Can you solve below mathematical equation?

2^1234 - 2^1233

There is one thing that goes round the house and also inside the house but never even share a brief touch. What is it?

A clock loses 10 minutes each hour. If the clock is set correctly at noon, what time is it when it reads 3 PM?

Which five letter word can be added at the end of below word to form a
valid word?

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It's a protector.
It sits on a bridge.
One individual can see directly through it, while others wonder what it hides.

What is it?

There was a minor accident with a doctor's son but the doctor noticed no major injury. After the treatment, the father of that doctors son is sitting with the son of the doctor without the doctor being in the room.

How can this be possible?

What number when divided in half becomes zero?

I shave every day, but my beard stays the same. What am I?

Consider this about a word: The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?

What is both possible and impossible at the same time?