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Hello,
Thanks for Asking.
Yes, after qualifying GATE exam, you can enter into the teaching field.
The benefits of qualifying Gate Exam:
* Pursue M.Tech or M.Sc from India or abroad.
* If your GATE score is low but you want to do M.Tech or MS from a reputed institute, you can work as an assistant to the professor for a year or two. This way you can get a really useful recommendation (LOR) necessary for pursuing higher studies abroad.
* If your score is high, get into an IIM (Indian Institute of Management) B-school through GATE Score
* You can teach at GATE coaching classes (Part-time or Full-time).
* Go for recruitment in PSUs such as BHEL, IOC, NTPC, BPCL, BARC, HPCL, etc.
Check How to get a Job in PSUs: https://medium.com/@Pooja1J/how-to-get-a-job-in-psu-government-job-a1038f7ce536#.wk4k0djvp
I hope it will help you.
Best of Luck.

Hello Amit,
Which university will give you admissions is hard to answer. Every university has different admission requirements and with different selection process. Some universities are more selective while some are not. Admissions and selection will also vary with a student's profile. If your overall application package is good, a competitive university may consider you even with so many backlogs. I will advice you decide what to study and visit the university websites. Check the admission requirements, email them and write to them. Universities like University of Melbourne and Sydney in Australia are competitive. There are many countries in Europe, you need to specify the country.