Answer:
The correct option is WHOSE.
Explanation:
Whose constitutes the possessive case of the pronoun who. It is used to indicate belonging or association with one person or thing. On the other hand, who’s represents the contraction of the words "who is" or "who has".
Bearing the above in mind, it could be said that the sentence provided would result as follow: WHOSE is the red book on the couch?
