GATE

Hello Zeeshan,
There is a huge competition in GATE and its completely uncertain to get a seat until/unless you are so talented.
But when it comes to GRE, there are thousands of options available. If not admitted to one university, you can get in another but same is not the case with GATE.
Better choose GRE and try for scholarship.
Also, if you think you can crack GATE then go for it.

Eligibility for GATE examination is a B.Tech/BE/AMIE or M.Sc. After 12th you can appear for JEE.

Eligibility is a Bachelors degree in Engineering/Technology (4 years after 10+2 or 3 years after B.Sc./Diploma in Engineering/ Technology) and those who are in the final year of such programs.

It is not mandatory to take admission, if your scores are excellent in GATE, then you can get PSU sector's jobs easily.

Only after completion of AMIE Section A and B you will be treated equivalent to graduation degree. Therefore, you can apply for M.Tech on completion of Section A & B of AMIE.

Check the sample papers of GATE and then see how much more preparation you require. If you need coaching, you may join it and prepare well. More you study regularly, better your chances of getting good score.

You can check the below mentioned college predictor: https://www.shiksha.com/engineering/course/m-tech-shri-guru-gobind-singhji-institute-of-engineering-and-technology-sggsie-t-nanded-193366

GATE is examination for M.Tech studies in India. Most of universities abroad use GRE score for admission in their MS program. You may plan to appear in both GATE & GRE for wider choices for doing postgraduate degree in Mechanical engineering after B.Tech.