Which is the correct sentence:
- He goes to museum twice a week
- He goes to museum twice in a week
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The correct form is, "He goes to the museum twice a week." (Note the word "museum" requires an article before it in your example.) It answers the implied question, "How often does he go to the museum?" Answer: "Twice a week."
There is nothing inherently wrong with "twice in." For example, if you were emphasizing the frequency of his trips, you might say, "He went to the museum twice in one day." In that case, you are choosing to emphasize the frequency as unusual. If you were simply stating a fact, you would say, "He went to the museum twice a day." That is, he made it a regular (ordinary) habit of visiting the museum twice a day.