In this reported speech question, the original direct sentence is The teacher said, "Tell me students, what have you learnt from the lectures this week", and you must choose the indirect form that correctly reports the teacher's question to the students, including appropriate changes in tense and time expression. Select the option that best follows the rules of reporting questions in English.

Introduction / Context:
This question tests how to convert a direct question with a present perfect tense and a time expression into indirect speech. The original sentence shows a teacher addressing students directly and asking them what they have learnt from lectures this week. In reported speech, we need to change the pronouns, adjust the tense from present perfect to past perfect, and shift the time word this week to that week. We also have to choose a suitable reporting verb such as asked and decide whether to keep a question structure or use an infinitive construction.

Given Data / Assumptions:

• Direct speech: The teacher said, "Tell me students, what have you learnt from the lectures this week".
• The teacher is making a request and a question at the same time.
• The reporting verb said is in the past.
• The embedded question uses present perfect have you learnt and the time expression this week.

Concept / Approach:
When reporting a request combined with a question, the polite imperative tell me can be transformed into an infinitive phrase to tell him, while the actual question part what have you learnt becomes a that clause with a backshifted tense. Present perfect in direct speech normally becomes past perfect in indirect speech when the reporting verb is in the past. Time expressions also need adjustment: this week becomes that week. The most complete and accurate indirect sentence will therefore use asked the students to tell him and will change have learnt to had learnt and this week to that week.

Step-by-Step Solution:
First, identify the reporting clause The teacher said and the full direct utterance Tell me students, what have you learnt from the lectures this week. Second, choose an appropriate reporting verb for a request and question, such as asked, and include the audience the students. Third, change the imperative tell me into an infinitive structure to tell him, since the teacher is now referred to in the third person. Fourth, convert the question what have you learnt into an affirmative clause what they had learnt, changing the pronoun you to they and the tense from have learnt to had learnt. Fifth, adjust this week to that week to reflect the shift in time from the original situation to the reporting context.

Verification / Alternative check:
To verify, imagine converting the chosen indirect sentence back into direct speech. From The teacher asked the students to tell him what they had learnt from the lectures that week you can reconstruct The teacher said, "Tell me students, what have you learnt from the lectures this week". The change from had learnt back to have learnt and that week to this week follows the standard pattern. The use of asked and to tell reflects the teacher's polite request. This confirms that the selected option is the most complete and accurate representation of the original utterance.

Why Other Options Are Wrong:
Option A, The teacher asked the students what they learnt from the lectures that week, does not include the request element tell me and uses learnt instead of had learnt, which does not fully apply tense backshift from present perfect.

Option B, The teacher asked the students to tell him what they learnt from the lectures that week, includes the request but still uses learnt instead of had learnt, so it partially ignores the shift from have learnt to had learnt.

Option C, The teacher wanted to know what the students learnt from the lectures that week, changes the reporting verb to wanted to know and again fails to show the backshift to had learnt; it is also less precise about the original wording.

Common Pitfalls:
Learners often forget to change the present perfect to past perfect when reporting questions that refer to recent completed actions. Another common problem is overlooking the time expression this week and leaving it unchanged in reported speech, which does not reflect the shift in perspective. There is also a tendency to simplify complex utterances by dropping parts like tell me, but examination questions generally expect the more complete indirect form when it is offered among the options.

Final Answer:
The indirect sentence that correctly conveys the teacher's request and question, with proper tense and time changes, is The teacher asked the students to tell him what they had learnt from the lectures that week.