Fill in the Blanks

Here a characteristic of a noun (i.e. Akbar) is discussed. Now, neither the word 'great starts with a vowel sound, nor it is the case of superlative degree. Thus, option 2 ans 3 are eliminated. Also, Akbar was one of the greatest kings. So, article 'a' is the correct usage.

A letter is written 'by' a person 'with' a pen/pencil 'on' a piece of paper and 'to' some other person.

Here the subject 'he' is a singular noun, and none other than option 2 is singular. Hence, option 2.

Here the top dicussed here belongs to mountains. And for possession we use preposition 'for'.

Here the actual subject is officers, not one.

Simple past is to be used when we talk about an event that happened at a particular time in the past. So, 'took' will be used.

"have been selected" 

The sentence expresses a hypothetical or contrary-to-fact condition, which requires the subjunctive mood. Were it possible is an inverted form of If it were possible. In formal English and conditional structures, were is used for all subjects in the subjunctive, even singular ones like it.

'Should' is used in conditional clauses when you are talking about things that might happen, seen in present/future unreal conditional sentences.

This is the case of present indefinite tense. As the sentence mentions about a 'general fact' of present, so we should use the first form of the verb without any helping verb. Thus, 'becomes' is the right choice.

Whenever the third form of the verb is followed by an infinitive (i.e. to), we use first form of the verb after it. Hence, 'had hoped to go'.

This is the case of proper prepositional usage. 'Walked towards' means to move in the direction of somebody.

This is the case of verb form usage. Whenever two incidents happen one after the other, and that too in the past, we use 'had' along with 'third form of the verb' for the former/prior action. Thus, 'had rung' is the right choice. This is the case of 'past perfect tense'.

in this situation when he was trying to sell the car but couldnt so "could not sell"stands as the right choice. 

This is the case of prepositional usage. We simply 'guess' something, rather than guessing about, with or of. So, no preposition is required.