When we use "give" (and many other ditransitive verbs) in a sentence, we can say either say "Keiko gave her flowers" (noun object) or "Keiko gave flowers to her" (prepositional object). That implies that we should be able to either of these questions: "Who did Keiko give flowers?"and "Who did Keiko give flowers to?" However, speaking purely based on my intuition, having grown up in the US (midwest + california dialects), the first question sounds very strange and potentially confusing.
So, is the question without "to" actually "wrong" (I mean, is there a commonly accepted grammar rule forbidding it), is it just less common, or is my intuition off?