I failed in 12th Maths but overall pass with 79%.Can I eligible for government exams...???
Yes, you are eligible for many government exams, but it depends on, for which exam are you aiming to crack.
Your Situation
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You failed in Mathematics in Class 12
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But your overall result is "PASS" with 79% marks
This suggests that:
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Your board has declared you as "pass" overall , even though you did not clear one subject (likely due to grace marks or best-of-five type rules)
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You might have to clear the failed subject later , depending on the exam
You are eligible for SSC, Railways, State PSC exams, Police /constable Just after 12th and if you will be done with your graduation UPSC, Banking Exam. But if you are aiming for NDA or JEE Maths is a mandatory subject. You must pass it separately (compartment/re-exam) .
