What is the value of 1/2 of 2/3 of 3/4 of 4/5 of 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 1000?

I have a mouth but I don't eat.
I have a bank but have no money.
I have a bed but i dont sleep.
I wave but have no hands.

Who Am I ?

Can you place six X (crosses) in below board without making three in a row in any way ?

A person was killed at a house party. When the police arrive, there are six people present in the house who are the friends of the victim. The name of the friends is Rohit, Aman, Nick, Gagan, and Randy.

Near the dead body, they find a few numbers written with blood by the victim on the floor. The numbers are 8, 5, 4, and 11.

The police arrests one of the friends for the murder. Whom did they arrest and why?

I am white when I am dirty, and black when I am clean. What am I?

I know a 5-digit number having a property that With a 1 after it, it is three times as large as it would be with a one before it.

Guess the number?

I have some blue and red sock in my drawer. I have a total of 4 socks. I pick 2 socks and the chance that I get a pair of red socks is 1/2.

What is the chance of picking a pair of blue socks?

A man calls his dog from the opposite side of a river. The dog crosses the river without a bridge or a boat and manages to not get wet. How is this possible?

If eleven plus two equals one, what does nine plus five equal?

It spends most of its day eating white, but when it’s quick enough, it gets to eat fruit and sometimes some blue things. It’s in a dark room, where the walls are blue, it runs from a ghost that roams the halls and haunts it all the time. What is it?