I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

Solve below rebus puzzle?

In a mathematical quiz, you are asked the following question:

Use three 9s in a mathematical expression without dividing or multiplying to form the number one.

Can you answer the question?

Get total of 120 by using five zeros 0,0,0,0,0 and any one mathematical operator.
Do you ?

Find The Missing Number In the Sequence.
6 25 64 ? 32 1

If,

A + B = C
D - C = A
E - B = C

Based on the above equations, find out the answer for:

D + F = ?

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?

John and Jacob are playing bets. John gives $10 to Jacob and Jacob deals four cards out of a normal 52-card deck which are chosen by him completely randomly. Jacob keeps them facing down takes the first card and shows it to John. John has a choice of either keeping it or looking at the second card. When the second card is shown to him, he again has the choice of keeping or looking at the third which is followed by the third card as well; only if he does not want the third card, he will have to keep the fourth card.

If the card that John is choosing is n, Jacob will give it to him. Then the cards will be shuffled and the game will be played repeatedly. Now you might think that it all depends on chance, but John has come up with a strategy that will help him turn the favor in his odds.

Can you deduce the strategy of John?

I am quite hot but become too cold if you remove the first two letters. What am I?

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?