Bay of Bengal is in which state?

Can you decipher the below rebus?

PBLUESAISNUERSES

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

Can you find the number?

What part of Turkey has the most feathers?

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?

I look at you, you look at me, I raise my right, you raise your left. What am I?

At a party, there are five people and a whole round cake lying at the centre of the table. Only four people will make a cut and take their piece and the last one will get the remaining piece on the table. How can they make sure that everyone gets a 1/5th of the piece?

Many have heard it, but nobody has ever seen it, and it will not speak back until spoken to. What is it?

A charming young lady was approached by a kind looking old woman in a restaurant. The old woman said to her, 'You look exactly like my younger daughter. Sadly she passed away a couple of months back. Could you do me a favor and say 'Goodbye, mother' with a kind smile on your face when I leave?

The young lady agreed for the same and said, 'Goodbye, mother' when the old woman left. Soon after, she got the most disengaging shock of her life.

Can you guess what the shock was?

You can take four of the five letters out of this word, but the pronunciation never changes. What is the word?