Known by all without exception, Forever here, for your protection, Sometimes strong, sometimes weak, Right after the night I come - hot and chic. And while millions of miles away, I always get to you, I find my way. No life around could do without me, Can you guess what I might be?

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

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?

John is found dead in a bare field. Nobody killed John,
John did not commit suicide.

Inspector Jacob found a bag just a few meters away from John which could save his life. What was in the bag?

Do you know who was buried in John's tomb?

A bomb goes off.
Carnage.
One person, only a few feet away, survives! How can this 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?

How many triangles can you find in this given picture?

A man embarked on a questionnaire game. He kept asking the same question to whomever he found. The answer each time was different.

Can you guess what the question was?

A rubber ball keeps on bouncing back to 2/3 of the height from which it is dropped. Can you calculate the fraction of its original height that the ball will bounce after it is dropped and it has bounced four times without any hindrance ?