Our product and our sum always give the same answer. Who are we?

The following four words might seem abrupt to you. But you can make them meaningful by just adding vowels.
RDSH
GGPLNT
TMT
NN

Hint: All of them are vegetables.

John was driving a bus and got stuck when passing through an underpass. Then came Jacob with a needle and got the bus out of the underpass.

What did the boy do?

I never was there, I am always to be.
You have never ever seen me, not ever you will.
Yet I am the confidence of everyone.

Who Am I?

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

How can you spell "White of an egg" in one word?
Hint: I know you can spell coke, poke, and joke.

If I put in one bird per cage, I have one bird too many. If I put in two bird per cage, I have one cage too many. How many cages and birds do I have?

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?

I am a type of word that is spelt incorrectly or used differently, on purpose for humour. What am I?
Hint 1: You can find me in a joke.
Hint 2: I am a play on words.

Can you find out which options fits best with the missing column?