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

What does the below rebus riddle means?

What am I?

I went to the bookshop and spent one-half of the money that was in my purse.

When I came out, I found that I had as many cents as I had dollars and half as many dollars as I had cents when I went in. Find the money in my purse when I entered the store.

Can you divide the below-given shape into four equal and identical pieces?

Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
x *
=====
* * *

Solve The below Equation:

ALFA + BETA + GAMA = DELTA

Sherlock Holmes was challenged to make a pre-drawn line smaller without erasing it. He did it in fractions of seconds. How?

A new Engineering building containing 100 offices had just been completed. John was hired to paint the numbers 1 to 100 on the doors. How many times will John have to paint the number nine (9)?

Replace the question mark with the number below given a simple math problem.