Why do people go to bed?

My location can be determined by the below rebus.
So where am i ?

Which letter of the alphabet has the most water?

You board a train. The train will have to enter a tunnel soon. You are claustrophobic. Which place is the best for you to sit?

I have thought of a number that is made up by using all the ten digits just once. Here are a few clues for you to guess my number:

First digits is divisible by 1.
First two digits are divisible by 2.
First three digits are divisible by 3.
First four digits are divisible by 4.
First five digits are divisible by 5.
First six digits are divisible by 6.
First seven digits are divisible by 7.
First eight digits are divisible by 8.
First nine digits are divisible by 9.
The number is divisible by 10.

Can you find out the number ?

If,

20 % 5 = 24

21 % 7 = 33

42 % 6 = 67

Then;

66 % 6 = ?

Intelligence Agency need to break the vault but the problem is that they are not able to break the vault.

On the vault, a text is written as:

31 11 33 33 43 45
21 25
31 24 11 31 51 41

To Break the code Intelligence Agency brings a mathematician named Joseph.
Minutes later he deciphers the code.

Whats the code?

A frog is at the bottom of a 30-meter well. Each day he summons enough energy for one 3-meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?

What number comes next in this sequence:
7 8 5 5 3 4 4 _

I start and end with 500 and carry a 5 in my heart. But I require the first letter and the first number to be complete. I am the name of a King.

Who am I ?