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Hii Niladri,
Yes you can freely apply and give jee mains exam in2020.It doesn't matter whether you will give your bsc 1st year exam,you can leave that exam if you want that will not have any relations with jee mains exam.Just after qualifying jee you will need your original certificates pf 10+2,for any colleges through it.
Hope it will help.
Thankyou
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