I shave every day, but my beard stays the same. What am I?

Twenty frogs are sitting on a log floating on the surface of a river. Two of them decide to jump off into the water.

How many frogs are there on the log at this moment?

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?

Bopanna was working on a murder case when he received a message about the location of the murder weapon.
The message was encrypted as below.

"deb mitciv eht edisni neddih si nopaew redrum ehT"

Tell me the location of the murder weapon.

How many words can a pen with half refill write?

A girl rode into a tourist spot out of the city on Thursday. She loved the place and decided to stay for a few days. She stayed for four days and then she left for back home on Thursday.

How can this be possible?

If I remove one from eleven it becomes Ten and if I remove one from nine also becomes Ten. How?

Two boys wish to cross a river. The only way to get to the other side is by boat, but that boat can only take one boy at a time. The boat cannot return on its own, there are no ropes or similar tricks, yet both boys manage to cross using the boat.

How?

In a mathematical quiz, you are asked the following question:

Use three 9s in a mathematical expression without dividing or multiplying to form the number one.

Can you answer the question?

The Federal bank of London is abducted by the robbers. The head of the robbers asked the cashier to empty their money vault to them and when suddenly cashier got a call from her father. To avoid any suspicion, the robber asked the cashier to pick the call and reply her father in the shortest manner possible.

The cashier told her father "Is there an emergency father, Call me when you are free and I will help you in your furnishing" and then the cashier hung up the phone.

After 10 minutes, police arrived at the crime scene.

How did the police know about the robbery?