The correct answer is option (C):
suspected of wrong doing
The idiom "under a cloud" means that someone or something is viewed with suspicion or that they are experiencing a period of disgrace or disfavor. This often implies that they are suspected of having done something wrong.
Let's look at the other options:
* "in the shade" simply means sheltered from the sun and has no relation to the idiom.
* "wet" refers to a physical state, and has no metaphorical relationship.
* "hopeful" describes an emotion or expectation and is the opposite of the implied meaning of being under suspicion.
Therefore, "suspected of wrong doing" is the only option that accurately captures the meaning of the idiom "under a cloud." This implies a stain on a person's reputation due to suspicion of wrongdoing, which aligns perfectly with the idiom's meaning.