They are the five precious gems of an everyday sort and all can be found on a Tennis Court. Who are they?

Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

What is harder to catch the faster you run?

An American nightclub called 'The Coconut Grove' had a terrible fire in which over 400 people died. A simple design flaw in the building led to a high death toll. Subsequently, regulations were changed to ensure that all public buildings throughout the country eliminated this one detail, which proved deadly. What was it?

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?

Count the number of triangles in the picture below:

The more you take me, the more you leave me behind.
Who Am I?

You can find some missing letters in the picture. By placing two particular letters in the spaces, you can form a nine lettered word beginning from one of the corners and going clockwise direction to the middle. Can you find out the letters and the word?

I travel all around the world but always stay in the corner. What am I?

The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?