What has hands, but can’t clap?

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.

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

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?

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

why?

You are in a room with no metal objects except for two iron rods. Only one of them is a magnet.
How can you identify which one is a magnet?

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?

Place the numbers from 1 to 9 in the circles in a manner that each side of the triangle sums up to 17.

Tell me the Hindi name of a Vegetable which if we remove 1st word will become a precious Stone and by removing the last word it will become a sweet eatable.

Nine marbles are arranged in the image below. Can you slide two marbles to form a square?