I shave every day, but my beard stays the same. What am I?

The teacher told the student that if he told a lie then he will be expelled from school and if he told the truth then he still is expelled from school.

What can a student say to prevent his being expelled from school?

I get hot but I never sweat,
I cook food but I am not a chef,
I have a door but you can't enter me,
I have a light but I am not a lamp.
Who am I?

In which direction should the missing arrow point?

The answer I give is yes, but what I mean is no. What was the question?

When we see 2 but call 10?

The person who makes it has no need for it. He who purchases it does not use it. The person who does use it does not know they are. What is it?

Two friends were stuck in a cottage. They had nothing to do and thus they started playing cards. Suddenly the power went off and Friend 1 inverted the position of 15 cards in the normal deck of 52 cards and shuffled it. Now he asked Friend 2 to divide the cards into two piles (need not be equal) with equal number of cards facing up. The room was quite dark and Friend 2 could not see the cards. He thinks for a while and then divides the cards in two piles.

On checking, the count of cards facing up is same in both the piles. How could Friend 2 have done it ?

There are three houses in a straight row. One is red, one is blue, and one is white. The red house is left of the middle. The blue house is right of the middle. Where's the white house?

What does the below mathematical rebus mean?