The word "there" is used when we're talking about the existence of something — especially in structures like:
"There is / There are..."
"Can there be..."
"Will there be..."
So in the sentence:
"What types of sciences can there be in this institute?"
—we're asking what types can exist in this place. "There" is needed because it's tied to the verb "be" used to express existence or possibility.
Now compare that with:
"What could be the best?"
In this sentence, we’re not talking about what exists, but about which option is the best. So we’re identifying or choosing — not expressing existence — which means we don’t need "there."
In simplest terms:
Use "there" when talking about what can exist or is present.
"What courses could there be?"
Don't use "there" when talking about what is best, is true, or is chosen.
"What could be the best option?"