The correct answers are The cat is hiding under the sofa. and The cat is sitting between the sofa and the lamp.

Here is why the other options give away the cat's disguise:

• You need two items (or a plural noun) to use between. A cat cannot sleep "between the rug," but it could sleep "between the rug and the wall."

• The preposition is next to, not just "next". So, it should be "next to the television."