If 21x = 79x, what is the value of x?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

Sweet & very intelligent katty has 8 puppets(Jane Bird Barbie Angel Colleen Nora Lass Missy).
All puppets are of different size. She arrange all puppets to face towards the guest and tell the guess the following clues :

* Jane has three puppets bigger on its left side
* Bird has two puppets smaller on its left side
* Barbie has one puppet bigger on its right side
* Angel has two puppets smaller on its right side
* Colleen has one puppet bigger on its left side
* Nora has one puppet smaller on its left side
* Lass has four puppets bigger on its right side
* Missy has three puppets smaller on its right side

Also some puppets are inside the bigger puppets.

Assuming you are the guest , can you tell the katty how the puppets are arranged ?

There are two words one resembles the "state of rest" and the other is related to "writing/reading material".

Can you name these two words which also sound similar?

Vin Diesel is pulling a theft and has planned to run away with all the cash kept in the safe. But the only way to open the safe is the 13 character password. He has a set of five clues given to him by a trustworthy source.

Exactly two of the below statements are false.
The password is contained within this sentence.
The password is not in this hint.
The password is within only one of these statements.
At least one of the above statements is a lie.

Which word does the below Plexor means ?

Can you find a number that lies one third of the distance between 1/3 and 2/3?

A dying old man wants to divide his entire land between his only two sons. Since his only wish is to treat them as equal as both of them have been too good to him, he wants to divide his land equally between them. The problem is that the land is significantly irregular in shape and thus there is no choice of cutting them into two equal halves.

Can you help him divide the land in a manner that both of his sons will be happy?

Jenifer is learning to drive her car. She went down a one way lane and in the wrong direction. But she do not break any law.

How come ?

You walk into a room that contains a match, a kerosene lamp, a candle and a fireplace. What would you light first?