What does this Rebus Picture means ?

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 ?

When it is alive we sing, when it is dead we clap our hands. What is it?

Take number 1000 and then add 20 to it.
Now add 1000 one more time.
Now add 30.
Now add 1000 one more time.
Now add 40.
Now add 1000 one more time.
Now add 10.

What is the total?

I am the one who remains awake when you sleep. But I need to rest when you awake. Who Am I?

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 ?

Your job is to measure 45 minutes if you have only two cords and matches to light the cords.

1. The two cords are twisted from various materials, so their different segments can burn at different rates.
2. Each cord burns from end to end in exactly one hour.

Describe your way of measuring the 45 minutes.

If Rajina's daughter is my daughter's mom, who am I to Rajina?

Check out the number list below and find what number comes next in the sequence.

111 , 113 , 117 , 119 , 123 , 137 , ?

Place a mathematical symbol between the numerals 5 and 9 in such a way that the resulting number is greater than 5 but smaller than 9.