What does does this rebus picture means ?

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

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

Find three whole, positive numbers that have the same answer when multiplied together as when added together.

Doctor Alex and a bus driver John are both in love with the same woman named Olivia. The bus driver need to go for a long trip of 10 days, Before he left he gave Olivia 10 apples.

Considering the below equation:

V + II - VI = 10
IV - X + VIII = 20
IV - VII + VI = 30

Then, I + II + III = ?

Tell me the Hindi name of a Vegetable which if we remove 1st word will become a precious Stone and by removing the last word it will become a sweet eatable.

There are a number of books on a shelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf?

A farmer went to a market and bought a wolf, a goat, and a cabbage. On his way home, the farmer came to the bank of a river and rented a boat. But crossing the river by boat, the farmer could carry only himself and a single one of his purchases: the wolf, the goat, or the cabbage. If left unattended together, the wolf would eat the goat, or the goat would eat the cabbage. The farmer’s challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it?

You are confined in a room and given two metal rods. Out of these two rods, one is magnet and the other is the iron rod. They look starkly similar. You don't have any other metal object in the room.

How will you decide which one of those is magnet?