Can you solve below mathematical equation?

2^1234 - 2^1233

Can you find the least possible number such that

If the number is divided by 3, it gives the remainder of 1;
If the number is divided by 4, it gives the remainder of 2;
If the number is divided by 5, it gives the remainder of 3;
If the number is divided by 6, it gives the remainder of 4.

What number divided by 4 is the same as that number minus 4?

You are given a cube that is made with the help of 10x10x10 smaller cubes summing up to a total of 1000 smaller cubes. You are asked to take off one layer of the cubes.
How many remain now?

Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
x *
=====
* * *

Replace each alphabet with the number (1-9) to make the below equation correct.

AB * C = DE - F = GH / I

Before the start of the car race, John and Jacob have the same amount of fuel in their car. With this fuel, John can drive for 4 hours while Jacob can drive five hours.
After a time they realize that the amount of fuel left in John's car is 1/4th of the fuel in Jacob's.

For how long they are racing?

How can I get the answer 24 by only using the numbers 8,8,3,3?

You can use the main signs add, subtract multiply and divide.

There is a number which when you multiply by 3 and subtract 2 from the result, then the resulting number is the reverse of the actual number.

What is the smallest number that stands true on the statement?

Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1