Hello,

If you have flunked the mathematics paper of 10th grade but still passed overall, it should not raise significant concerns for becoming an assistant professor in a government college more so because you have already completed your graduation. For teaching positions, especially assistant professor, your emphasis rests on your higher education qualification, at least a bachelor's degree, or a master's degree in the same stream from which you have acquired it, and any other eligibility like NET/SET, which is a must for the post of assistant professor.

This doesn't really have much of a direct bearing on performance in 10th grade, except perhaps in the event of a failure in one of the subjects. More importantly, your performance in the subject area you have opted for as your area of specialization, the experience you have garnered from research activities, and whether or not you are qualified for relevant exams or interviews. So long as you can clear all the requirements and employability criteria, this should not be a barrier to assistant professorship.