Can you solve below mathematical equation?

2^1234 - 2^1233

What comes
Once in a Year
Twice in a Month
4 times in a Week
6 times in a Day

You can win me and lose me but never buy me
You can not eat me and never want to part with me
I can make you cry or bring you joy
I am not a machine and definitely not a toy
You keep me but i am not forever just yours
You might find me in a case or on a shelf next to a vase
I am hard and i am tall if you bump me i am sure to fall
I am made of different materials and am at many events
If your lucky and fight hard I might be yours
What am I ?

What 8 letter word can have a letter taken away and it still makes a word. Take another letter away and it still makes a word. Keep on doing that until you have one letter left. What is the word?

Two friends were stuck in a cottage. They had nothing to do and thus they started playing cards. Suddenly the power went off and Friend 1 inverted the position of 15 cards in the normal deck of 52 cards and shuffled it. Now he asked Friend 2 to divide the cards into two piles (need not be equal) with equal number of cards facing up. The room was quite dark and Friend 2 could not see the cards. He thinks for a while and then divides the cards in two piles.

On checking, the count of cards facing up is same in both the piles. How could Friend 2 have done it ?

What number should come in place of the question mark below?

Below rebus represent famous DiCaprio movie. Can you name it?

If Rajina's daughter is my daughter's mom, who am I to Rajina?

A girl was standing near the window thinking something. All of a sudden she decides something and throws something out of the window. She dies very soon after throwing it. She was perfectly healthy and had no disease or allergy. No one killed her and she did not commit suicide.

Can you think of any possible explanation that is logical as well for what happened there?

Decode below three cipher riddles:

26 L of the A
7 D of the W
1000 Y in a M