I have branches, but no fruit, trunk or leaves. What am I?

You can win me and lose me but never buy me
You can not eat me and never want to part with me
I can make you cry or bring you joy
I am not a machine and definitely not a toy
You keep me but i am not forever just yours
You might find me in a case or on a shelf next to a vase
I am hard and i am tall if you bump me i am sure to fall
I am made of different materials and am at many events
If your lucky and fight hard I might be yours
What am I ?

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

What do you answer even though it never asks you questions?

Rearrange the letters in "new door" to make one word.

Nodes are shown below and you need to connect them based on the following rule: Every node can be connected to the number of nodes inside them, i.e. the first node there is a value of 1 which indicates that the first node can connect to exactly one node only.Can you do it?

I start and end with 500 and carry a 5 in my heart. But I require the first letter and the first number to be complete. I am the name of a King.

Who am I ?

What happened when the wheel was invented?

What does this mathematical rebus means ?

If all the below statements are true

1. Gianni was either in Italy or France in 1997.
2. If Gianni did not kill Versace, Hilton must have killed him.
3. If Versace died of suffocation, then either Gianni killed him or Versace committed suicide.
4. If Gianni was in Italy in 1997, then Gianni did not kill Versace.
5. Versace died of suffocation, but he did not kill himself.

Who killed Versace and where was Gianni in 1997?