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

Count the Triangle in the figure given below:

If,

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

Then

4 / 5 = ?

Jack was having a candle light dinner with his girlfriend. Suddenly a cold gush of wind entered through the open window and three of the ten candles were extinguished. Assuming that none of the other candles were extinguished.

How many candles are they left with in the end ?

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?

I never stop running even when I standstill. If I am formed by joining two identical bodies together, can you guess who I am?

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

A boy was at a carnival and went to a booth where a man said to the boy, "If I write your exact weight on this piece of paper then you have to give me $50, but if I cannot, I will pay you $50." The boy looked around and saw no scale so he agrees, thinking no matter what the carny writes he'll just say he weighs more or less. In the end the boy ended up paying the man $50. How did the man win the bet?

By including only four matchsticks in below picture, you have to make "Four Triangles And Two Squares"

There is a five-letter word which has 3 consonants(all are same) and 2 different vowels.
Also, something wrong is associated with the word.

Can you name it?