In the question below, four sentences have been given. Out of four sentences, one sentence is error-free. Find out which of the following sentence is error-free. If all the given sentences have errors, then choose option ‘None is correct’ as the answer choice.

To identify the error-free sentence, let us analyze each option step-by-step:

1. "Despite his best efforts, the conclusion he arrived lacked coherence and failed to address the premise."
Error: The verb "arrived" requires the preposition "at" when referring to reaching a conclusion. It should be "the conclusion he arrived at lacked coherence...". Thus, this sentence is grammatically incorrect.

2. "Scarcely had the rebels laid down arms when fresh skirmishes erupted near the northern border."
Grammar Rules Applied:
- The correlative conjunction pair "Scarcely... when" is used correctly.
- When "scarcely" begins a sentence, subjective-auxiliary inversion is required ("had the rebels laid down" instead of "the rebels had laid down"), which is correctly followed here.
- "Laid" is the correct past participle form of the transitive verb "lay" (meaning to put down), and it has the direct object "arms".
Therefore, this sentence is grammatically correct and error-free.

3. "Whosoever they appoint for the post must demonstrates both integrity and strategic foresight."
Error: The modal verb "must" must be followed by the base form of the verb ("demonstrate"), not the singular verb form ("demonstrates"). Thus, this sentence is grammatically incorrect.

4. "Not until the investigation was completed we knew the extent of the financial discrepancies."
Error: When a sentence begins with a negative adverbial phrase like "Not until...", the main clause must undergo inversion. It should read: "Not until the investigation was completed did we know...". Thus, this sentence is grammatically incorrect.

Therefore, the only error-free sentence is: "Scarcely had the rebels laid down arms when fresh skirmishes erupted near the northern border."