The correct answer is option 2 i.e. at a cup.

1. The error lies in part 2 of the statement because of the wrong use of "Preposition".
2. We need to replace "At" with "Over" to make the statement grammatically correct.

Grammatical Concept:-

• Over is used to indicate the activity that accompanies something e.g., a discussion over a meal, a conversation over drinks.
• "Over a cup of coffee" is the correct use of the preposition here.
• The chosen option contains the ERROR hence, it will be the correct answer.

The correct sentence will be- We had a long discussion over a cup of coffee.

The correct answer is Option 1 i.e. I am insisting.

We need to replace "am insisting" with "Insist" to make the statement grammatically correct.

Grammatical concept:- 

• There is a list of verbs that can't be used in continuous form.
• Verb - Promise, Suggest, Apologise, Advise, Insist, Agree, Refuse etc.
• These verbs are used only in the simple or perfect form of the tense.
• The verb "insist" also belongs to this category hence we need to keep it in a simple form.

The correct sentence will be-  I insist that my decision should be followed by all the aspirants.

The correct answer is option 3, i.e. to finish quickly.

The given sentence in it's latter half tries to denote two actions, to answer accurately and to finish quickly.

The original sentence uses a quick finish in the comparison, which is a noun phrase.

The other part of the comparison is answer accurately, where "accurately" is an adverb modifying the verb "answer."

For proper parallelism, both sides of the comparison need to follow the same structure: a verb + adverb phrase.

Hence, the answer is to finish quickly.

The correct answer is option 1, i.e. a good deal of.

• The given sentence has an error in the underlined section because it makes incomplete sense.
• 'Good deal of' has been used in a singular sense to indicate an uncountable noun, which in this case is money.
• So, the sentence is incomplete because before 'good deal' we don't have an article (a/an/the) to indicate the singularity of the phrase.
• Hence, the correct answer is 'a good deal of'.

The correct answer is option 3, i.e. has effect some changes.

• 'Has effect' is an inaccurate way of putting together the words as the given sentence tries to talk about the probability of changes that might have occurred due to the new leadership in the party.
• The past form of the verb can indicate such a sense correctly. Hence, the correct form here would be to use 'effected'.

The correct answer is option 2, i.e. one of the best books.

• When we use the phrase 'one of the', we generally mean to distinguish one amongst many others.
• So, to indicate the many others in the sentence it is necessary to use a plural form, else it would be inaccurate.
• This is why the aforementioned option is the correct answer, because it uses the plural form 'books'.

The correct answer is option 1, i.e. for three days.

• 'Since' means 'because', but the context of the sentence doesn't try to say that the cousin has been ill because of three days.
• So, by using 'for' we are able to make proper sense because 'for' denotes the time-period during which the said illness have lasted.
• Hence, this option makes the whole sentence complete and accurate.

The correct answer is option 4,  i.e. In order for he.

• 'He' can only be used as the subject of a verb, but in this case the action (verb) is to be done by the object.
• Whenever we use a demonstrative pronoun to indicate the object of a verb we use 'him', 'her', 'their', etc.
• So, the correct form would be 'in order for him'.

The correct answer is option 2, i.e. carried out.

• 'Carried out' means to put into execution or to accomplish a given task.
• An 'order' also means a 'given task' that needs to be executed/accomplished.
• Which is why it is correct to use 'carried out' instead of any of the other given options because the others portray a different sense and altogether makes the statement inaccurate.

The correct answer is option 1 i.e. was able to meet.

As the first part of the sentence is in Past tense we have to keep the second part in the Past as well.

The only chosen option is in the past so it will be correct.

The correct sentence will be-

My recent London trip was really special because I was able to meet my nephew and his family after many years.