Can you solve below mathematical equation?

2^1234 - 2^1233

I never was there, I am always to be.
You have never ever seen me, not ever you will.
Yet I am the confidence of everyone.

Who Am I?

Intelligence Agency need to break the vault but the problem is that they are not able to break the vault.

On the vault, a text is written as:

31 11 33 33 43 45
21 25
31 24 11 31 51 41

To Break the code Intelligence Agency brings a mathematician named Joseph.
Minutes later he deciphers the code.

Whats the code?

There are three boxes of different sizes with three cupcakes inside each of the boxes in Christina's kitchen. At night her daughter wakes up and goes to the kitchen. She opens a box and eats all three cakes.

But in the morning Christina finds out that each box still had three cupcakes. How?

John's five friends Rachel, Jacob, Phoebe, Joey and Chandler live on the same road.

Rachel lives in the house: A, Jacob lives in the house: B, Phoebe lives in the house: C, Joey lives in the house:D, Chandler lives in the house: E

Mathematically
B*C*D = 1260
B + C + D = 2E
2A = E

The road numbers run from 2 to 222.

Can you tell me the house number of each of John's friends?

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------

In a jungle where there are no street lights or any other artificial source of lights, I notice a black snake crossing the road.
How did I get sight of the snake?

What English word has three consecutive double letters?

Two batsman each on 94 runs. Seven runs needed to win in last 3 balls. Both make 100*. How?

What Does this text mean:

important=important