Can you solve below mathematical equation?

2^1234 - 2^1233

In two decks of cards, what is the least amount of cards you must take to be *guaranteed* at least one four-of-a-kind?

Rectify the following equality 101 - 102 = 1 by moving just one digit.

In a rainy season, one day 3 huge ladies walked under a normal-sized umbrella.
The umbrella is not huge enough to accommodate all 3 ladies yet not a single lady got wet. Why?

I came first on earth but second on the heaven.
I also came twice in a week but found just once in a year.
I stay away from months but you can find me in February.

What am I?

I have a hole in my back and legs I lack.
I live where I can’t breathe and I eat without teeth.
What 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?

In a kingdom, King George did not allow any citizen to visit the world outside. Also, only a person with proper paperwork was allowed to enter or he was sent back. A wooden bridge was what connected the kingdom to the world. The king had appointed a sharpshooter who would check the every five minutes on the bridge to check. After checking, he would go back to his hut and return exactly after five minutes again. The bridge took 9 minutes to cross.

A merchant was able to escape the kingdom without harming the shooter. How?

What do you answer even though it never asks you questions?

You have to put a letter on the following to make it a meaningful word. The only challenge is that you can't use 'E'.

S E Q U E N C _