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

In my garden, I have many trees but only one of them is the mango tree. In these mango trees, there are some mangoes(as expected).

But after a strong wind, there are neither mangoes on the tree nor on the ground. Explain?

You need to remove two matchsticks to make the below equation true. Can you do it ?

A king sentenced a man to the death sentence for some crime he had committed. Known for his kindness, the king told the culprit that he had a choice to die in a way he decides.

The culprit was clever and said something that saved him from death. What method do you think he must have chosen for his death?

Can you complete the sequence puzzle?

AR TA GE CA LE VI LI _

When it is alive we sing, when it is dead we clap our hands. What is it?

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

Who am I?

Twenty frogs are sitting on a log floating on the surface of a river. Two of them decide to jump off into the water.

How many frogs are there on the log at this moment?

In the image below, you can see two glasses and two matchsticks.You need to move four matchsticks in such a manner that the crosses come inside the glasses. Note: you cannot move the crossed.

By using all numbers, i.e. 123456789 and subtraction/addition, operators number 100 can be formed in many ways.
Example: 98 + 7 + 6 - 5 - 4 - 3 + 2 - 1 = 100

But if we add a condition use of the number 32 is a must. Then there are limited solutions.
One of such solution is: 9 - 8 + 76 + 54 - 32 + 1 = 100

Can you tell me any other solution?