What is harder to catch the faster you run?

Below, you can see three complete equations and one incomplete. Based on the three complete ones, can you complete the incomplete one?

5 $ 4 $ 3 $ 9 = 4215
6 $ 9 $ 2 $ 6 = 3816
4 $ 7 $ 3 $ 3 = 1122
7 $ 2 $ 7 $ 4 = ____

Can you find a five letter word that is left with only two letters if one is removed?

A man was telling some of his war stories to his grandchildren.
"When the World War I was on the verge of end, I was awarded for my bravery for I had saved a group of my men." He coughed and then added, "When we were fighting in northern France, an enemy soldier threw a grenade at us. Before it could explode, I picked it up and threw it away. For my act of bravery, right before the war ended, A General gave me a sword engraved with the words "Awarded for Display of Bravery and Heroism in World War 1"."

Hearing this, one of the grandson spoke up. "Grandpa, this is not a true story. It can"t be true!"

The truth is that it was not. How did the grand children know it?

There was a competition where the contestants had to hold something. At the end of the event, the winner was a person who had no hands or feet. What was it that the contestants had to hold?

Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

I have a hole in my back and legs I lack.
I live where I can’t breathe and I eat without teeth.
What am I?

Can you circle exactly four of these numbers such that the total is twelve?

1 6 1
6 1 6
1 6 1
6 1 6

The day before yesterday I was 25 and the next year I will be 28. This is true only one day in a year. What day is my birthday?

I am the beginning of the end, and the end of time and space. I am essential to creation, and I surround every place. What am I?