Logic Riddles

Question: You are trapped in a haunted house with no electricity. There are four doors to get out of the house only one is safe. In one door a man will stab you, in another you will get electrocuted, in another one you will get shot at, in the final one it is filled with vicious dogs. Which door is safe?

Question: There are two boys at an international math contest in December 2013; one is British and one is American. They both write their names, the date, and their answers on the paper. The only problem is that they both have the same name and the papers cannot be told apart.

What is the date?

Question: Most people are born on one, die on one, and experience some of their most blissful moments upon it.

Question: What's higher than mountains, Smaller than trees?

Question: A woman is in the hospital for a routine procedure. The doctor leaves the room locking the door before he goes, the woman is alone. The doctor comes back to find the woman has died and there is another person is in the room. The door was still locked.
How is this possible?