What goes up but never comes down?

What is the last thing you take off before bed?

You see a mathematical expression in the picture. Can you think of a movie that this expression refers to?

Jim has three close friends at his school: Michael, John and Alice. Two of them play football, two play basketball and two play hockey. The friend who does not play hockey does not play basketball as well. The friend who does not play football does not play hockey.

Can you identify which sport/s is played by which person?

Three doctors said that Bill was their brother. Bill says he has no brothers. How many brothers does Bill actually have?

What has a ring but no finger?

The dirtier I get, the whiter I look. Who am I?

Make the seating arrangement of 10 children in such a way that there are 5 rows with 4 children in each row.

Replace the question mark in the picture below.

A man plots the murder of his wife. His plan is full proof. Nobody saw them leaving their house. He stabbed her with a knife while driving. She died on the spot. He threw her body in a valley. He threw the knife carefully wiping his finger prints on a random garbage bin. Then he went back to his home and no one was watching him this time as well.

After an hour, he was called by the local police department who informed him that his wife was murdered. They asked him to reach the scene of crime immediately. But as soon as he arrived at the crime scene, he was arrested by them.

How did the police know that he himself is the murderer?