Can you solve below mathematical equation?

2^1234 - 2^1233

A girl is twice as old as her brother and half as old as her father. In 50 years, her brother will be half as old as his father. How old is the daughter now?

I am first found in caves, now prolific online; I am a depiction, a drawing, a symbol, or sign. I will convey whichever mood you could wish; or for that matter, a fist, flask, or fish. What am I?

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

You are a cab driver who pools passengers. You pick 3 people from a destination and drop 1 after an hour. 2 people climb aboard at the same time and you drop 3 at the next destination. After some time, you pick 2 passengers only to drop 1 after a short distance where 3 more passengers climb up the cab. You leave the rest of the passengers one by one to their destination and then come back home.

Can you tell the eye color of the cab driver?

Spelt forwards I’m what you do every day, spelled backwards I’m something you hate. What am I?

If six children and two dogs were under an umbrella, how come none of them got wet?

If you’ve got me, you want to share me; if you share me, you haven’t kept me. What am I?

What can go up a chimney down, but can’t go down a chimney up?

If there are fifteen crows on a fence and the farmer shoots a third of them, how many crows are left?