I shave every day, but my beard stays the same. What am I?

There are three Athletes (John, Tarun and Harish) and their individual Coaches (Jacob, Meenaxi and Priyanka) standing on the shore.
No Coach trusts their Athlete to be near any other Coach unless they are also with them.
There is a boat that can hold a maximum of two persons.
How can the six people get across the river?

Which wheel of car does not rotate when you turn your car right?

I am the one who remains awake when you sleep. But I need to rest when you awake. Who Am I?

Can you find the missing number in the third row?
35 20 14
27 12 18
5 2 ?

Chocolate costs 6 rupees and a Toy costs 5 rupees. If you have 32 rupees in total, how many chocolates and how many Toys can be purchased with that amount?

A pond had 60 fish, out of which, all but 20 died.
How many fishes are now present in that pond?

This is a famous paradox which has caused a great deal of argument and disbelief from many who cannot accept the correct answer. Four balls are placed in a hat. One is white, one is blue and the other two are red. The bag is shaken and someone draws two balls from the hat. He looks at the two balls and announces that at least one of them is red. What are the chances that the other ball he has drawn out is also red?

I am not a bull but I have horns.
I am not an ass but I have a pack saddle.
Wherever I go, I leave silver behind me.

Who am I?

A Detective reviewed the information they had on the case so far.

A lady named 'Caterina' was found shot and they already had a list of suspects - Ankit, Tarun, Harish, Manoj and Manish.
The killer is a fan of challenges him by leaving notes ad various places.
* The first was found in a toilet room.
* The second was found in an art room.
* The third was in a restroom.
* the fourth in an underwater room.
* The fifth at the no-smoking room.

All of the notes read the same thing, 'The clues are where you find the notes.' Yet, nothing was found at any place the notes were.
Detective the genius, immediately solved the case.
Who was the killer?