I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?

In the four images below, can you find the odd one out?

Name the three-letter word that can complete the below words?

A) L O _ _ _ E
B) E D U _ _ _ E
C) _ _ _ E R
D) _ _ _ T L E

There is a circular car race track of 10km. There are two cars, Car A and Car B. And they are at the exact opposite end to each other. At Time T(0), Both cars move toward each other at a constant speed of 100 m/seconds. As we know both cars are at the same speed they will always be the exact opposite to each other.
Note, at the center, there is a bug which starts flying towards Car A at time T(0). When the bug reaches car B, it turns back and starts moving towards the car A. The speed of bug is 1m/second. After 5 hours all three stop moving.
What is the total distance covered by the bug?

In particular commonwealth games, a female participant won silver and gold medals for a single event.

How can this be possible?

Where do fish keep their money?

Can you find a number that lies one third of the distance between 1/3 and 2/3?

There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

The dirtier I get, the whiter I look. Who am I?

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?