Can you solve below mathematical equation?

2^1234 - 2^1233

A worker is to perform work for you for seven straight days. In return for his work, you will pay him 1/7th of a bar of gold per day. The worker requires a daily payment of 1/7th of the bar of gold. What and where are the fewest number of cuts to the bar of gold that will allow you to pay him 1/7th each day?

Can you write down eight eights so that they add up to one thousand?

Complete the given grid with valid words. You can only use the letters AAEEIIMMPPTT.

Hint: The grid reads the same across as down.

We have four gears with below features=> Both Gear A and D has 60 teeth=> Gear B has 40 teeth=> Gear C has 20 teeth=> Every two minutes, Gear B makes 25 full turns.What is the relative speed of Gear A and Gear B?

Why do we preferably have round manhole covers and not square ones?

What can jump higher than a building?

The below given figure comprises of a pattern through which you can determine the missing letter. Can you push your mind to find the pattern and add the missing letter?

If,

A = 1

B = 2

C = 3

...

...

Z = 26.

Based on above rule, you need to find an eleven letter word whose letter sum is equal to 52.

Which digit occurred maximum times between the number 1 and 1000?