If six children and two dogs were under an umbrella, how come none of them got wet?

A girl was standing near the window thinking something. All of a sudden she decides something and throws something out of the window. She dies very soon after throwing it. She was perfectly healthy and had no disease or allergy. No one killed her and she did not commit suicide.

Can you think of any possible explanation that is logical as well for what happened there?

I look flat, but I am deep. Hidden realms I shelter. Lives I take, but the food I offer. At times I am beautiful. I can be calm, angry, and turbulent. I have no heart but offer pleasure as well as death. No man can own me, yet I encompass what all men must have. What am I?

Which is the correct shadow of the bird?

Using Only Five 5's and any mathematical operator make sum as 37

Before the start of the car race, John and Jacob have the same amount of fuel in their car. With this fuel, John can drive for 4 hours while Jacob can drive five hours.
After a time they realize that the amount of fuel left in John's car is 1/4th of the fuel in Jacob's.

For how long they are racing?

John, a 5-year-old boy, was really fond of the chocolates. He asked his Mother to give him some money to buy his favourite chocolates. His Mother gave him $45. He went to the shopkeeper and asked, "How much is one chocolate for?". The shopkeeper said $3 for one chocolate. Also, if you give me the wrappers of three chocolates, I will give you one for the exchange.
In total, how much chocolate could John eat?

I never was there, I am always to be.
You have never ever seen me, not ever you will.
Yet I am the confidence of everyone.

Who Am I?

An ape is trying to climb on a pole that is 60 feet high. Due to the slippery surface, the ape climbs 3 feet in a minute only to slip back 2 feet.

How much time do you think the monkey will take to reach the top of the pole?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10