Which is the correct shadow of the bird?

If,

20 % 5 = 24

21 % 7 = 33

42 % 6 = 67

Then;

66 % 6 = ?

I am a word of 12 alphabets.

* Alphabets 12, 4, 7, 2, 5 : Eastern beast of burden
* Alphabets 1, 8, 10, 9 are street made famous by Sinclair Lewis.
* Alphabets 11, 3, 6 are past.

On whole it means a person suffering from delusions of greatness.

What Is it ?

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

During a secret mission, an agent gave the following code to the higher authorities
AIM DUE OAT TIE MOD

However, the information is in one word only and the rest are fake. To assist the authorities in understanding better, he also sent them a clue, If I tell you any one character of the code, you can easily find out the number of vowels in the codeword.

Can you find out the code word?

I start and end with 500 and carry a 5 in my heart. But I require the first letter and the first number to be complete. I am the name of a King.

Who am I ?

In front of you, there are 9 coins. They all look absolutely identical, but one of the coins is fake. However, you know that the fake coin is lighter than the rest, and in front of you is a balance scale. What is the least number of weightings you can use to find the counterfeit coin?

One night, a woman receives a call from the police. They tell her that her husband was murdered and that she should come to the crime scene as soon as possible. The woman drops the phone, shocked, and drives 20 minutes to the crime scene. As soon as she reaches the crime scene, the police arrest her and she is convicted of murder. How do the police know she committed the crime?

I am the beginning of the end, and the end of time and space. I am essential to creation, and I surround every place. What am I?

Can you think of any three-dimensional shape that comprises of exactly two surfaces?