Verbal Ability - Selecting Words - Discussion

What is the difference between 'few' and 'a few' ?

As both wrds have same meaning
- Amounting to or consisting of a small number
bt few is used when we consider things that are not noun
eg.one of my few bad habits
and
a few is used with noun
eg.A few of the books have torn jackets.

Few:has negative meaning.

Eg:few students suffer from fever. It means that none is suffering from fever.

A few :has positive meaning.

The few:not many, but all.

Can some one tell me about fewe?

I feel that the answer is wrong the answer should be a few because few has a negative meaning and a few has a positive meaning.

I went to the dentist and he found few cavities. Few = not many. My teeth are in relatively good condition.
I went to the dentist and he found a few cavities. A few = several. My teeth are in somewhat poor condition.

Can you explain why 'few' is used here not 'a few'?

Here as Aswini said.,

Few refers to negative meaning - so Encyclopedia and Britannica are the only two that are existed presently and no other will serve as like them., which indirectly says only these two are existed and no other. Hence I'm sure that

Few works of reference are valuable as Encyclopedia, Brittanica.
Is correct.

Few, when used without a preceding a, means "very few" or "none at all". On the other hand, a few is used to indicate "not a large number". The difference is subtle, yet there are instances where the two can mean completely opposite things.

I have a few objections to the vendor's proposed approach. Implies that I am not on board with the vendor's proposal. I have some objections, but not so many as to say "I have several objections. ". Nevertheless, I have objections that need to be addressed.

I have few objections to the vendor's proposed approach. Is a more positive statement that implies I am more or less on board with the proposal. It is not a whole-hearted endorsement, but I barely have any objections at all.

Few refers to negligible and a few refers to a certain numbers of people. SOP according to me the correct answer is option :A.

I think a few determined an smallest number than the word few. So it should be a few instead if few.