Hello,
Unfortunately, failing in 3 subjects especially in class 9th won't lead to promotion in class 10th. 10th and 12th are the most crucial classs of every student's life and failure in 3 subjects in class 9th shows you are not prepared to face class 10th due to lack of understanding of the subject. In case you fail, most schools offer retest and on the basis of that the promotion is decided.
I hope this helps,
Thank you
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