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

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?

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

You along with your friend are standing in front of two houses. Each of those houses inhabits a family with two children.

Your friend tells you the below two facts:
1) On your left is a family that has a boy who likes accounts but the other child loves science.
2) On the right is a family with a seven-year-old boy and a newborn baby.

You ask him, "Does either of the family have a girl?"

To this, he replies, "I am not quite sure. But can you guess that? If you are right, I will give you $500."

Which family do you think is likely to have a girl?

In the picture, you can see a chess board. On the top left position, the K marks a knight. Now, can you move the knight in a manner that after 63 moves, the knight has been placed at all the squares exactly once excluding the starting square?

Find The Next Number in this series.
1, 2, 6, 42, 1806 ?

I am green and found in the forest and have needles instead of leaves. What am I?
Hint 1: It can be used for Christmas decorations.
Hint 2: I have a strong, scent that is used in air fresheners.

Solve the alphametic puzzle by replacing the alphabet with the number.

S T O R M +
S O L E S
=========
T O W E L
=========

I know a 5-digit number having a property that With a 1 after it, it is three times as large as it would be with a one before it.

Guess the number?

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.