In Sentence I, the word "absence" is correctly used as a noun meaning the state of being away from a place or person. It fits the context perfectly.
In Sentence II, the word "absence" is again correctly used to indicate the lack or non-existence of something - in this case, concrete evidence. This usage is appropriate and grammatically sound.
In Sentence III, the plural form "absences" is correctly used to refer to multiple instances of being away or not present at school. The usage is both natural and correct.
All three sentences use the word "absence" appropriately in context and form.
Hence, option (e) is the answer.
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