of the best in the government sector.
BSNL, MTNL, Electric board, etc. also recruits EEE scholars.
Similar way, in private sectors also, many jobs are available for engineers either in core field or IT sector depends on your interest.
Non-Technical Job:
In India, probably the most reputed job is considered as Indian civil services. If one is interested in the administrative job rather than core field then CSE is the best option. It is one of the most difficult exams also.