It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

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?

2, 3, 5, 9, 17, _ What is the next number in the sequence?

Which of the following words don't belong in the group and why?
CORSET, COSTER, SECTOR, ESCORT, COURTS

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

I have a big mouth and I am also quite loud! I am NOT a gossip but I do get involved with everyone's dirty business.

Can you solve the below rebus?

John and Jill are madly in love with each other. To remind Jill of his pure love, John wants to send her a ring by post but in their country where burglary is quite prominent, any package that is not locked comes under the risk of being stolen for the contents.

John and Jill possess many padlocks but neither one of them has the other key.

Can you find a way John can send the ring to Jill safely?

The day before yesterday I was 25 and the next year I will be 28. This is true only one day in a year. What day is my birthday?

100 prisoners are stuck in the prison in solitary cells. The warden of the prison got bored one day and offered them a challenge. He will put one prisoner per day, selected at random (a prisoner can be selected more than once), into a special room with a light bulb and a switch which controls the bulb. No other prisoners can see or control the light bulb. The prisoner in the special room can either turn on the bulb, turn off the bulb or do nothing. On any day, the prisoners can stop this process and say "Every prisoner has been in the special room at least once". If that happens to be true, all the prisoners will be set free. If it is false, then all the prisoners will be executed. The prisoners are given some time to discuss and figure out a solution. How do they ensure they all go free?