Can you find out the remainder when 3^300 is divided by 5?

John killed hundreds of people mercilessly and yet the police were not able to put her behind the bars. Why?

Two boys were admitted to a school. When the headmaster asks them about their parents, they tell him that they have same parents (father and mother). On further inquiry, it turns out that they both share the same date for their birthday.

"Are you twins," ask the headmaster.
"No," replies the boys.

Is it possible?

You are in a room with no metal objects except for two iron rods. Only one of them is a magnet.
How can you identify which one is a magnet?

How many triangles are there in the picture below?

Six glasses are in a row. The first three are filled with milk and the last three are empty. By moving only one glass, can you arrange them so that the full and the empty glasses alternate?

Which wheel of car does not rotate when you turn your car right?

What breaks yet never falls, and what falls yet never breaks?

Until it is measured, not known. Yet how you miss it when it has gone. What is it?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain