The correct answer is: A. to ask him
The sentence “It is no use to ask him” means that there is no point in asking him something because he is too busy to answer. The other options are incorrect because they do not make sense in the context of the sentence.
Option B, “asking him,” is incorrect because it is a gerund phrase. Gerund phrases are used as nouns, and in this case, it would mean that “asking him” is the thing that is no use. This does not make sense in the context of the sentence.
Option C, “that you ask him,” is incorrect because it is a that-clause. That-clauses are used as subjects or objects, and in this case, it would mean that “that you ask him” is the thing that is no use. This does not make sense in the context of the sentence.
Option D, “if you asked him,” is incorrect because it is an if-clause. If-clauses are used to express conditions, and in this case, it would mean that “if you asked him” is the condition that is no use. This does not make sense in the context of the sentence.