Based on the current NEET 2025 eligibility criteria and the general guidelines, here's how your situation would likely be considered:

The primary requirement for NEET eligibility concerning your Class 12th subjects is that you must have passed with Physics, Chemistry, and Biology/Biotechnology as core subjects, along with English. The minimum percentage in PCB (Physics, Chemistry, and Biology taken together) is also a crucial factor, which is generally 50% for the unreserved category, 40% for OBC/SC/ST, and 45% for PwD candidates.

You mentioned scoring 51% in PCB with grace marks in Physics. Grace marks are generally considered part of your final score. If your total percentage in PCB is 51% after including the grace marks, you currently meet the minimum percentage requirement for the general category.

Regarding the "one sitting" guideline, this usually refers to passing the Class 12th or equivalent examination in one attempt. Appearing for a betterment exam in only one subject (Physics, in your case) after having passed the overall Class 12th examination is generally not considered a break from the "one sitting" rule for NEET eligibility. The purpose of betterment exams is to improve your score in specific subjects, and it's a provision offered by many boards.