West Bengal

IIT Kharagpur is the best. Then there is Jadavpur University and NIT, Durgapur after it.

No, you can apply without the West Bengal domicile too, you are not only eligible for Jadavpur University but also for other universities through WBJEE exam.

Hello Aryan,
I appreciate your interest in pursuing engineering from best colleges. To help you with choosing colleges, kindly refer to the link below for more information:
https://goo.gl/EloIdg
You can check the reviews about the various colleges on the link above. I hope this answers your question. If you have any further questions, kindly revert.

Hi Tanmoy,
If I talk about MBA, there are a good amount of college with list of reputation. So, I suggest you to go for: Army Institute of Management, Indian Institute Of Social Welfare And Business Management, Netaji Subhash Engineering College, Pailan College of Management & Technology (MBA Division), George College (Department of Management Studies), Camellia School of Business Management, and many more. You can choose from it as per your convenience.
Good Luck.

IISBWM and IBMR are known colleges in Kolkata. You can check the below link-
https://www.shiksha.com/mba/colleges/part-time-mba-colleges-in-kolkata

Yes, but you need to join integrated courses like BBA + MBA, which is generally of 5 years duration. If you want to do MBA, then you need to either complete your graduation or be in the final year to be eligible for the various MBA entrance exams like CAT, XAT, etc.
After scoring well in these exams, you need to perform well in the interview rounds, then you will be given admission into the respective college.
I hope it helps.

Hi Rakhi,
It is better to go with full time course. You can study BBA at Kolkata as it will fetch you something great.
All the best.