Hello Asha,
As far my knowledge yes you can appear for BITs.
To take admission in BITs you need to give BITSAT which an entrance exam for the program you selected to do.
And now we talk about 12th class improvement exam. You will apply for it after the final board results are out and admission this year in any college will done through the marks scored by you this year.
If you fill the form you will give improvement exam I guess next year. So you have 1 full year for it. And improvement exam is basically for improving your marks in 12th class which you can do simultaneously with your college studies.

So right now don't think much about it. Focus on your exam and focus on clearing BITSAT exam for admission purpose.

I hope this helps you.
All the best !!

BITS Pilani

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