Can you replace the question mark with the correct number?

I know a country, If you remove the last alphabet of its name, it will become a part of your body. Do you name it?

Before reading ahead, you must know the fact that only one of the people here is telling the truth.

A says that B is lying.
B says that C is lying.
C says both A and B are lying.

Can you find out who is speaking the truth?

Can you arrange four 9's and use at most 2 math symbols, to make the total 100?

I have eight fingers and two thumbs but I do not live. What Am I?

There are 2 cops parked along a one-way street looking for traffic violations. They spot a taxi driver going in the wrong direction, yet they do nothing.

Why?

Queen Elizabeth organised a royal party.

To Avoid uninvited guest royal family set a password.
Jack (an uninvited person) plan to enter the party. He stand nearby the door.

First guest comes, the security person said 'twelve' and guest replied with six.
Second guest comes , the security person said 'six' and guest replied with 'three'.

Jack thought is enough and he walked to the entry point. The security person said 'eight' , Jack replied smilingly 'four'.
He was immediately thrown out of the party. why ?

A network of 20 x 10 squares is given to you.

Can you calculate how many unique squares and rectangles can be formed combining two or more individual squares ?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

There was a minor accident with a doctor's son but the doctor noticed no major injury. After the treatment, the father of that doctors son is sitting with the son of the doctor without the doctor being in the room.

How can this be possible?