This question tests your understanding of modal verbs in English, which are used to express permission, ability, obligation, or possibility. Let's analyze the sentence step by step.

Step 1: Analyze the first blank.
The first part is a question asking for permission: "_______ I come in?". The most appropriate modal verb for politely asking for permission is May.

Step 2: Analyze the second blank.
The response to the request is "No, you ______". This is a refusal of permission. The correct negative form to refuse permission is can't (cannot). While "may not" is also grammatically correct for refusing permission, "can't" is more common in everyday spoken English in this context.

Step 3: Analyze the third blank.
The reason for the refusal is given: "I am very busy now. I ______ write a report." This expresses a strong obligation or necessity due to the current situation. The modal verb that expresses a strong obligation is must.

Final Answer: Therefore, the correct option to fill the blanks is may/can't/must.

The complete sentence reads: "May I come in? No, you can't. I am very busy now. I must write a report."

Related Topic: Modal Verbs

Modal verbs are auxiliary verbs that modify the main verb to express mood or tense. The key modal verbs are:

• May: Used to ask for or give permission (e.g., May I leave?) or to express possibility (e.g., It may rain).
• Can/Can't (Cannot): Used to express ability (e.g., I can swim) or permission (e.g., You can't go out). "Can" for permission is less formal than "may".
• Must: Used to express strong obligation or necessity (e.g., I must finish my homework). Its negative form, "mustn't", is used to express prohibition (e.g., You mustn't smoke here).

Choosing the right modal verb depends on the context and what you want to express—permission, ability, obligation, or possibility.

Related Formulae (Rules)

While there are no mathematical formulae, here are the grammatical rules applied:

• Asking Permission: Use "May I...?" or the less formal "Can I...?"
• Refusing Permission: Use "No, you can't/may not."
• Expressing Obligation: Use "must" for a personal or strong sense of duty.