Can you solve below mathematical equation?

2^1234 - 2^1233

I throw two dice simultaneously.

What is the probability of getting a sum as 9 of the two numbers shown?

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

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?

I am working in a bus company. The company recently went under expansion and therefore there was not enough room for all the buses. As a result, twelve buses had to be stored outside.

If the company decides to expand the garage space by forty percent, enough space to accommodate the current buses will be created leaving enough space for twelve more buses if the need arises in future.

Can you calculate the number of buses that the company owns at present?

Three brothers Jacob, John, and James live in Mexico City. The product of the ages of these brothers is 175. Jacob and John are twins. How old is James?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

John can place six large boxes or nine small boxes into a carton.

Can you find out in how many cartons can he place sixty-six boxes in total?

What does this mathematical rebus means ?

I want to fill my bucket using both cold and hot water.
I have two taps for both cold and hot water. The hot water tap fills the bucket in exact 6 hours and the cold water tap fills the bucket in exact 4 hours.
I turn both of them simultaneously but I forgot to turn off another tap which removes the water out of the bucket. This tap can empty the bucket in 12 hours.

How Long will it take to fill the bucket?