There are no such rules regarding the Government jobs examination, that the student who have cleared the 10th examination in multiple attempts aren't eligible. So you are eligible for any jobs on the basis of 10th qualification. Apart from this, I would recommend you to study further and you can do great job positions after your graduation or 10+2.

For more information regarding the Government job examination in India consider the link below:

https://competition.careers360.com/articles/government-jobs

I hope this helps. Wish you a great day!