Correct the following sentences:

He announced that he will take the plane to Dhaka.

= He announced that he would take the plane to Dhaka.

They all rejected that idea of the Captain's.

= They all rejected the captain's idea."

He knew Mr. Khan stopped smoking five years before. = He had known Mr. Khan had stopped smoking for five years.

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.

On arriving in Dhaka, his friends meet him at the station. = When he arrived in Dhaka, his friends met him at the station

He said that the earth moves round the sun.

In reported speech, when the direct speech expresses a universal truth, a scientific fact, or a habitual action, the tense of the verb in the reported clause does not change, regardless of the tense of the reporting verb (e.g., 'said').

Even though the reporting verb "said" is in the past tense, the fact that "the earth moves round the sun" is an eternal truth. Therefore, its tense remains in the simple present tense ('moves') in the indirect speech.