Dear Anshu,

Case1:

You have made a big mistake as you are realising it. Wrong spelling of of your name will cost you. Yes you can give the paper on the request of Principal and Director of your school,and also you have to carry application with you in examination hall in qhiwh it has been mentioned that by mistake your name is misprinted or wrong written, All these for your Boards.

Case 2:

Yes you can give the exam of Jee mains if your name is wrongly mentioned in admit card, because many times in exam Invisilator don't check the spelling of names they just see the photos of your. And match with Your identity card, but at the time of Admission you have to face many trouble, may be you can't take admission in the college. After all it all depends on your luck.

And don't forget to write application to the board committee about this issue. They will provide you the solution to this problem and help you so you can't face any problems in future, may be they make new admit card, but they extra charge you for making it.

Hope for the best.