Hi Aspirant!
As per the information available, there are very few chances that you might get into trouble.
------)) Ultimately, you will be considered as the 12th class passed out student from the State Board only as you did not appear for the 12th exam in CBSE board and you do not have the marksheet/related documents for same.
>>> Also, if you only show the documents for the State Board only, then definitely there is no problem in that. And you will be given admission accordingly only on the basis of State Board exam marks.
Thankyou!
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