Hey ,

If it's not a compulsion I would suggest you not to loose a year to re study 11th . If you have some sort of compartmental exam facility please go for the same and clear your maths paper .
As you have mentioned you are quite a good student having your concepts wise on your subjects . So you need not worry about marks as whenever you go for any top colleges all that matters is your 12th marks not 11th . So there is very less probability of your 11th affecting your future or career in long run . Even if you do not score enough in 12th , you still have a chance to crack the entrance examinations of various colleges that actually are the basis of selection .
It's not about repeating 11th , but about loosing a year , a fine crucial year . So I would suggest, if you could talk about your problems to your school and ask them to promote you to higher grade then that would be advantageous for you . But if it's not possible and you repeat class 11th then there won't be any problem regarding the same for your future .
After all it's the boards that matter .
Make sure you are well thorough throw the concepts, as 12th is all about application based from 11th concepts .
You do not even carry your 11th marksheet to any interview . So there is no question of people knowing about your 11th repeat .

Possibly post a application for re-examination so that you can clear your paper .

All the best , study hard you will definitely have a bright future . For any further information or queries feel free to ask .

Thank you .

Many of us have been there at that point once in our lives. So you cannot be judged if you cannot appear for an exam or if you have to repeat the exams. We can understand it must have been a very tough call to repeat the class inspite of being a high scorer. Leaving that aside, your future depends on the path you choose. Now that many Intergrated programmes have come up, it will help you cope up with the time lost. If you are a Commerce student, you can pick up CA or CS which will help you in the long run. Then you have B.Com LLB, BBA, CMA. You might feel that you are lagging when compared to your friends but when you become successful it doesn't matter how long it took you to be there.