Hey there, Congratulations on scoring 587 marks in NEET. These marks are very good for you and it will help you a lot while taking admission in good colleges. You can take admission in very good colleges at these marks. I would suggest you check for government colleges, semi-government colleges, and even some good private colleges too in your state as you can get a seat in reserved quota too. Even you can check for some colleges in Delhi too and that will be better for that. 

 I would personally suggest you use the NEET Predictor and explore various colleges according to your category and home state quota and choose the best one for you as this college will be your future lifeline.

https://medicine.careers360.com/neet-college-predictor?icn=neet-clgpd_landing-page&ici=prediction-section_c360-home

Hey.
Here is a list of various government medical college in Jharkhand and their respective cut offs in the previous year for admission under the State quota for the general category. Considering your rank you seem to have a fair chance.

1. Patliputra Medical College, Dhanbad

Rank- 15,716 Marks- 532

2. Rajendra Institute of Medical Sciences, Ranchi

Rank-  9319 Marks-558

3. M G M Medical College, Jamshedpur

Rank- 13755 Marks- 539

Hey Rishikant.

See the marks u have scored is enough for u to bag a seat in the govt college under ur state quota to pursue ur higher studies in the field of ur interest under MBBS courses. I m providing u a link for ur help

https://www.google.com/url?sa=t&source=web&rct=j&url=https://medicine.careers360.com/articles/neet-cut-off/amp&ved=2ahUKEwih1JbL6obiAhUZ6nMBHccvDzEQFjAKegQIARAB&usg=AOvVaw13ncSIsRF6_r3F1MyqcLzL&ampcf=1

Ask if any query. Good luck

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