Although the document verification has been gone through and you have been selected for the job, it is advisable to have the details updated. Approach the HR personnel and show them the supporting documents. Explain the error which you made and request them to update the correct details in their record. The other subjects may or may not be relevant to the particular post you applied for and got. Yet, it may make a difference later if those subjects are relevant to some other similar but higher-paying position. It may also be important later, when you switch jobs and, say, the next employer checks with this employer details of your application.
It is always best to be upfront and honest at the outset in letting the employer know the mistakes made in a job application. Never give any kind of misleading data or incorrect/incomplete facts, in this case, the subjects you studied and appeared for in the Class 10 exam. In case you have not yet started on the job, communicate the information to them. Ideally, visit the office personally and submit a photocopy of the relevant document again (if required, it should be a self-attested one), with a cover letter explaining the error and take along the original as well to show as proof.
When you make a commitment, you create hope. When you keep a commitment you create trust! ~ John C. Maxwell