While both are correct, I found an interesting discussion about 'watched' and 'was watching' on a site: "These are both absolutely fine. They convey a slightly different tone that I'm finding it difficult to explain. 'was watching' places the emphasis more on the time (i.e. it happened while she was watching) whereas 'watched' places the emphasis a little more on that activity (the watching). I instinctively prefer 'watched', but it depends on the context and the tone of the piece." https://forum.wordreference.com/threads/was-watching-watched.3137427/ Hope it helps. Have a great day.

Hi! I would like to say "Nah" to Fausto's. A is absolutely wrong. We never say that. You couldn't be aware of his ongoing activity while you were sleeping. You just noticed the fact that he had watched TV.

Both answers are potentially correct. We use A if we are viewing the action as ongoing in the past, we use B if we are viewing the action as having been completed in the past. This is called “aspect”. The question doesn’t contain enough context to rule out one or the other. What textbook are you using? Is it by a major English textbook publisher like Cambridge University Press?

You will hear native speakers say both. However, I believe B is technically correct. I think that it's more common to say the was doing something part of the sentence first, followed by the simple past: I was sleeping while Jack watched TV. That sounds more natural to me.

They are both not wrong but I think you would not use "was" twice in this instance.