Is it correct?
1)You have an aberration from the truth.
2)She abhors cats.
3)The teacher was brusque.
4)She cajoled her sister into buying some sweets.
5)He is going to cajole a new car out of his father.
6)He is a callous man.
7)She is avaricious.
8)His pecuniary avarice is making him withdrawn.
9)he will never acquiesce.
10)The fruit appeased his hunger.
11) Appease my curiosity.

Question

Is it correct?
1)You have an aberration from the truth.
2)She abhors cats.
3)The teacher was brusque.
4)She cajoled her sister into buying some sweets.
5)He is going to cajole a new car out of his father.
6)He is a callous man.
7)She is avaricious.
8)His pecuniary avarice is making him withdrawn.
9)he will never acquiesce.
10)The fruit appeased his hunger. 
11) Appease my curiosity.

Answer

The best verb for sentence ten is 'to sate.'

"The fruit sated his hunger."

Sentence one does not really make sense and I'm not sure that sentence eight means what you want it to mean.

As you rightly say in sentence four, we usually cajole somebody into doing something - so I don't think sentence five sounds very natural - cajole her father into buying her a car would be much more natural.

All of the other sentences are fine.

Answer

8)His pecuniary avarice is making him withdrawn.   I don't think you need to use pecuniary here, as avarice puts the sentence into context without the need for pecuniary.
10)The fruit appeased his hunger.   I would use satisfied (or sated) instead of appeased, but appeased is still valid.
11) Appease my curiosity.  Again, I would use satisfy, but appease does work.