Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

Two in a corner, one in a room, zero in a house, but one in a shelter. What am I?

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.

In front of you, there are 9 coins. They all look absolutely identical, but one of the coins is fake. However, you know that the fake coin is lighter than the rest, and in front of you is a balance scale. What is the least number of weightings you can use to find the counterfeit coin?

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

In particular commonwealth games, a female participant won silver and gold medals for a single event.

How can this be possible?

What can go through glass without breaking it?

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?

John left on a horse on Thursday , was gone for two days, and came back on Thursday after completing his work. How did that happen?

What does this Rebus Picture means ?