4. (Whose, Who's) book is that on my desk?

short answer whose

Explanation:

Whose" is a possessive form meaning "of whom" or "belonging to who" and is used in the following way:

Whose books are these?

The men, whose lives were ruined, claimed compensation from the government.

I do not know whose shoes smell worst.

If you are in any doubt, consider whether the who's/whose you are using can be replaced by who is or who has. If it can, then you need "who is", if not you will need "whose".

Whose

Explanation:

The reason it is whose is because if you do who's it is "who is book"