Rule: Simple Past Tense for Completed Actions. This rule is used for actions that started and finished at a specific time in the past. The sentence describes a completed event (finishing the project). 'Managed' correctly places this action in the past. Option (b) 'had managed' is the past perfect tense, which is incorrect as it would require another past action to relate to (e.g., 'By the time the supervisor checked, the team had managed...'). Option (c) 'was managing' is the past continuous tense, suggesting an ongoing action in the past, which doesn't fit the context of a completed project. Option (d) 'manages' is in the simple present tense, which is incorrect for a past event.

For interrogative sentences starting with "Who", the passive form begins with **"By whom"**. The active sentence is in the **Simple Past Tense**. The passive structure for a question is **Wh-word + was/were + Object + Past Participle (V3) + ?**. Thus, "By whom was this article written?" is the correct form. Option (b) is incorrect as "who" is the subjective case. Options (c) and (d) are grammatically awkward and less standard.

The sentence is in the **Present Continuous Tense**. The passive structure is **Object + is/am/are + being + Past Participle (V3) + by + Subject**. The object "a new bridge" is singular, so we use "is". The past participle of "build" is "built". Thus, "A new bridge is being built..." is correct.

The active sentence is in the **Present Perfect Tense**. The object is "me," which becomes "I" in the passive voice. The passive structure is **Object + have/has + been + Past Participle (V3)**. The agent "by them" is often omitted when it is clear or unimportant. Option (d) is the most common and natural passive form. Option (a) is also grammatically correct.

This is a **yes/no question** in the **Simple Past Tense**. The passive structure for such a question is **Was/Were + Object + Past Participle (V3) + by + Subject + ?**. "Her duty" is the object. Thus, "Was her duty done by her?" is the correct form. The other options use incorrect auxiliary verbs and tenses.

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.