Hello, I know how you feel although I haven’t had the same experience. You are ready to work hard for the next time. It’s a great and tough decision to take and I wish you luck with that. Main thing is be confident that you can achieve.
So let me tell you what I do when it comes to exams.
BITSAT is, as you already know, online multiple choice exam.
You need to focus more on what you are strong for a few days and check any errors and mistakes you might have done in your exams. There are many practice materials for BITSAT, JEE. Just take one from somewhere and start solving them. After completing one complete test paper or in some, chapters, check your answers with the solutions provided. Try to find out where you have gone mistaken. There might be some cases where you may feel that you’re right and the solution might be wrong. In that case, go to the lecturer or teacher and ask them about it. After you get to find the errors, just note them down and try to solve them after you know the solution. Do it for every test paper or chapter you complete.
As you are saying that you might have screwed up at the time part, put yourself a timer and sit somewhere where you are not disturbed. Try going to a near library, if you want and can. Compete with time in your practice tests and that will help. About the online test thing, initially practice solving questions, then think of competing with timing. Then go to online exams, there are some trials available on the internet.