Fill in the blanks with the most appropriate option:-

I fell asleep while I ________ my favourite show.

was watching

The most appropriate option to fill in the blanks is was watching.

The sentence "I fell asleep while I was watching my favorite show" is in the past continuous tense, which is used to talk about an action that was happening when something else happened. The other options are not as appropriate.

• Is watching is the present continuous tense, which is used to talk about an action that is happening now. This does not make sense in the context of the sentence, as the speaker is talking about an action that happened in the past.
• Has watched is the present perfect tense, which is used to talk about an action that started in the past and is still happening now. This does not make sense in the context of the sentence, as the speaker is talking about an action that happened in the past and is not still happening now.
• Watched is the simple past tense, which is used to talk about an action that happened in the past and is finished. This does not make sense in the context of the sentence, as the speaker is talking about an action that was happening when something else happened.