M.Tech

Distance education is not allowed in engineering but you have to attain the practical. For example B.E is the part time course whose classes are scheduled in the evening and practical work on the weekends. For more information you can visit any IIT website for eligibility criteria. You can found it on GATE section. Many information is already available in previous answer.All the best.

To pursue M.Tech in any stream you need to have a B.E/B.Tech degree

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SRM
VIT
AMITY
JAYPEE

Thapar university is one of the highly reputed engineering college in terms of education level and placement record
You need to have good GATE score to get admission in M. Tech

M.tech is not only for teaching purpose. It will enrich your career in your study field. And you too will get good job in any good core company with good package.

You can choose Ireland or Germany.
Best of luck.