Colleges in Kolkata

You may get some good colleges but not sure that it would be a govt college. With this rank, your ward may opt for the desired branch in some college of West Bengal.

Yes, many B-schools gives seat of MBA without entrance, like Chandigarh Business School does not take an entrance test, Chitkara Business School, etc. But their main campuses take entrance test.

Yes you can definitely get an admission.

Hi Deb,
Fees has not been disclosed by the college officials on their website. It is advisable to get in touch with the college administration for detailed information on the same.
Regards

Check the list of all B.Tech in Instrumentation Technology colleges/institutes in India listed on Shiksha at the link provided below. Get all information related to admissions, fees, courses, placements, reviews & more on B.Tech in Instrumentation Technology colleges in India to help you decide which college you should be targeting for B.Tech in Instrumentation Technology admissions in India. https://www.shiksha.com/b-tech/colleges/b-tech-in-instrumentation-technology-colleges-india.

Please elaborate your question as which Vivekananda college are you talking about, Delhi University's Vivekananda or anyone else?

https://www.shiksha.com/b-tech/resources/wbjee-college-predictor
Please go through this college predictor link I am sharing to know about it.
Good luck.