What is both possible and impossible at the same time?

It spends most of its day eating white, but when it’s quick enough, it gets to eat fruit and sometimes some blue things. It’s in a dark room, where the walls are blue, it runs from a ghost that roams the halls and haunts it all the time. What is it?

Jack have ten pairs of black socks, eight pairs of white socks and seven pairs of green socks. Everything is mixed in a draw. As there is no light he were not able to identify the colour of the socks. How many of the socks did he want to take to match one pair

We know that the number 7 is the prime followed by a cube. Which next number is also a prime followed by a cube?

I’m orange, I wear a green hat and I sound like a parrot. What am I?

I welcome the day with a show of light, I stealthily came here in the night. I bathe the earthy stuff at dawn, But by noon, alas! I'm gone.

Is the statement valid that it does not matter how much older a sibling is, eventually the younger one will be half as old as the older one?

John was visiting his friend Jacob. He found out that his friend's wife had just killed a burglar in self-defense.
John asks Jacob about what happened and he told that "His wife was watching television when suddenly the bell rang. She thought that it is her husband Jacob but she found the burglar who attacked her instantly and she got so frightened that she killed the burglar immediately with the knife.
John asked the police to arrest his friend's wife. Why?

Replace the 'X' with any mathematical symbol to make the expression equal to 111.

18 X 12 X 2 X 3 = 111

I add 5 to 9 and get 2. The answer is correct, so what am I?