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

Imagine a box with two cogwheels, one big with 24 teeth and one small with 8 teeth. The big one is firmly attached to the center of the box which means it does not turn or move while the small one rotates around the big one.

How many times do you think that the smaller wheel will turn compared to the box when it turns once around the big one?

What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first two, and the last is three times the second?

The doctor advised his patient to take a tablet after every fifteen minutes. He gave him five tablets in total.

How much time will he take to have all the five tablets?

It is an eleven letter word.
The first, second, third and fourth letters form a banquet's name.
The fifth, sixth and seventh letters form a car's name.
The eighth, ninth, tenth and eleventh letters form a mode of transport.

Can you identify what word it is?

In the following series, a set of numbers is progressing with a particular pattern. Can you deduce that pattern and find the missing set?

(2 + 6), (21 + 6), (58 + 6), (119 + 6), ___

What English word has three consecutive double letters?

What number comes next in the series?

5 15 5 18 5 24 14 20 _

A famous swimmer can swim downstream in a lake in exactly 40 minutes with the lake current.
He can swim upstream in that lake in exactly 60 minutes against the lake current.
The length of the lake is 2 km.

How long he can cover the distance of one side at a still lake with no current?

Prove that twice of ten is the same as twice of eleven.