Yes, you are eligible for many government exams, but it depends on, for which exam are you aiming to crack.

Your Situation

• You failed in Mathematics in Class 12

• But your overall result is "PASS" with 79% marks

This suggests that:

• 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)

• 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) .