Can you arrange four 9's and use at most 2 math symbols, to make the total 100?

When I get multiplied by any number, the sum of the figures in the product is always me. What am I?

I am a five-letter word and comprises two different vowels and three same consonants. I am so strong that I can spoil your entire work.

Can you find out who am I?

It spends most of its day eating white, but when it’s quick enough, it gets to eat fruit and sometimes some blue things. It’s in a dark room, where the walls are blue, it runs from a ghost that roams the halls and haunts it all the time. What is it?

A spaceship was lost. The detective was given a piece of paper. This was the location of the spaceship! This is what the slip had scribbled on it:
Juice, Umbrella, Potato, Ice, Tomato, Elephant, Rice.

Where is the spaceship?

Three ants are going up a hill, one behind the other. The last ant then says to the other ants, 'There is an ant behind me!'' How come?

A murder has been committed in a house. You are a detective and have to find out the murderer.

You investigate by asking three questions to each of the six suspects. Out of those six suspects, four are liars. It is not necessary that they speak everything a lie. But in their answers, there must be at least one lie. One of the six is the murderer.

There are eight rooms in the house in which the murder has been committed: Kitchen, Living Room, Bathroom, Garage, Basement, 3 Bedrooms.

At the time of the murder, only the murderer was present in the killing room. Any number of people can be present in any of the other rooms at the same time.

Can you identify the murderer and the four liars? Also, can you find out who was in which room?

The responses of all the suspects are mentioned below.

Joseph:
Peter was in the 2nd bedroom.
So was I.
David was in the bathroom.

Mandy:
I agree with Joseph that David was in the bathroom and Peter was in the 2nd bedroom.
But I think that Joseph was in the living room, OH MY GOD!

Peter:
Mandy was in the kitchen with Christopher.
But I was in the bathroom.

David:
I still say Peter was in the 2nd bedroom and Jennifer was in the bathroom.
Joseph was in the 1st bedroom.

Jennifer:
Peter was in the bathroom with Christopher.
And Mandy was in the kitchen.

Christopher:
David was in the kitchen.
And I was in the 2nd bedroom with Peter.

PS: The corpse was found in the Living Room.

I am taken from a mine and shut up in a wooden case, from which I am never released, and yet I am used by almost every person. What am I?

There are a number of books on a shelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf?

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