The sentence is in the **Simple Past Tense**. The passive voice structure is **Object + was/were + Past Participle (V3) + by + Subject**. The object is "the national anthem" and the past participle of "sing" is "sung". Therefore, "The national anthem was sung..." is correct.

This is a Wh-question in the **Simple Past Tense**. The passive structure is **Wh-word + was/were + Object + Past Participle (V3) + by + Subject + ?**. The object is "such a letter". The auxiliary verb "was" must come before the object in a question. Hence, "Why was such a letter written..." is the correct form.

The active sentence is an **imperative sentence** starting with "Please," which indicates a request. The standard passive form for such requests is **"You are requested to + V1 + Object"**. Therefore, "You are requested to shut the door" is the most appropriate answer. While (b) and (c) are grammatically possible passive forms for a command, the presence of "Please" makes (a) the best choice.

**Rule**: In a complex sentence with two clauses, only the clause with a transitive verb and an object can be changed to passive voice. Here, the main clause 'The smugglers did not realize' has no object. The subordinate clause 'the police were watching them' can be passivized. - **Correct Answer (a)**: The main clause remains active. The subordinate clause, which is in the Past Continuous Tense, is changed to passive: 'they were being watched by the police'. - **Incorrect Answer (b)**: Passivizing the main clause ('It was not realized') is possible but creates a more cumbersome sentence than option (a). - **Incorrect Answer (c)**: 'were not realized' is an incorrect passive construction for the verb 'realize' in this context. - **Incorrect Answer (d)**: This incorrectly changes the tense of the subordinate clause to Past Perfect.

**Rule**: For a sentence in the Simple Past Tense, the passive voice structure is **Object + was/were + V3 + by + Subject**. - **Correct Answer (a)**: The object 'The Mayor's speech' becomes the subject. Since it's singular, 'was' is used. The adverb 'loudly' is correctly placed before the past participle 'cheered'. - **Incorrect Answer (b)**: This incorrectly changes the tense to Simple Present. - **Incorrect Answer (c)**: This incorrectly changes the tense to Present Perfect. - **Incorrect Answer (d)**: This incorrectly changes the tense to Past Continuous.

**Rule**: To convert a Future Perfect Tense sentence to passive voice, the structure is **Object + will/shall + have been + V3 + by + Subject**. - **Correct Answer (a)**: The object 'him' becomes the subject 'He'. The verb form 'will have been acquitted' is the correct passive construction for the Future Perfect Tense. - **Incorrect Answer (b)**: This incorrectly changes the tense to Future Simple. - **Incorrect Answer (c)**: 'would' is an incorrect modal change. - **Incorrect Answer (d)**: This incorrectly changes the tense to Present Perfect.

**Rule**: For a Present Perfect Tense sentence, the passive structure is **Object + has/have + been + V3**. The agent ('by them') is often omitted when it is vague or obvious from the context. - **Correct Answer (d)**: The object 'the flight' becomes the subject. Since it is singular, 'has' is used, followed by 'been' and the past participle 'cancelled'. Omitting 'by them' is natural here. - **Incorrect Answer (a)**: This incorrectly changes the tense to Past Perfect. - **Incorrect Answer (b)**: This incorrectly changes the tense to Simple Past. - **Incorrect Answer (c)**: This incorrectly changes the tense to Simple Present.

**Rule**: Imperative sentences that make a request (often starting with 'Please' or 'Kindly') are converted into passive voice using the phrase **'You are requested to'** followed by the base form of the verb. - **Correct Answer (a)**: The word 'Kindly' indicates a request. Therefore, the passive form 'You are requested to...' is the most appropriate structure. - **Incorrect Answer (b)**: The original sentence is a request, not an order. - **Incorrect Answer (c)**: While 'Let' can be used for imperatives, 'You are requested to' is a better fit for polite requests starting with 'Kindly'. - **Incorrect Answer (d)**: 'Should' suggests advice or obligation, which does not accurately reflect the tone of the request.

**Rule**: For interrogative sentences with modal verbs, the passive structure is **Modal verb + object + be + V3 + by + subject?** The modal verb does not change its position at the start of the sentence. - **Correct Answer (a)**: The modal 'Can' remains at the beginning. The object 'this problem' follows. Then 'be' and the past participle 'solved' are used. The agent 'by us' is correctly placed at the end. - **Incorrect Answer (b)**: 'Could' is a different modal and changes the meaning from ability to possibility. - **Incorrect Answer (c)**: While grammatically correct, it omits the agent 'by us' which was present in the original sentence. - **Incorrect Answer (d)**: This is a statement, not a question. The interrogative structure has been lost.

**Rule**: A sentence in the Present Perfect Tense is converted to passive voice using **Object + has/have + been + V3**. The negative 'No one' in the active voice becomes 'never' in the passive voice. - **Correct Answer (a)**: The object 'this mountain' becomes the subject. The verb 'has never been climbed' correctly reflects the negative meaning and the Present Perfect Tense in passive form. The agent 'by no one' is omitted. - **Incorrect Answer (b)**: This incorrectly changes the tense to Simple Past and uses a double negative ('never' and 'no one'), which is grammatically incorrect. - **Incorrect Answer (c)**: This incorrectly changes the tense to Simple Present. - **Incorrect Answer (d)**: This incorrectly changes the tense to Past Perfect.