Hello aspirant

Yes you can appear for re exam from open university.

NIOS will be the best choice. NIOS is National Institute of Open Schooling.  The Institute is government recognised and nios marks are accepted in any college or university of India.

You must fill the form and appear for reexam .

After getting passed you can apply for your further studies.

Many students who fail in class xi or class class xii gjve retest through nios and then they get next year's admission in june.