Hello,
The opening rank and closing rank in JEE Mains admission refers to the maximum and minimum rank which were scored by students for a particular branch in a particular college through JEE Mains.

For example, the opening rank for last year for NIT delhi last year was 1562, which means that the seats at NIT delhi started filling with rank of 1562.
The closing rank for NIT delhi was 16042 which means that the rank was the last rank which was secured by students for admission. No admission were done beyond that rank in JOSAA counseling.

Closing rank in JEE Mains can be termed as the cutoff rank for a particular Institute.

Please visit this link for detailed JEE Mains cutoff

Hope it helps

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