If you did not get the seat in the first round of the counselling then there is a hope for the seat allottment in the second round only if the seats are vacant after the first round of the counselling. You have obtained 376 marks and I would like tell you that the cutoff marks for the west bengal state quota seats were 349 in the previous year. So the cutoff marks have increased to 30-40% and that can be the reason that you did not get any seat in the govt. institute. In the second round go through the list of the vacant seats, if any, released by the admission committee and then go for the further counselling.

Hey.
The cut off for admission in government colleges in West Bengal under the State quota for the SC category in the previous year 2018 was a rank of 122666 and a score of 349 marks.
The cut off changes each year due to several factors like level of difficulty or level of Competition etc. This year as the paper was easier the cut off based on marks will be higher than before.
Considering this your rank needs to be better than the previous year last rank  to have a fair chance of Admission here.
You can use the link below to check the previous year trends.
https://www.google.com/amp/s/medicine.careers360.com/articles/neet-cutoff-west-bengal/amp
Best of luck.

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