Dear student,
You have not mentioned the that which exam or post you are talking about. So I will recommend you please mention the exam or post name so that we can help you accurately.
Now, if we talk in general, then yes you can apply for the admission or posts provided that at the time of document verification, your last semester exam will be over and also you can get marksheet before the time you have show the documents for the post or admission you are looking for.
Many exams have such eligibility criteria that even if you are appearing for final exam of the course you are pursuing, you can apply for the post and admission for which the criteria seems to have completion of that course.
I hope this information helps you.
All the very best.
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