Make correction on the following incorrect sentences:

They all rejected that idea of the Captain's.

= They all rejected the captain's idea."

In formal English, the conjunction "as" is used to introduce a clause or a phrase that indicates a comparison or the manner in which something is done. In this sentence, "as in the old days" describes how the evening was spent, implying "in the way it was done in the old days."

Conversely, "like" is primarily used as a preposition to mean "similar to" or "in the manner of," and is typically followed by a noun, pronoun, or noun phrase. While "like" is often used informally in place of "as" or "as if," it is generally considered incorrect in standard written English when introducing a clause or an adverbial phrase of comparison.

For example:

    
• Incorrect: She sings like she is a professional.
    
• Correct: She sings as if she is a professional.
    
• Correct: She sings like a professional. (Here, 'like' is a preposition followed by a noun phrase 'a professional'.)

Therefore, "as in the old days" is the grammatically correct and more formal choice for this context.

The definite article "the" is required before "Oxford of the East" because it functions as a specific and unique title or epithet for Dhaka University. When a common noun (like "Oxford" used metaphorically) is made specific by an "of" phrase (like "of the East"), the definite article "the" is typically used to indicate that specificity. In this context, "Oxford of the East" refers to a singular, well-defined entity or comparison, highlighting Dhaka University's reputation and academic standing in the region, analogous to how Oxford University is perceived in the West.

The original sentence contains a common grammatical error known as a dangling participle or dangling modifier. A participial phrase or other introductory phrase is said to "dangle" when the noun it describes is not clearly stated in the sentence, or when it modifies a word other than the one intended.

In the sentence "Walking down the road, a bus hit Mr. Khan," the participial phrase "Walking down the road" incorrectly seems to modify "a bus." Logically, it is Mr. Khan who was walking down the road, not the bus.

To correct a dangling modifier, you can:

    
• Change the main clause so its subject is the noun that the modifier describes. (e.g., "Walking down the road, Mr. Khan was hit by a bus.")
    
• Rewrite the participial phrase as a subordinate clause with its own subject. (e.g., "While Mr. Khan was walking down the road, a bus hit him.")

The corrected sentence "Walking down the road, Mr. Khan was hit by a bus" makes it clear that Mr. Khan is the one performing the action of walking, thereby resolving the ambiguity and correcting the dangling modifier.

He was accused of a crime he did not commit. 

This boy is good at mathematics.