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

A mathematician couple was having a Frappuccino in Starbucks sitting opposite to each other. Suddenly the guy noticed the text written on the paper in front of them and exclaimed that it was wrong. The girl denied it and said it is appropriate. Both are correct. What is written on the paper?

What does below pictogram mean?

When it is alive we sing, when it is dead we clap our hands. What is it?

A prisoner is told: "If you tell a lie, we will hang you and if you tell the truth, we will shoot you." What did the prisoner say to save himself?

There was a greenhouse.
Inside the greenhouse, there is a white house.
Inside the white house, there is a red house.
Inside the red house, there are lots of babies.

What is It?

The doctor prescribed you to take one pill from the bottle every half an hour. The bottle is now left with only three pills.

How long do you think you have before you run out of pills?

What kind of storm is always in a rush?

John, Jack and Jill are in a desert. John doesn't like Jill and hence decides to murder him. He poisons the water supply of Jill. Since it is a desert area, Jill must drink or he will die of thirst.

Jack does not know of the actions of John and also decides to murder Jill. To succeed in his ill motives, he removes the water supply of Jill so he dies of thirst.

Jill dies due to thirst. Who murdered Jill?

With the help clues provided in the image, can you find the 5 digit key?