Hello Rahul,
Careers360 provides you with the eligibility criterion for neet have a look https://medicine.careers360.com/articles/neet-eligibility-criteria
Goodluck

Yes you can appear as per DOB. SINCE you will be 17 by the end of 2019. All the best.

Eligibility Criteria based on Age:
The minimum age for the candidate must have completed17 years of age at the time of admission (or) should complete the age on or before 31st December of the year of the candidates admission to the 1st year MBBS/BDS Course.

For reference, please visit this link below,

https://neet2019.net/eligibility-criteria-2019/

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