Electrical Engineering

You need to qualify GATE, and with your GATE score you can apply in NTPC or BHEL or in other PSUs.

BITS Pilani is Tier I engineering college equivalent to legacy IITs. I will recommend that you opt for BITS Pilani for an excellent career and growth opportunities.

Yes, electrical engineering along with mechanical engineering and civil engineering are the core branches at JECRC, Jaipur. We do have core companies coming for campus placements.
Along with electrical engineering, mechanical engineering and civil engineering, our college also has information technology, electronic and communication engineering and computer science engineering.

All three engineering options are equally good for career in the filed of engineering. Scope of various engineering branches varies from time to time. Currently job opportunities are as follows in order of precedence: Computer Science, Electronics and Electrical engineering.

If you want to pursue physics then you should pursue B.Sc (Hons) in physics instead of B.Tech. After completing your Bachelor's degree in physics you will be eligible for IAS too.

ECE has more scope than electrical engineering.

MIT - Pune is good.