Select the most appropriate option to fill in the blank.

Despite repeated demands from the authorities, the investigator refused to ______ the location of the hidden documents.

The correct answer is give away.

Explanation:
To determine the correct phrasal verb for the blank, we need to analyze the context of the sentence and understand the meanings of each option.

Sentence Context:
The sentence describes a situation where authorities are demanding information, but the investigator refuses to reveal or disclose the secret location of the hidden documents.

Analysis of Options:
1. give away: Means to reveal, disclose, or expose secret information. Refusing to give away the location means refusing to disclose where the documents are hidden. This fits the context perfectly.
2. hand in: Means to submit or turn in something (e.g., handing in an assignment or a report).
3. take off: Means to remove clothing, to depart from the ground (aircraft), or to rapidly gain popularity/success.
4. break out: Means to escape from confinement (like prison) or for something sudden (like a war or disease) to begin.

Therefore, give away is the most appropriate phrasal verb to complete the sentence meaningfully and grammatically.