What does this phrase mean : At one's wit's end?

1.He ran fast —— he could not get the bus. The right word in the gap will be.

2.The police picked —— the theif.

3.The antonym of '$scarcity^{\prime}$ is–

4.What is the synonym of '$Abolish^{\prime}$–

5.Which of the following sentences is correct?

6.Would you do me a small favour? I —— very much.

7.I was very surprised —— that she didn't pass the exam.

8.No sooner had he reached the station —— the train left.

9.The winter has set —— very late this year.

10.Who is called the 'poet of $beauty^{\prime}$?

11.Adjective of the word '$people^{\prime} is$ —

12.In TV terms, the opposite of '$live^{\prime}$ is–