Electronics and Communication Engineering

The scope of big data/ analytics is generating immense data everyday that get unmanageable over time.
Passion for coding is definitely a primary requirement for a data scientist or big data analyst at any level.
Btw, coding will be a very common practice 40 years down the line.
Work experience surely matters in the Masters courses of Business Analytics to make your profile stand out, to check the real-world credibility of your skills.
It should always be there regardless of the course.
If you do big data and want to do analysis then yes you would be a data analyst and progress from there. It all boils down to which field you want to specialize in. Job opportunities aren't an issue if you are well prepared and know all the major concepts and have a great project portfolio to show.

The best part of being an Electronic and telecommunication engineering is that you have plenty of options. You will be eligible for core electronics companies, software companies, telecom companies and in some cases electo-mechanical and production companies too.
Software companies- TCS, Infosys,IBM etc.
Telecom companies such as Tata communication ,vodaphone,huawai etc.
Production companies such as Tata motors,Denso etc.
Embedded system and VLSI related jobs are too good options. WIPRO,Tata,Intel etc are places where you can try.
If you are interested in research then you can prepare for GATE. And meanwhile you can join as an JRF in DRDO,CSIR etc. Make sure you get couple of research papers published in good journals.