No child … have drawn that picture.

Analyze the question: The sentence is "No child ____ have drawn that picture." We need a modal verb that works with "have + past participle" (drawn) and fits the meaning.

Explain the concept: When a modal verb is followed by "have + past participle," it refers to the past. Here we are talking about something that already happened (the drawing of the picture). The sentence expresses a judgment that it was impossible, or very unlikely, for a child to have done something so good.

• can have / will have: "Can have" is not normally used this way in standard English for past possibility. "Will have" expresses a prediction or assumption (e.g., "He will have arrived by now") and does not suit the meaning here.
• may have: This expresses possibility ("A child may have drawn it"). In the negative with "No child," it doesn't make sense, because "No child may have drawn" is awkward and doesn't convey impossibility.
• could have: This is used for past ability or possibility. "No child could have drawn that picture" means it was not possible for any child to have drawn it, which is the intended idea.

Solution: "No child could have drawn that picture." This is grammatically correct and has the right meaning: the picture is too skilled to be a child's work.

Answer: C. could

Tip: When you see "have + past participle" after a blank, think of perfect modals such as could have, should have, would have, might have, must have. Words like "can" and "will" rarely fit in this past-time structure. For impossibility in the past, use could not have / no one could have.