‘Few’ The adjective requires here is for the countable noun, i.e. books. "A little" would be an incorrect choice here as it is used for uncountable nouns. Now, the fight is between "few" and "a few". "The few" would be incorrect to use here.

The difference between "few" and "a few" is explained below:

"few" = not very many, with a focus on the fact that this number is (remarkably) small.

"a few" = not very many, but at least more than one

Let's understand it with some examples:

"I have a few friends" is just the same as saying "I have some friends".

"I have few friends", however, implies that you don't have many friends (as opposed to many). In some contexts (not always!), it can also imply that you don't feel very well about it, that you wish you had more friends.

Here, the sentence mentions that there are barely any books in the library, so the correct filler here would be "few".

Let's first understand the meaning of the given words:-

Cherish = protect and care for (someone) lovingly.
e.g. Although I cherish my children, I do allow them their independence.

Nurture = care for and protect (someone or something) while they are growing.
e.g. She wants to stay at home and nurture her children.

Ignore = refuse to take notice of or acknowledge; disregard intentionally.

Destroy = end the existence of (something) by damaging or attacking it.

Forsake = renounce or give up (something valued or pleasant)

The idiom "down and out" means to be without money, a job, or a place to live; destitute.

e.g. After losing his job, car, and home, he was completely down and out.

The idiom "no love lost" means strong hatred, hostility, or enmity.

e.g. They were polite with each other, but it was clear that there wasno love lostbetween them.

Let's first see the meanings of the words:

Oblivious = lacking remembrance, memory, or mindful attention.
e.g. The cat had crept in silently, and we were oblivious to its presence in the room.

Sensitive = quick to detect or respond to slight changes, signals, or influences.

Obvious = easily perceived or understood; clear, self-evident, or apparent.

Ignorant = lacking knowledge or awareness in general; uneducated or unsophisticated.
e.g. I was largely ignorant of the effects of radiotherapy.

Attentive = paying close attention to something.

Let's first see the meanings of the given words:
Morbid = characterized by an abnormal and unhealthy interest in disturbing and unpleasant subjects, especially death and disease.
e.g. Some people have a morbid fascination with crime.
Lovely = very beautiful or attractive.
Healthy = in a good physical or mental condition; in good health.
Liberal = willing to respect or accept behaviour or opinions different from one's own; open to new ideas.
Cheerful = noticeably happy and optimistic.
e.g. They were cheerful people, sharing what they possessed with each other, and especially loving as parents. 
Hence, option D is the correct answer.

The underlined part of the sentence is grammatically incorrect.

• When we use "not only" at the beginning of a clause, we invert the subject and the verb i.e. we use the inversion rule.
   
• Also, the latter part of the sentence has used the V2 (was). Thus, we will use the past tense in the underlined part too. 

• The correct way of writing is "was it raining".

• Thus, “was it raining all day” is the most suited one.

So, the correct sentence will be:Not only was it raining all day at the wedding but also the band was late.

Option B has the grammatically incorrect part. 

• Drip means to let fall or be so wet as to shed small drops of liquid. 
   
• The correct preposition that can be used here is "off".
   
• "Off" is used with actions in which something is removed or removes itself from another thing.
  
  e.g. One of my buttons has come off.

The correct sentence will be: Water was dripping off the trees, and the grass was wet.

Let’s learn the meanings of all the words:

Agony = extreme physical or mental suffering.
e.g. She lay there screaming in agony.

Torture = the action or practice of inflicting severe pain
e.g. Half of the prisoners died after torture and starvation.

Success = the accomplishment of an aim or purpose.

Happiness = the state of being happy.

Soundness = the state of being in good condition; robustness.

The idiom'cut the Gordian knot' means to solve a difficult problem or situation.

e.g. Shecut the Gordian knotby allowing tenants the right to buy at discounted prices, trading one benefit for another.