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

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?

How can you take 2 from 5 and leave 4?

Which city is three-fifths chick two third cat and 50% goat?

John is 45 years older than his son Jacob. If you find similarities between their ages, both of their ages contain prime numbers as the digits. Also, John's age is the reverse of Jacob's age.

Can you find their ages?

I am a type of word that is spelt incorrectly or used differently, on purpose for humour. What am I?
Hint 1: You can find me in a joke.
Hint 2: I am a play on words.

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.

Can you find the mistake in the below statement?

When I asked a girl's name she told me her name is the date '07/09/2001'.

I thought for a few seconds and then I got her name. Do you?

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?