I am first found in caves, now prolific online; I am a depiction, a drawing, a symbol, or sign. I will convey whichever mood you could wish; or for that matter, a fist, flask, or fish. What am I?

You have 10 balls with you. A friend of yours out of nowhere asks you to place those ten balls in five lines such that each of the lines has exactly 4 balls on them. He needs to check your intelligence. Prove him by doing the task.

Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.
They need to guess their own hat colour by writing it on a piece of paper, or they can write 'pass'.
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
What is the best strategy?

Two in a corner, one in a room, zero in a house, but one in a shelter. What is it?

He runs but never walks. Murmurs, but never talks. Has a bed, but never sleeps. And has a mouth, but never eats?

A blonde put eyeliner on her head. Why?

Can you count the number of quadrilaterals in the picture below?

A rubber ball keeps on bouncing back to 2/3 of the height from which it is dropped. Can you calculate the fraction of its original height that the ball will bounce after it is dropped and it has bounced four times without any hindrance ?

It belongs to you, but other people use it more than you do. What is it?

The Judge knows that Alamgir was killed by his girlfriend Jasline, but the judge is unsure whether to punish her. Why?