Can you solve below mathematical equation?

2^1234 - 2^1233

Two boys wish to cross a river. The only way to get to the other side is by boat, but that boat can only take one boy at a time. The boat cannot return on its own, there are no ropes or similar tricks, yet both boys manage to cross using the boat.

How?

I sleep during the day and fly at night, but I have no feathers to aid my flight. What am I?

Buy me, smell me or deliver me, I do not change.

Who am I?

What can go through glass without breaking it?

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?

If I put in one bird per cage, I have one bird too many. If I put in two bird per cage, I have one cage too many. How many cages and birds do I have?

1 dollar = 100 cent
= 10 cent x 10 cent
= 1/10 dollar x 1/10 dollar
= 1/100 dollar
= 1 cent

=> 1 dollar = 1 cent

solve this tricky problem?

Who can jump higher than a Mountain?

There was a competition where the contestants had to hold something. At the end of the event, the winner was a person who had no hands or feet. What was it that the contestants had to hold?