Hii

Yes ofcourse it is possible to prepare in 1 month if you are completely dedicated towards your studies and you focus on what you are studying.
You need not to leave the chance to appear in the exam. What can happen if you do not know a concept, some marks will be deducted and you will get a low scores. But what you will achieve will be an experience which will be helpfull for you in your future, so do appear in the exam.
Now coming to your preparations.
If your 12th syllabus is completely done, your half work is done. Now for 11th class course, take each and every formula and try to by heart these formulas and keep them handy for last time revision.
Once you are done with the formulas, try to implement them on the questions, Start with chapterwise question and keep on solving as many questions as you can.
Use the previous year papers to improve your confidence as well as preparation.
know well where to use which formula and yes make sure you know all the facts mentioned in the NCERT books.
Use a guide which will be published for BITS exams itself like we have The Pearson Complete Guide to the BITSAT. or any other guide which you can find easy to study.
Having all the formulas and facts on fingertips will surely help you in your exam.
Remember to keep on practicing as much as you can till the end and yes do not loose hope.

All the best.