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 ?

There are nine letters in the below-given diagram. You have to form a nine-letter word using these letters.

What is greater than gold but cannot be bought. it can never be sold and can earn if its sought. though it can be broken, it can still be fixed. for by birth it can't start nor by death it is ended.what am i?

Below the four parts have been reorganised. The four partitions are exactly the same in both arrangements. Why is there a hole?

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

Below is the sum of symbols in each row and column in the figure. Analyzing the figure, can you find out the value of the symbols?

They came out at night, without being called.
They lost at day, without being stolen.
Who are they?

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?

A detective visits his friend John just to discover that John's neighbour Dr Jacob was murdered. Dr Jacob, who is a mathematician wrote the murderer's name in a code word "Hcqtfz". There were five suspects
1. Ajit
2. Pankaj
3. Ganpat
4. Deenu
5. Hariya

The Detective was instantly able to find the murderer.
Can you?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain