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

Use only one mathematical symbol and all numbers (0-9) to get a sum of 99

Rectify the following equality 101 - 102 = 1 by moving just one digit.

Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

A number can be multiplied by multiple of nine
i.e 9 18 27 36 45 ...

and the resulting number consist of only one digit.

Can you identify the number ?

Imagine a box with two cogwheels, one big with 24 teeth and one small with 8 teeth. The big one is firmly attached to the center of the box which means it does not turn or move while the small one rotates around the big one.

How many times do you think that the smaller wheel will turn compared to the box when it turns once around the big one?

It begins where the time ends.
Its second is an expression of surprise.
Its third is a question.
Its fourth is urinate.
It ends with a drink.

Which country it is?

There are a hundred statements.

First person says: At least one of the statements is false.

Second person says: At least two of the statements is false.

Third person says: At least three of the statements are false.

Fourth person says: At least four of the statements are false.

..

..

..

Hundredth person says: At least a hundred of the statements are false.

Analysing it, how many statements do you think are false and how many are true?

When I got four, I have it none.
When I got two, I have it some.
When I got none, I have it all.

What is it?

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?