Yes, after 10th, you can definitely update your DOB in aadhar card using your 10th marksheet. But if want to change the DOB in your aadhar card before you pass out your 10th class, you can do so by physically visiting any of the aadhar center and asking them to do so. They will ask you for the DOB proof, as a proof of DOB, you can provide your birth certificate.
Hope this helps.
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