Can you solve below mathematical equation?

2^1234 - 2^1233

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

There once were seven dwarfs who were all brothers. They were all born two years apart. The youngest dwarf is seven years old. How old is his oldest brother?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

A number can be multiplied by multiple of nine
i.e 9 18 27 36 45 ...

and the resulting number consist of only one digit.

Can you identify the number ?

A rain drop fell from one leaf to another leaf and lost 1/4th of its volume. It then fell to another leaf and lost 1/5th of the volume. It again fell on another leaf and lost 1/5th of the volume.



This process kept repeating till it fell on the last leaf losing 1/75th of its volume.



Can you calculate the total percentage of loss from the initial volume when the drop has fallen to the last leaf accurate up to two decimal places?

What is the value of 1/2 of 2/3 of 3/4 of 4/5 of 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 1000?

You need to arrange three 7 and mathematical symbols to form number 1?

While house hunting in London, I came across a very good leasehold property Discussing the lease the landlady told me:

'The property was originally on a 99 years lease and two-thirds of the time passed is equal to four-fifths of the time to come. Now work it out for yourself and see how many years are to go!