I am the one who remains awake when you sleep. But I need to rest when you awake. Who Am I?

No matter how little or how much you use me, you change me every month. What am I?

You find yourself in a strange place guarded by two guards.One of the guard always say truth while other always lies.You don't know the identity of the two.You can ask only one question to go out from there. What should you ask?

In the figure that has been attached to this question, each digit represents a digit. The similar letters carry the same integer value. Can you expose the original digits?

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

Consider all the numbers between 1 and 1 million. Among all these numbers, there is something very special about the number 8 and the number 2202. What is it?

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

Pronounced as 1 letter, And written with 3, 2 letters there are, and 2 only in me. I’m double, I’m single, I’m black blue and grey, I’m read from both ends, and the same either way. What am I?

If you had an infinite supply of water and 5-quart and 3-quart pails, how would you measure exactly 4 quarts? What is the least number of steps you need?

A brand new Mobile Phone was on sale at 20% as a promotional offer. By what per cent must the Mobile price be increased to sell it at the original price again?