Hello,
it would be better to meet personally to your intermediate institute and enquiry them. I think they will help you out better that you have to show your mark sheets or they will provide another marksheet where all the subjects are enlisted. they can tell that accurately.
About the admission in UPSEE, as long as you have a proof that you have passed your 10+2 successively there won't be any problem. you are qualified your 12th and you have your grades. So, better to apply for it and give a your best shot to clear it in one go.
Hope it helps!
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