The underlined part is grammatically incorrect. 

• The first sentence is in the simple present tense. 
  
  It is talking about how a person cannot explain (something) right then. He told the other person to discuss it the next day. 
  
  
• The use of the word 'tomorrow' suggests that the second sentence will be in the simple future tense. 

• The given sentence is simple past tense.

• The past tense is used to refer to actions that were completed in a time period before the present time.

• In the Simple Past, the process of performing the action is not important. What matters is that the action was completed in the past.

• The action may have been in the recent past or a long time ago.

• Here, the first part of the sentence is in the past tense, so, the latter one should also be in the past tense.

• Thus, “would be finished before” is the best-suited one.

• The expression "one of the" is generally preceded by a plural noun/pronoun. And a singular verb is used for it.
  • E.g. :-
    1. One of our teachers is good.
    2. One of my friends is ill.

• And when the mentioned expression is preceded by "who/which/that". It takes plural verb after it. i.e. "one of the + plural noun/pronoun + who/which/that + plural verb".
  • E.g. :- Gandhiji is one of the famous leaders who are famous all over the world.

• Thus, 'One of my teachers has' is the best-suited one.

• The correct sentence should be :- 'One of my teachers has received the Sahitya Akademi award.'

The underlined part is grammatically incorrect. 

• Let's first see the meanings of the words:
  
  Scrutinising = examine or inspect closely and thoroughly.
  
  Revising = reread work done previously to improve one's knowledge of a subject, typically to prepare for an examination.
  
  Recapitulating = summarize and state again the main points of.
  
  Recollecting = remember (something); call to mind.
  
  
• The person is preparing for the exams that are going to be held soon. Thus, he must be 'revising' all the questions. 
  
  
• Also, for the noun questions, we need an adjective to describe them. Thus, 'difficult' is the correct word. 
  
  
• The correct preposition will be 'for' which will show the purpose of revising all the questions. 

The underlined part is grammatically incorrect. The linking verb 'is' requires a subject. "Make a map" cannot be considered as a subject (as we have used the verb 'make' here). We can change it to the infinitive structure and in that way, we will have our subject. Thus, change 'make a map' to "to make a map". We can place the phrase 'by definition' in the middle as well. Other options do not fit in the sentence grammatically (structurally). 
Hence, option A is the correct answer. 

The underlined part is grammatically incorrect.

• Here, the subject is "Picking". It is a singular subject.
  
• Thus, we will use a singular verb in place of "take" (a plural verb).
  
• Also, the article before "week" should be "a" (and not "the") as the sentence is telling us how much time the whole process of picking the fruits takes. And it takes around one week. 
  
• Also, after the modal "will", we take the base form of the verb.
  
• Thus, the underlined part must be replaced with "takes about a week".

The underlined part is grammatically incorrect.

• The correct preposition that should come after the verb "treat" is "to" for the above sentence. 
  
  
• Because the construction treat + someone + to usually means to pay for someone else's food, drink, or entertainment.
  
  e.g. I'll treat you to ice cream.
  
  
• Thus, replace the underlined part with "treated us to".