See in general during the time of your admission you have submitted the documents and those are required for the registration in general. Now as you know that the registration are done in 9th/11th. So if you don't have birth certificate then no problem, as per law you can use your 10th registration certificate as a certificate of your age.

So if required you can submit it as a document.

I hope my answer helps. All the very best for your future endeavors!