Filling the gaps:

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.

He was accused of a crime he did not commit. 

This boy is good at mathematics.

In English grammar, the verb 'call' can be used in several ways, and its usage dictates whether a preposition is required. When 'call' means 'to telephone someone', it functions as a transitive verb and directly takes an object without any preposition. For example, one would say "Please call Mr. Khan" to mean telephoning him.

Conversely, if 'call' is used to mean 'to pay a brief visit to someone', it typically forms a phrasal verb with the preposition 'on', as in "to call on someone". For instance, "We will call on our neighbours tomorrow."

Given the structure "Please call – Mr. Khan tomorrow morning", the most common and grammatically appropriate interpretation is that Mr. Khan should be telephoned. Therefore, no preposition is needed in the blank, and the sentence correctly reads "Please call Mr. Khan tomorrow morning."