What brings you down but never up?

A girl was sitting in her hotel room when she heard a knock on the door. She opened the door and found that a man was standing outside. The man said, "Oh! I am really sorry, I thought this was my room." He then walked through the corridor to the elevator. The girl did not know the man. She closed her door and called security asking them to apprehend the man. What made her suspicious of that man? He might have been genuinely mistaken.

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

Can you find the thief by just looking at the picture below?

I am soft and cuddly that soothe your heart. But, If you pick my last name I am going to tear you all apart. Who am I?

If,

A + B = C
D - C = A
E - B = C

Based on the above equations, find out the answer for:

D + F = ?

I live in a bowl. I can swim. I have a tail. I also have fins and big eyes. What am I?

Aman has 1.15 rupees in his pocket. There are a total of 6 coins in his pocket.

When his friend asked him for a change, he could not give change for a rupee and five paisa.

Can you tell which coins he has?

There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

Who can jump higher than a Mountain?