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

Imagine a box with two cogwheels, one big with 24 teeth and one small with 8 teeth. The big one is firmly attached to the center of the box which means it does not turn or move while the small one rotates around the big one.

How many times do you think that the smaller wheel will turn compared to the box when it turns once around the big one?

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

The two towns are exactly 100 km apart. John leaves City A driving at 30 km/hr and Jacob leaves City B half an hour later driving at 60 km/hr. Who will be closer to City A when they meet?

The doctor advised his patient to take a tablet after every fifteen minutes. He gave him five tablets in total.

How much time will he take to have all the five tablets?

What number comes next in the series?

5 15 5 18 5 24 14 20 _

Many have heard it, but nobody has ever seen it, and it will not speak back until spoken to. What is it?

In a supermarket, there is an intelligent glass pane before a refrigerating unit. This glass pane allows cherries and apples through it but does not allow grapes and Orange to pass through it.

Can you identify the rule that the glass pane is following?

I am taken from a mine and shut up in a wooden case, from which I am never released, and yet I am used by almost every person. What am I?