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

Which of the following words don't belong in the group and why?
CORSET, COSTER, SECTOR, ESCORT, COURTS

Today is John's birthday.
A year ago, John had five candles and he lit all the candles except the one at the last.
Now he is going to light all the candles.

How old is John Today?

(He is not five today.....)

A California farmer owns a beautiful pear tree. He supplies the fruit to a nearby grocery store. The store owner calls the farmer to see how much fruit is available for him to buy. The farmer knows the main trunk has 24 branches. Each branch has exactly 12 boughs and each bough has exactly 6 twigs. Since each twig bears one piece of fruit, how many plums will the farmer be able to deliver?

We have arranged an array of numbers below. What you have to do is use any kind of mathematical symbol you know excluding any symbol that contains a number like cube root. You can use any amount of symbols but you have to come up with a valid equation for all of them.

0 0 0 = 6
1 1 1 = 6
2 + 2 + 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

On a certain day, John celebrated his birthday. Two days later, his older twin brother Jacob celebrated his birthday.

Is this even possible? How can it be?

What goes up but never comes down?

Replace the question mark in the picture below.

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

Buy me, smell me or deliver me, I do not change.

Who am I?