I am white when I am dirty, and black when I am clean. What am I?

what does the below math rebus puzzle mean?

What can you hold in your right hand, but never in your left hand?

There are 2 people near the river and both of them want to get on the other side. The boat can only take one of them. But they got across.
How?

A blonde put eyeliner on her head. Why?

My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years ?

I am a ten letters word
The first four letters have the power to rule,
Next, four-letter can be eaten.
The next three-letter represents a lady.
I can fly as well

what am I looking for?

If we tell you that there is a relation between the numbers and letters in the given figure, can you analyze it and find the missing letter in the last box?

John’s parents have three sons: Snap, Crackle, and what’s the name of the third son?

A detective visits his friend John just to discover that John's neighbour Dr Jacob was murdered. Dr Jacob, who is a mathematician wrote the murderer's name in a code word "Hcqtfz". There were five suspects
1. Ajit
2. Pankaj
3. Ganpat
4. Deenu
5. Hariya

The Detective was instantly able to find the murderer.
Can you?