Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

If,

20 % 5 = 24

21 % 7 = 33

42 % 6 = 67

Then;

66 % 6 = ?

A shepherd had 18 sheep, out of which, all but ten died.

Can you tell us how many sheep was he left with?

Here is a mathematical expression that also secretly tells a movie name. What movie is that?

Replace the question mark with the correct number.

2 + 2= 4
3 + 3= 18
4 + 4= 48
5 + 5= ?

There are three light switches outside a room. One of the switches is connected to a light bulb inside the room.
Each of the three switches can be either 'ON' or 'OFF'.

You are allowed to set each switch the way you want it and then enter the room(note: you can enter the room only once)

Your task is to then determine which switch controls the bulb?

Can you find a five letter word that is left with only two letters if one is removed?

You Throw The Outside, Cook The Inside
Eat The Outside, Throw The Inside.

What Is It?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?