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?

During which month do people sleep the least?

I drive at an average speed of 30 miles per hour to the railroad station each morning and catch my train. On a particular morning, there was a lot of traffic and at the halfway point, I had averaged only 15 miles per hour. How fast must I drive for the rest of the way to catch my train?

When I got four, I have it none.
When I got two, I have it some.
When I got none, I have it all.

What is it?

If it took eight men ten hours to build a wall, how long would it take four men to build it?

Spelt forwards I’m what you do every day, spelled backwards I’m something you hate. What am I?

What is black when you buy it, red when you use it, and gray when you throw it away?

A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?

If Rajina's daughter is my daughter's mom, who am I to Rajina?

There are five people. One of them shot and killed one of the other five.
We know following clues:
1. Dan ran in the NY City Marathon yesterday with one of the innocent men.
2. Mike consider being a farmer before he moved to the city.
3. Jeff is a top notch computer consultant and wants to install Ben new computer next week.
4. The murderer had his leg amputated last month.
5. Ben met Jack for the first time six months ago.
6. Jack has been in seclusion since the crime.
7. Dan used to drink heavily.
8. Ben and Jeff built their last computers together.
9. The murderer is Jack's brother. They grew up together in Seattle.

Consider yourself to be a famous detective "Sherlock Homles", Can you find the killer?