What has many teeth, but cannot bite?

If you had a pizza with crust thickness 'a' and radius 'z', what's the volume of the pizza?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

I have some blue and red sock in my drawer. I have a total of 4 socks. I pick 2 socks and the chance that I get a pair of red socks is 1/2.

What is the chance of picking a pair of blue socks?

If,

A + B = C
D - C = A
E - B = C

Based on the above equations, find out the answer for:

D + F = ?

Rectify the following equality 101 - 102 = 1 by moving just one digit.

What can you deduce from the following BrainBat?

CRY
LMKI

Before reading ahead, you must know the fact that only one of the people here is telling the truth.

A says that B is lying.
B says that C is lying.
C says both A and B are lying.

Can you find out who is speaking the truth?

John is 45 years older than his son Jacob. If you find similarities between their ages, both of their ages contain prime numbers as the digits. Also, John's age is the reverse of Jacob's age.

Can you find their ages?

What is black when you buy it, red when you use it, and gray when you throw it away?