Can you solve below mathematical equation?

2^1234 - 2^1233

I cannot talk, but I always reply when spoken to. What am I?

A father's child, a mother's child, yet no one's son.

Who am I?

You’re out on the water and see a boat filled with people. You look away for a second and look back again, but this time you don’t see a single person on the boat. Why? Hint: The boat did not sink.

There are four 3-link chains. All you have to do is join them into a big 12-link chain. For joining two closed links, one of the links must be cut and placed onto the other link for closing.

How many minimum links will you have to cut to make the big chain?

Can you name four days which start with the letter 'T'?

When I got four, I have it none.
When I got two, I have it some.
When I got none, I have it all.

What is it?

I am lying and I always lie. Tell me whether I am lying or telling the truth.

What 8 letter word can have a letter taken away and it still makes a word. Take another letter away and it still makes a word. Keep on doing that until you have one letter left. What is the word?

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.