What is the NEET-UG rank that is required to quality for MBBS course in this Institution?

if you want admission to prestigious colleges like in rs, RG kar or sskm medical college in Kolkata then you must be given to score in excess of 500 and if possible in excess of 520 out of 720
Sskm for example head cut off for 510 marks for the year 2018 in the neet examinations
what is most important is that you stop thinking about marks and try to maximize your potential in answering as many questions positively and minimising your negative marks in the examination for which you need to improve on your question selection and time management skills by a repeated mock examinations in the MCQ format
All the best hope it helps

Which institution are you referring to? Please mention it so that we can help you solve your query.

Usually to get admission in any of the Government College across India for MBBS the cutoffs are pretty high. Cut offs changes every year no doubt but usually it is above 590-600.