A transitive verb is a verb with a direct object.  That means that there is some action, and some object is taking the action.  In this case, the object is the book and the verb is “to find”, or “found.”

The only one of these sentences that can have a transitive verb is c. 

“The book has been found” is in Present Perfect Continuous tense/aspect. It has an implied/assumed Subject, "you" or "he/she."  If you paraphrase with an explicit Subject, it will look like this.

You found the book.

In this paraphrase, it is a little more obvious that the verb is transitive and the object of the transitive verb is “book.” With the implied/assumed Subject, the verb “find” is changed to “has been found” in the perfective aspect of the sentence. Don't get this confused with Passive Voice, which is constructed like this:

• auxiliary be form + -ing participle form main verb + by (optional)

• "Found" is the past and the -ing particple form the main verb "find".

An implied/assumed Subject means there is no directly designated "actor" doing the finding, the actor is "you." The verb "find" must always be transitive. You might note that "laugh" may be intransitive or transitive.