Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

In a supermarket, there is an intelligent glass pane before a refrigerating unit. This glass pane allows cherries and apples through it but does not allow grapes and Orange to pass through it.

Can you identify the rule that the glass pane is following?

There were five men at church, and it started raining while they were outside. The four that ran still got wet, but the one that was still stayed completely dry. Why did he stay dry?

John was gifted a new Hayabusa. He drove x miles at 55mph. Then he drove x+20 miles at 40mps. He drove his bike for 100 minutes. How much distance did he travel?

Replace the question mark in the picture below.

I have a hole in my back and legs I lack.
I live where I can’t breathe and I eat without teeth.
What am I?

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

There are 2 cops parked along a one-way street looking for traffic violations. They spot a taxi driver going in the wrong direction, yet they do nothing.

Why?

Can you solve the photo plexer logic ?

A man was found murdered on Sunday morning. His wife immediately called the police. The police questioned the wife and staff and got these alibis: The Wife said she was sleeping. The Cook was cooking breakfast. The Gardener was picking vegetables. The Maid was getting the mail. The Butler was cleaning the closet. The police instantly arrested the murderer. Who did it and how did they know?