Solution:

It can be done as shown in the picture below. Key to solving such problems is to fill the prime number first.

Solution:

7, 4, 6, 5, 8

Solution:

A
D
C
A
B

Solution:

Both will rotate at Same speed.

Explanation:
Gears of the same size will always rotate at constant speeds despite any smaller or larger gears in between them.

Solution:

Since every bacterium divides into two in two minutes and we know the fact that the dish was half filled with bacteria at 3 pm, after exactly 2 minutes, all will divide into two and will fill the petri dish. Thus, the petri dish will become full at 3:02 pm.

Solution:

10

Explanation:
Equation 1 + 9 + 11 = 1 can be derived from
One (o) + nine (n) + eleven (e) = one => 1

Similarly for equation,
12 + 11 + 9
Twelve (t) + eleven (e) + nine (n) => ten (10)

Solution:

It can be solve as shown below.

Solution:

The three errors are as follows:
a) fynd is spelled wrong. The correct spelling is 'find'.
b) that is not appropriate to use here. It should be 'this'.
c) There are only two errors in the question and that is the third error because the questions asks us to find three.

Solution:

2100 miles.

Each vowel equivalent to 500 and each consonant equivalent to -200

Solution:

None

The sum of numbers from 0-9(0,1,2,3,4,5,6,7,8,9) is 45 and therefore can be divisible by 3 and 9.

Solution:

The brain teaser can be solved as shown in the image below.