Hi Swarnava,
There are no specific eligibility criteria for the GRE / GMAT Exam that deters one from giving the exam had the candidate already done his / her M. Tech. Anyone can register for both GRE and GMAT Exam and there is also no prescribed age limit as of now.
However, I would like to enlighten you with the fact that GRE / GMAT scores are valid for a period of 5 years. So if you're planning to settle abroad, you can give the exam as early as you can so as to avoid any last minute discrepancies. But even if you want to give it after completing your M. Tech, that is totally fine.
Hope this was helpful.
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