I am never scared but became petrified and can’t live in a house but would die to make one. What am I?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

A tree doubled in height each year until it reached its maximum height over the course of ten years. How many years did it take for the tree to reach half its maximum height?

The King of a distant land had heard that Birbal was one of the wisest men in the East and so desired to meet Birbal. He sent Birbal an invitation to visit his country.

In due course, Birbal arrived in the distant kingdom. When he entered the palace he was flabbergasted to find not one but six kings seated there. All looked alike. All were dressed in kingly robes. Who was the real king?

The very next moment he got his answer. Confidently, he approached the king and bowed to him.

How did Birbal know who was the real king?

Christina is practising her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, Niharika is standing in the 4th position from either end of the row.
Can you find out how many girls are practising together?

How many cubic feet of dirt are in a hole of one foot deep, three feet long, and two feet wide?

I’m orange, I wear a green hat and I sound like a parrot. What am I?

There is so small cabin inside a deep forest.
All the forest burned out to worst possible but the inside of the cabin is still the same.
However all the person inside the cabin die.

How come ?

Solve the mathematical equation in the picture below.