I see. If I have a singular word "There is a cat in the room." Is "there's" more natural than "there is"? or a plural noun: "There are cats in the room." Is "There're" more natural than "There are." In such cases too. I am asking because I was completing exercises in "English Grammar in Context" by Simon Clarke. There are no short forms.
Well, then:
Conversationally, many or most English speakers often say
there's instead of
there are simply because it rolls off the tongue much more easily.
It's a shortcut. That doesn't make it strictly grammatical, and it doesn't make
there are incorrect or unnatural.
So in conversation you can say either "There's a computer and a TV" or "There are a computer and a TV." Both are fine.
Personally, I go both ways conversationally, depending on how careful I'm being at the moment, and in writing I use
there are.
It's you're choice, as long as you know the difference. (And it looks like you do.)
Since your exercise doesn't offer contractions (short forms), I'd use
are, not
is.