I am lying and I always lie. Tell me whether I am lying or telling the truth.

What has many keys but can’t open a single lock?

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?

Below, you can see three complete equations and one incomplete. Based on the three complete ones, can you complete the incomplete one?

5 $ 4 $ 3 $ 9 = 4215
6 $ 9 $ 2 $ 6 = 3816
4 $ 7 $ 3 $ 3 = 1122
7 $ 2 $ 7 $ 4 = ____

As easy as you can get into me, it is as hard to get out of me.

Do you know what I am?

You have a three-gallon and a five-gallon measuring device. You wish to measure out four gallons.

A tree doubled in height each year until it reached its maximum height over the course of ten years. How many years did it take for the tree to reach half its maximum height?

15 caves are arranged in a circle at the temple of doom. One of these caves has the treasure of gems and wealth. Each day the treasure keepers can move the treasure to an adjacent cave or can keep it in the same cave. Every day two treasure seekers visit the place and have enough time to enter any two caves of their choice.

How do the treasure seekers ensure that they find the treasure in the minimum number of possible days?

Solve the rebus riddle in the picture below.

I am a type of vehicle that has two wheels and is powered by humans. What am I?
Hint 1: You can ride me for exercise.
Hint 2: I am environment-friendly.