If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

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?

What does the below rebus puzzle mean?

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

There are 20 people in an empty, square room. Each person has full sight of the entire room and everyone in it without turning his head or body, or moving in any way (other than the eyes). Where can you place an apple so that all but one person can see it?

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?

A girl was standing near the window thinking something. All of a sudden she decides something and throws something out of the window. She dies very soon after throwing it. She was perfectly healthy and had no disease or allergy. No one killed her and she did not commit suicide.

Can you think of any possible explanation that is logical as well for what happened there?

The Judge knows that Alamgir was killed by his girlfriend Jasline, but the judge is unsure whether to punish her. Why?

The doctor advised his patient to take a tablet after every fifteen minutes. He gave him five tablets in total.

How much time will he take to have all the five tablets?