359 would not be a promising score to secure a seat in a government college since you belong to OBC category I must say, on the basis of previous cut off observation you'll notice you need to score above 480 least to secure a seat. 

Also, on the basis of this score I will say you should apply for counselling and wait till mop up round . 

~Good luck.

Dear aspirant,

According to previous years cut off analysis which is subjective as cut off ranks change every year,depending upon level of difficulty of neet this year,no of candidates applying to neet this year to govt colleges through karnataka state quota from obc category also rank fallout pattern is entirely different from previous year so nothing can be predicted with 100% sureity, keeping in mind above factors i am mentioning below list of colleges in which you have probable chances of getting into with their closing ranks and marks according to previous year(i.e. 2018)through state quota:

• Kodagu Institute of Medical Sciences, Madikeri: cr=125523 marks=347
• Karwar Institute of Medical Sciences, Karwar:cr=119459 marks=352
• Chamarajanagar Institute of Medical Sciences, Chamarajanagar:cr=126087 marks=346
• Gadag Institute of Medical Sciences, Gadag:cr=129691 marks=343
• Gulbarga Institute of Medical Sciences, Kalaburagi:cr=124890 marks=347
• ESIC Medical College, Gulbarga:cr=116953 marks=355
• ESI Post Graduate Institute of Medical Sciences and Research, Bangalore:cr=126416 marks=346
• Raichur Institute of Medical Sciences, Raichur:cr=134520 marks=338
• Bidar Institute of Medical Sciences, Bidar:cr=123860 marks=348

Hope this helps

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