Go for BITSAT, period.
Why? Because it will be easier to prepare for in the short span of time you have. You'll just have to brush up what you studied for JEE Mains, and you're good to go.
The only thing more will be the few extra topics in organic chemistry, and English. But that can be easily taken care of.
In case JEE Advance, you'll have to rigorously revise and master concepts to the point of exhaustion. Because the level of questions in Advance will be well beyond Jee mains.

Ohh no problem.Do not worry.If you feel you will get qualified in JEE Mains and feel you have the caliber to cope up the mistakes you did in mains then obviously go for Advanced.If not like you are scared and all go for BITSAT.But do remember BITS is costly a bit in comparision to IIT's,NIT's and IIIT's.Firstly you need to practise doing questions with speed and accuracy.Go through the syllabus of BITSAT and firstly cover all the concepts because most of them you would have covered for Mains preparation.Then write BITSAT mock tests.All the best

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