Hello dear. 

I think electronics and instrumentation field is one of finest domain to work in core engineering. After pursuing this course one can have career in following domain-

• Petrochemical is one of the most preffered industry by the instrumentation engineer.
• Embedded system is also one good option, as in EIE we will study electronics also and embedded is covered in that.
• Automation industry is also one of the good option .
• Defence industry requires instrumentation engineer.
• Automotive embedded and sensor depends solely on instrumentation department.
• Masters in networking is one of the best option as industry requires networking+control engineer.

Also there are various options for further studies after graduation in EIE. So one can get various opportunities in core engineering in n number of domains.

Hope this might have helped….