With pointed fangs I sit and wait; with piercing force I crunch out fate; grabbing victims, proclaiming might; physically joining with a single bite. What am I?

A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?

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?

Akbar called Birbal and asked him to draw a line on the floor. He asked Birbal to make that line smaller without erasing it. Birbal smiled and did it before Akbar could blink his eyes.

How did he managed to do it?

You find yourself in a strange place guarded by two guards.One of the guard always say truth while other always lies.You don't know the identity of the two.You can ask only one question to go out from there. What should you ask?

Two-person want to cross a river. Only one boat is present on the riverside that can carry only one person at a time.

However, they still manage to cross the river. How is it possible?

One day, all the courtiers from Akbar's court were gathered in the assembly hall when one of them told the Emperor that all his valuables had been stolen by a thief the previous night.
This shocked the Emperor to his core as the place where that courter stayed was the most secured in the kingdom. The Emperor thought that it is not at all possible for an outsider to enter into the courtier's house and steal the valuables. Only another courtier could commit this crime. He quickly called Birbal to identify the thief.
Birbal thought for a while and successfully solved the mystery by identifying the thief in just one statement.
What did Birbal say?

If,

20 % 5 = 24

21 % 7 = 33

42 % 6 = 67

Then;

66 % 6 = ?

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

Until it is measured, not known. Yet how you miss it when it has gone. What is it?