Hello student as per eligibility criteria yes you're eligible in GATE and if you'll score good marks in GATE you can get job on the basis of that.

ELIGIBILITY - Candidates must have passed or appearing graduation in engineering/technology 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