There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

What breaks yet never falls, and what falls yet never breaks?

A few friends are enjoying their sea voyage in a boat full of apples. On the way, they felt hungry and thus decided to eat the apples. Together, they ate two dozen of apples. When they have eaten the apples, will there be any change in the water level?

I am the largest in my family of fifty.
The youngest of our family lives separately from the rest of the family and so do I.
I am regarded as harsh and tough.
I am so large, you cut me in two equal halves,
each half would still be larger than the second largest member of the family.
Who am I?

I am a normal creature, but I have five hands. I can even have more but even then I will be considered normal.

Who am I?

Why do we preferably have round manhole covers and not square ones?

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

Count the number of triangles in the picture below:

What is the fewest number of coins that would be required in order to make sure each and every coin touches exactly three other coins?

A man calls his dog from the opposite side of a river. The dog crosses the river without a bridge or a boat and manages to not get wet. How is this possible?