What is the centre of gravity?

What can run but never walks, has a mouth but never talks, has a head but never weeps, has a bed but never sleeps?

What is harder to catch the faster you run?

Nodes are shown below and you need to connect them based on the following rule: Every node can be connected to the number of nodes inside them, i.e. the first node there is a value of 1 which indicates that the first node can connect to exactly one node only.Can you do it?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

I was speeding and ran through a stop sign, yet two traffic officers who were there do nothing about it.

why?

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

What is the probability of choosing the correct answer at random from the options below?

a) 1/4
b) 1/2
c) 1
d) 1/4

Count the number of triangles in the below picture?

I am weightless, but you can see me. Put me in a bucket, and I'll make it lighter. What am I?