I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

I am taken from a mine and shut up in a wooden case, from which I am never released, and yet I am used by almost every person. What am I?

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.

You are given a cube that is made with the help of 10x10x10 smaller cubes summing up to a total of 1000 smaller cubes. You are asked to take off one layer of the cubes.
How many remain now?

What occurs twice in a week, once in a year but never in a day?

John was visiting his friend Jacob. He found out that his friend's wife had just killed a burglar in self-defense.
John asks Jacob about what happened and he told that "His wife was watching television when suddenly the bell rang. She thought that it is her husband Jacob but she found the burglar who attacked her instantly and she got so frightened that she killed the burglar immediately with the knife.
John asked the police to arrest his friend's wife. Why?

Can you find the odd number in the following five choices?

1) 482636
2) 259807
3) 865195
4) 104739
5) 391744

Which is Odd One Out and why?

4377

3954

9862

8454

9831

Is the statement valid that it does not matter how much older a sibling is, eventually the younger one will be half as old as the older one?

What can you see in the middle of March and April that you can never see in any other month?