Yes you can.Upper age limit for the exam is 25 years.Since you have passed 10+2 exam in Science stream you can apply for NEET.To fulfill the Neet eligibility candidate must pass in Physics, Chemistry, Biology /Biotechnology and English individually in the 12 boards exam.

General candidates must acquire mininum 50% 

Sc /St candidates require 40 % mininum. 

OBC  candidates require 45% minimum in the qualifying exam.

Your graduate degree will not affect in your application for the exam.

Thank you.