What is both possible and impossible at the same time?

Peter wakes up daily to pick up his cycle and crosses the border between Spain and France daily with a bag on his shoulder. He is investigated daily by the officials but they don't find anything suspicious.

If we tell you that he is smuggling something what would it be?

What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller than 9?

Find the missing letter in the last circle logically in the given below picture.

There is a brick of gold and a brick of iron in a boat (both 10-inch blocks), if they are both dropped into the water which will make the water level higher?

The product of three consecutive numbers is 7980.
Then the sum of these consecutive numbers would be?

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?

What kind of tree can you carry in your hand?

One day, I thought of ways that can be used for creating a palindrome. So I decided that I will turn into a larger number by adding the reversed digits to the original number and keep doing it till I finally obtained a palindrome.

I am not sure if this process will always result in a palindrome eventually but I was able to produce a four-digit palindrome. Can you guess my starting number?

You can hear me, but you can't touch or see me.

What am I?