The sentence is in the **Present Continuous Tense (Active Voice)**. The passive structure is **Object + is/am/are + being + Past Participle (V3) + by + Subject**. "The mouse" is the object. Hence, "is being chased" is correct. Option (b) is in the past tense. Options (c) and (d) use incorrect tenses.

The original sentence is in the **Past Continuous Tense (Active Voice)**. To change it to Passive Voice, the structure is **Object + was/were + being + Past Participle (V3) + by + Subject**. Here, "The lecture" is the object, and "the students" is the subject. Therefore, "was being listened to" is the correct verb form. Option (b) is incorrect because it uses the present tense. Options (c) and (d) use the wrong tense and form.

The sentence is in the **Simple Past Tense**. The passive structure is **Object + was/were + Past Participle (V3) + by + Subject**. The object is "me," which becomes "I" in the subject position of the passive sentence. "Kept" is the past participle of "keep." Therefore, "I was kept awake..." is correct. Options (b) and (c) use the wrong tense. Option (d) incorrectly changes the meaning.

This is a question in the **Present Continuous Tense**. For questions starting with "Who," the passive form starts with **"By whom"**. The structure is **By whom + is/am/are + Object + being + Past Participle (V3) + ?**. "A noise" is the singular object. Therefore, "By whom is a noise being made?" is the correct structure.

For imperative sentences starting with "Let," the passive structure is **Let + Object + be + Past Participle (V3) + by + Agent**. Here, "the task" is the object and "him" is the agent. Therefore, "Let the task be finished by him" is the correct passive construction.

The sentence is in the **Future Perfect Tense**. The passive voice structure is **Object + will + not + have been + Past Participle (V3) + by + Subject**. "The book" is the object. Thus, "will not have been read" is the correct verb construction. Option (b) incorrectly uses "would". Options (c) and (d) are in the wrong tense.

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.