GATE

Yes, GATE exam is compulsory for all the students who wants to go for higher studies after B.Tech and through GATE exam score, you can get the college.

GATE Online Application Processing System (GOAPS) is open now. You may submit your application at http://gate.iitg.ac.in/

Hello Shubham,
It depends upon your interest. If you are happy with the package, and if do not wish to go for further study, then you may not give the exam. It totally depends upon your choice.

Students with B.Tech Automobile Engineering degree from recognized engineering colleges or universities are eligible to appearing GATE.

Hello Aniket,
You can get the syllables for GATE exam in the link provided just select your branch and download the syllabus:
http://www.gate.iitg.ac.in/?page_id=55

Eligibity criteria for appearing on GATE is that candidate must have completed 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. Even if you had backs, you are eligible to appear for GATE.

Based on your profile you are eligible to seek admission in some German universities.

They mostly rely on GRE, based on GRE score, it's good to join MS industrial engineering. They prefer GRE and their test for MS in Germany.

Firstly, clear all your concepts from the subjects in B.Tech EEE and stay focused. Go for Made easy (GATE coaching institute) take the test series or classes on weekend or online lectures that would be suitable for you. The questions in GATE are based on the logic which can be cracked by through in-depth study.
Good luck.