What is at the end of a rainbow?

One day, all the courtiers from Akbar's court were gathered in the assembly hall when one of them told the Emperor that all his valuables had been stolen by a thief the previous night.
This shocked the Emperor to his core as the place where that courter stayed was the most secured in the kingdom. The Emperor thought that it is not at all possible for an outsider to enter into the courtier's house and steal the valuables. Only another courtier could commit this crime. He quickly called Birbal to identify the thief.
Birbal thought for a while and successfully solved the mystery by identifying the thief in just one statement.
What did Birbal say?

What 8 letter word can have a letter taken away and it still makes a word. Take another letter away and it still makes a word. Keep on doing that until you have one letter left. What is the word?

Using the clues below, what four numbers am I thinking of?

The sum of all the numbers is 31.
One number is odd.
The highest number minus the lowest number is 7.
If you subtract the middle two numbers, it equals two.
There are no duplicate numbers.

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

Can you write down eight eights so that they add up to one thousand?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.

Irene killed hundreds of people mercilessly and yet the police were not able to put her behind the bars. Why?

Which statement is true out of the following?
One statement here is false.
Two statements here are false.
Three statements here are false.

Can you find out the number of the parking space in which the car is parked?