Can you solve below mathematical equation?

2^1234 - 2^1233

Birbal was jester, counsellor, and fool to the great Moghul emperor, Akbar.
The villagers loved to talk of Birbal's wisdom and cleverness,
and the emperor loved to try to outsmart him.
One day Akbar (emperor) drew a line across the floor.
"Birbal," he ordered, "you must make this line shorter, but you cannot erase any bit of it."
Everyone present thought the emperor had finally outsmarted Birbal.
It was clearly an impossible task.
Yet within moments the emperor and everyone else present had to agree that Birbal had made the line shorter without erasing any of it.
How could this be?

I can be cracked, made, told, and played. What am I?

In a town, there are four houses located at different distances from each other. Following are the distances:

The third house is 60 meters apart from the first house.
The fourth house is 40 meters apart from the second house.
The third house is 10 meters nearer to the fourth house than it is to the second house.

Can you find out the distance between the fourth and the first house?

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different.

How do you measure 45 minutes?

Can you decipher the two rows to find the hidden word?

Tell me the Hindi name of a Vegetable which if we remove 1st word will become a precious Stone and by removing the last word it will become a sweet eatable.

Paul's height is six feet, he's an assistant at a butcher's shop and wears size 9 shoes. What does he weigh?

I am the fastest animal but cannot climb the tree. What am I?

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------