How can you tell a raw egg from a hard-boiled egg?

I inserted a coin in a bottle and closed its mouth with the help of a cork. Now, I was able to take the coin out from the bottle without taking out the cork or breaking the bottle. Can you tell me how I did it?

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?

Can you find the key in the picture below?

What can you catch but never throw?

What do you get if you add 2 to 100 four times?

Ten coins have been arranged as you can see in the given picture. In this arrangement, a triangle is formed pointing upwards. You have to invert the position of the triangle and make it point downwards while changing the position of 3 coins only. Can you do it?

Can you place three balls such that the equation shown in the picture holds true?

In the attached figure, you can see a chessboard and two rooks placed on the chess board. What you have to find is the number of squares that do not contain the rooks. How many are there?

Three brothers Jacob, John, and James live in Mexico City. The product of the ages of these brothers is 175. Jacob and John are twins. How old is James?