As we can say that ,
The correct word is filled in the above given sentence :-
When people around you are losing their heads, it is very difficult to remain serene. It needs a lot of patience.

Correct Option: A

As we can say that ,
The correct word is filled in the above given sentence :-
When people around you are losing their heads, it is very difficult to remain serene. It needs a lot of patience.
So , required answer will be option A .

As we can say that ,
Vague notion is a right choice. Imagination is in itself vague (unclear). While expressions cannot be vague. Theory is out of place for the context. Thoughts can be vague or unclear or unstable.
The correct word is filled in the above given sentence :-
I had a vague notion that the lady originally belonged to Scotland.

Correct Option: A

As we can say that ,
Vague notion is a right choice. Imagination is in itself vague (unclear). While expressions cannot be vague. Theory is out of place for the context. Thoughts can be vague or unclear or unstable.
The correct word is filled in the above given sentence :-
I had a vague notion that the lady originally belonged to Scotland.
Therefore , option A is required word .

As we can say that ,
‘dull of ’ and ‘dull for’ can be out rightly rejected as they do not fit well with the word ‘understanding’. ‘Dull in’ is correct. When we understand it enters --- in ---- our mind so with understand ‘in’ is used.
The correct word is filled in the above given sentence :-
No child is dull in understanding. One has to wait and provide proper guidance.

Correct Option: B

As we can say that ,
‘dull of ’ and ‘dull for’ can be out rightly rejected as they do not fit well with the word ‘understanding’. ‘Dull in’ is correct. When we understand it enters --- in ---- our mind so with understand ‘in’ is used.
The correct word is filled in the above given sentence :-
No child is dull in understanding. One has to wait and provide proper guidance.
So , required word will be option B .

As we know that ,
(d) is rejected because the word should suggest that the fact goes “in favour of ” the manager. If the profitability declines it would go against the manager. A good managet adds to the profitability. In other words, the profitability increases.
The correct word is filled in the above given sentence :-
The Director pointed out in favour of the manager that the profitability of the plant had increased since he had taken over.

Correct Option: B

As we know that ,
(d) is rejected because the word should suggest that the fact goes “in favour of ” the manager. If the profitability declines it would go against the manager. A good managet adds to the profitability. In other words, the profitability increases.
The correct word is filled in the above given sentence :-
The Director pointed out in favour of the manager that the profitability of the plant had increased since he had taken over.
Therefore , option B is required word .

There were no expectations of the meeting; it was only “by chance”. In other words, the meeting was accidental.
The correct word is filled in the above given sentence :-
I had not expected to meet him; it was quite an accidental meeting.

Correct Option: D

There were no expectations of the meeting; it was only “by chance”. In other words, the meeting was accidental.
The correct word is filled in the above given sentence :-
I had not expected to meet him; it was quite an accidental meeting.
Therefore , option D is required word .