You can take four of the five letters out of this word, but the pronunciation never changes. What is the word?

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

I am a word of 12 alphabets.

* Alphabets 12, 4, 7, 2, 5 : Eastern beast of burden
* Alphabets 1, 8, 10, 9 are street made famous by Sinclair Lewis.
* Alphabets 11, 3, 6 are past.

On whole it means a person suffering from delusions of greatness.

What Is it ?

John enters a small room. The Door Closes.
When the door opens, John is in a larger room.

Explain?

A dying old man wants to divide his entire land between his only two sons. Since his only wish is to treat them as equal as both of them have been too good to him, he wants to divide his land equally between them. The problem is that the land is significantly irregular in shape and thus there is no choice of cutting them into two equal halves.

Can you help him divide the land in a manner that both of his sons will be happy?

It's a protector.
It sits on a bridge.
One individual can see directly through it, while others wonder what it hides.

What is it?

I add 5 to 9 and get 2. The answer is correct, so what am I?

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?

Only one colour, but not one size,
Stuck at the bottom, yet easily flies.
Present in sun, but not in rain,
Doing no harm, and feeling no pain.
What is it?

As we know that white starts the game of chess. Can you find the scenario shown in the picture below is possible when all the white pieces are at the original place while the black pawn is not as in the below picture?