Hi Aditya,
Hope you are doing good. Coming to your question... Yes you are very much eligible to give one paper exam (in biology) from open school after you have passed your 12th with PCM (Physics-Chemistry-Mathematics) from Bihar Board.
However, if you are planning this to write your NEET, it won't be any problem, true. But at the time of document verification certain colleges might not accept it.
Hope this helps.
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