Can you solve below mathematical equation?

2^1234 - 2^1233

I have cities, but no houses. I have mountains, but no trees. I have water, but no fish. What am I?

Known by all without exception, Forever here, for your protection, Sometimes strong, sometimes weak, Right after the night I come - hot and chic. And while millions of miles away, I always get to you, I find my way. No life around could do without me, Can you guess what I might be?

Two fathers and two sons went fishing one day. They were there the whole day and only caught 3 fish. One father said, that is enough for all of us, we will have one each. How can this be possible?

I am a type of vehicle that has two wheels and is powered by humans. What am I?
Hint 1: You can ride me for exercise.
Hint 2: I am environment-friendly.

A man says, "Brothers and sisters, have I none, but that man's father is my father's son." Who is that man?

There were two grandmothers and their two granddaughters.
There were two husbands and their two wives.
There were two fathers and their two daughters.
There were two mothers and their two sons.
There were two maidens and their two mothers.
There were two sisters and their two brothers.
Yet there are only six, who are buried here,
All are born legitimate and relationships clear.
How can this happen?

Trying to tease Birbal, Akbar gave him one gold coin and ask him to buy
* something for him to eat
* something for him to drink.
* something to feed the cows
* something to plant in the garden
and most important you need to buy only one thing.

What must Birbal buy to silence Akbar?

What has hands, but can’t clap?

I make a loud sound when I’m changing. When I do change, I get bigger but weigh less. What am I?