What word is pronounced the same if you take away four of its five letters?

Which is the smallest number that you can write using all the vowels exactly once?

Two in a corner, one in a room, zero in a house, but one in a shelter. What is it?

Solve the mathematical equation in the picture below.

Three cars are driving on a track that forms a perfect circle and is wide enough that multiple cars can pass anytime. The car that is leading in the race right now is driving at 55 MPH and the car that is trailing at the last is going at 45 MPH. The car that is in the middle is somewhere between these two speeds.
Right now, you can assume that there is a distance of x miles between the leading car and the middle car and x miles between the middle car and the last car and also, x is not equal to 0 or 1.
The cars maintain their speed till the leading car catches up with the last car and then every car stops. In this scenario, do you think of any point when the distance between any two pairs will again be x miles i.e. the pairs will be x distance apart at the same time ?

My first is in chocolate but not in ham. My second is in cake and also in jam. My third at tea time is easily found. Altogether, this is a friend who is often around. What is it?

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?

What 8 letter word can have a letter taken away and it still makes a word. Take another letter away and it still makes a word. Keep on doing that until you have one letter left. What is the word?

What number should come in place of the question mark below?

Can it be possible to build a house that has all its four walls facing towards the South?