What 8 letter word can have a letter taken away and it still makes a word. Take another letter away and it still makes a word. Keep on doing that until you have one letter left. What is the word?

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?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

A 3 digit number is such that it's unit digit is equal to the product of the other two digits which are prime. Also, the difference between it's reverse and itself is 396.

What is the sum of the three digits?

I look flat, but I am deep. Hidden realms I shelter. Lives I take, but the food I offer. At times I am beautiful. I can be calm, angry, and turbulent. I have no heart but offer pleasure as well as death. No man can own me, yet I encompass what all men must have. What am I?

A boy was driving a car, a girl took a lift from her. She asked his name. The boy said - my name is hidden in my car’s number, find it if you can. After this, she got down Car number was [ WV733N ] Can you guess the name now?

What has 13 hearts but no other organs?

Always in you, Sometimes on you;

If I surround you, I can kill you.

What am I?

I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?