In the following question, a sentence is given in Direct speech. Out of the four alternatives, select the one which best expresses the same sentence in Indirect speech and mark your answer. The teacher said, "Nobody can solve the problem."

Introduction / Context:
This question tests knowledge of converting Direct speech into Indirect or Reported speech. The original sentence contains a reporting verb in the past tense (said) and a reported clause with the modal can. The candidate must choose the transformation that preserves meaning while following standard backshifting rules for modals in reported speech.

Given Data / Assumptions:

• Direct speech: The teacher said, Nobody can solve the problem.
• Reporting verb: said, in simple past.
• Reported clause: Nobody can solve the problem.
• Options contain various combinations of nobody, somebody, can, could, and should.

Concept / Approach:
When converting from Direct to Indirect speech with a past tense reporting verb, modals like can usually change to their past forms, such as could. We also remove quotation marks and introduce a conjunction such as that. The negative and subject remain the same unless there is a change in meaning. Therefore can in the original clause should become could in reported speech, while nobody remains unchanged. The approach is to apply backshifting systematically without altering the core message that no person is able to solve the problem.

Step-by-Step Solution:
Step 1: Drop the quotation marks and introduce that after the reporting verb: The teacher said that ...Step 2: Keep the subject and negative as they are, since nobody already expresses universal impossibility.Step 3: Change the modal can to could because the reporting verb said is in the past tense.Step 4: The reported clause becomes that nobody could solve the problem.Step 5: The final sentence is: The teacher said that nobody could solve the problem, which matches option D.

Verification / Alternative check:
Compare each option quickly with the rules. Option A keeps can instead of changing it to could, which may be acceptable only when the fact is permanently true, but exam patterns usually prefer backshifting when the reporting verb is past. Option B introduces should, which changes the meaning from ability to obligation. Option C replaces nobody with somebody, which is the complete opposite of the original statement. Therefore only option D accurately follows the rule and preserves the original sense of universal inability to solve the problem.

Why Other Options Are Wrong:
Option A: The teacher said that nobody can solve the problem fails to show backshift of the modal, and many exam keys treat this as incomplete transformation. Option B: That nobody should solve the problem switches the meaning from cannot to should not, implying prohibition rather than inability. Option C: That somebody can solve the problem directly contradicts the original that nobody can. These options either break grammatical rules or distort the message.

Common Pitfalls:
A frequent mistake is to ignore backshifting and simply copy can into indirect speech after a past reporting verb. Another pitfall is confusion between can and should in exam choices, especially when students rush and focus only on the presence of a modal. To avoid mistakes, remember the general pattern: can to could, may to might, will to would when reporting with a past tense verb, unless the statement describes a permanent universal truth like two and two make four. Here, the problem is a specific one, so backshifting to could is expected.

Final Answer:
The correct Indirect speech form is The teacher said that nobody could solve the problem.