What is more useful when it is broken?

I am quite hot but become too cold if you remove the first two letters. What am I?

If you say my name, I will no longer exist. What am I?

Find three numbers such that

* When we multiply three numbers, we will get the prime numbers.
* The difference between the second and the first number is equal to the third and second.

Who always enjoys poor health?

I welcome the day with a show of light, I stealthily came here in the night. I bathe the earthy stuff at dawn, But by noon, alas! I'm gone.

Can you name an animal whose killing cannot be performed without spilling your own blood?

A time long back, there lived a king who ruled the great kingdom of Trojan House. As a part of the renovation of the kingdom to meet future security needs, he asked his chief architect to lay down a new play in a manner that all of his 10 castles are connected through five straight walls and each wall must connect four castles together. He also asked the architect that at least one of his castles should be protected with walls. The architect could not come up with any solution that served all of King's choices, but he suggested the best plan that you can see in the picture below. Can you find a better solution to serve the king's demand?

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

If you remove one from eleven, it becomes ten. If you remove one from nine, it becomes ten.

How is this possible?