Can you solve below mathematical equation?

2^1234 - 2^1233

There are hundred red gems and hundred blue gems. The blue gems are priceless while the red gems equal wastage. You have two sacks one labeled Heads and the other Tails. You have to distribute the gems as you want in the two sacks. Then a coin will be flipped and you will be asked to pick up a gem randomly from the corresponding sacks.

How will you distribute the gems between the sacks so that the odds of picking a Blue gem are maximum?

John was so frustrated to be the suspect of being a sleeper terrorist that he shoot himself right between the eyes with a revolver in his toilet. The revolver and the bullets were accurate. Minutes later John walks out of the toilet unharmed.
How can this be possible?

I am taken from a mine and shut up in a wooden case, from which I am never released, and yet I am used by almost every person. What am I?

Can you make four (4) nines (9) equal 100?

A fresh card pile is taken out of a box (the pile has 54 cards including 2 jokers). One joker is taken out and then the cards are shuffled for a good amount of times. After shuffling, two piles are made by dividing that one pile.



What is the possibility that one of the piles will have a card sequence from A to K in order?

I am something people love or hate. I change peoples appearances and thoughts. If a person takes care of them self I will go up even higher. To some people I will fool them. To others I am a mystery. Some people might want to try and hide me but I will show. No matter how hard people try I will Never go down. What am I?

A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?

I am weightless, but you can see me. Put me in a bucket, and I'll make it lighter. What am I?

The teacher told the student that if he told a lie then he will be expelled from school and if he told the truth then he still is expelled from school.

What can a student say to prevent his being expelled from school?