I have a mouth but I don't eat.
I have a bank but have no money.
I have a bed but i dont sleep.
I wave but have no hands.

Who Am I ?

The day before yesterday I was 25 and the next year I will be 28. This is true only one day in a year. What day is my birthday?

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

Most people think of me as money. But when they find me in the water, they won’t get any money out of me. What am I?

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

An apple seller is hosting a competition. He offers 1000 apples and 10 boxes to the people who pass by. The challenge is to put those 1000 apples in the 10 boxes in such a manner that if he asks for any amount of apples, the person can directly give him the boxes or a combination of boxes. If the person can do it, he promises to give a thousand apples for free.

If you happen to pass by the apple seller, will you be able to win a thousand apples?

What word is pronounced the same if you take away four of its five letters?

Nodes are shown below and you need to connect them based on the following rule: Every node can be connected to the number of nodes inside them, i.e. the first node there is a value of 1 which indicates that the first node can connect to exactly one node only.Can you do it?

There are hundred red gems and hundred blue gems. The blue gems are priceless while the red gems equal wastage. You have two sacks one labeled Heads and the other Tails. You have to distribute the gems as you want in the two sacks. Then a coin will be flipped and you will be asked to pick up a gem randomly from the corresponding sacks.

How will you distribute the gems between the sacks so that the odds of picking a Blue gem are maximum?

It is always ahead of me yet I can never see it. What is it?