What is both possible and impossible at the same time?

Two in a corner, one in a room, zero in a house, but one in a shelter. What is it?

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?

How will you measure 15 minutes using two hourglasses of 7 minutes and 11 minutes respectively?

Can you solve below mathematical equation?

2^1234 - 2^1233

Alex opened 24 presents
Jonah opened 8 presents
Clara opened 1 present

Can you find out how many presents were opened by Candy?

I hide my treasure in the ground, my tail is big and fluffy. If you spot me in a tree, please don’t call me scruffy. What am I?

An ant is travelling on a 1-meter-long rope at 1 cm/second but also the entire rope is being stretched by an extra 1 meter/second. Is it possible for the ant to reach at the end of the rope?

He digs out tiny caves and stores gold and silver in them. He also built bridges of silver and made crowns of gold. They are the smallest you could imagine. Sooner or later everybody needs his help, yet many people are afraid to let him help them. Who is he?

Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209