Hello Hariom, 

To be honest the mistake in your 12th boards admit card is a major problem that really needs to be solved first. To address the major problems I recommend you to mail at the official email-id of the exam you are giving. Send them a photo or screenshot of your admit card by marking your problem along with a valid proof which justifies your problem. If you get a valid reply to that mail then you can take the print out of that mail along with you in the exam so as to save yourself from any misunderstandings during the exam between you and invigilator. 

If you can't get any as such reply then only thing possible is to take valid id cards along with you as proof so as to justify your problem to invigilator during the exam but mailing should be your first priority.

That should be the first thing to do and after that contact with your school principal or any other higher authorities and let them know about your problem and seek help.

Hope this helps.