Fill in the blanks with the most appropriate option:-

I __________ my homework since 10:30 pm last night.

have been doing

The correct option to fill in the blanks is have been doing.

The sentence "I have been doing my homework since 10:30 pm last night" is in the present perfect continuous tense, which is used to describe an action that started in the past and is still happening now. The other options are not as appropriate.

• Have done is the present perfect tense of the verb "to do". This does not make sense in the context of the sentence, as the action of doing homework is still happening now.
• Did is the simple past tense of the verb "to do". This does not make sense in the context of the sentence, as the action of doing homework did not start and end at 10:30 pm last night.
• Was doing is the past continuous tense of the verb "to do". This does not make sense in the context of the sentence, as the action of doing homework is still happening now.