hi,

as for 2021 gate notification which is conducts by IIT  bombay, students of third year of b.tech course or the final year of b.tech course or students who has already completed the bachelor of technology course in any discipline are eligible to apply. however the m.sc or masters degree in relevant discipline graduates or students of final years of masters degree course are also eligible to apply.

candidates of any stream of btech may chose any of the engineering stream , so you can take cse or ece or both of the course since from 2021 gate, candidates are eligible to apply for two gate papers in one application.

follow the below link to know in details:

https://gate.iitb.ac.in/brochure.php

Hello student yes you can appear in GATE entrance examination from any stream if you've pursued your bachelor degree in EEE then yes you can appear GATE examination in CSE or ECE.

All you need to fulfill the eligibility criteria of GATE.

Eligibility - Candidates must passed or appearing

B.tech from any recognized University or Master's degree in any relevant science subject.

For more details refer to the link mentioned below - https://www.google.com/amp/s/engineering.careers360.com/articles/gate-eligibility-criteria/amp

Feel free to comment if you've any doubt

Good luck