What is both possible and impossible at the same time?

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?

You need to move three matchsticks to form three squares. Can you do it?

You are given 2 eggs.
You have access to a 100-storey building.
Eggs can be very hard or very fragile means it may break if dropped from the first floor or may not even break if dropped from 100th floor, Both eggs are identical.
You need to figure out the highest floor of a 100-storey building an egg can be dropped without breaking.
Now the question is how many drops you need to make. You are allowed to break 2 eggs in the process

There is a basket full of hats. Three are white and two are black. Three men, Tom, Tim, and Jim, each take a hat out of the basket and put it on their heads without seeing the hat they selected or the hats the other men selected. The men arrange themselves so Tom can see Tim and Jim’s hats, Tim can see Jim’s hat, and Jim can’t see anyone’s hat. Tom is asked what color his hat is and he says he doesn’t know. Tim is asked the same question, and he also doesn’t know. Finally, Jim is asked the question, and he does know. What colour is his hat?

A new clothing store has a unique method of pricing items. A vest costs $20, a tie costs $15, a blouse costs $30, and underwear costs $45. How much would pants cost?

Count the number of balls in picture below:

If you had a pizza with crust thickness 'a' and radius 'z', what's the volume of the pizza?

Sachin bought a car with a strange 5 digit numbered plate.The water image of the number is 78633 more than my car number. All the digits of car number are distinct.

What is the original number on number plate?

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