Electronics Engineering

Yes, you can go for GATE exam but you have to clear the cutoff to get admission in IIT, Bombay.

You can definitely get a decent job in Kolkata if you have the required skills. Electronics and instrumentation engineering do provide a lot of scope in both IT and non-IT sector. But remember one thing, don't be assured that a company will allow you to work only at one city. You may have to go at other places as well.

There is a wide difference between the fields you are talking about and you can study further in any branch you take up, I would suggest that choose a field of your interest. And yes if you wish to study abroad then definitely DJSCOE has an upper hand as it provides more exposure.
All the best.

Hello Alap,
If you really want to join automation industry after your degree, then it will really be helpful for you. Industries like Honeywell automation, Mitsubishi etc. Can give you a wonderful exposure. So, develop the skills add up these in your resume and keep going. Good luck.

You have already selected the course, which one is best is not the kind of question I guess.

Hello Manish,
Nowadays, GIMT is not on that level from where you can take good placements. Due to less admissions in engineering colleges in India, a number of colleges are unable to provide placement nowadays.