Our product and our sum always give the same answer. Who are we?

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 chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?

Spelt forwards I’m what you do every day, spelled backwards I’m something you hate. What am I?

What is the next shape from answers A, B, C, and D figure?

In a town, there are four houses located at different distances from each other. Following are the distances:

The third house is 60 meters apart from the first house.
The fourth house is 40 meters apart from the second house.
The third house is 10 meters nearer to the fourth house than it is to the second house.

Can you find out the distance between the fourth and the first house?

How can you make a TV, a bed, a dog, and a car liquid?

Solve the puzzle by telling what does below picture means.

You need to move three matchsticks to form three squares. Can you do it?

The below given figure comprises of a pattern through which you can determine the missing letter. Can you push your mind to find the pattern and add the missing letter?