I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

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?

How many points are there on the globe where, by walking one mile south, then one mile east and then one mile north, you would reach the place where you started?

what does the below math rebus puzzle mean?

You have three orange, two pink and five purple balls in the drawer beside your bed. There is no electricity and the room is entirely dark. How many balls must you take out to ensure at least one ball of each colour at least?

I know a 5-digit number having a property that With a 1 after it, it is three times as large as it would be with a one before it.

Guess the number?

There is a box full of marbles,
all but two are blue,
all but two are green,
and all but two are red.

How many marbles are in the box?

What is the fastest way to double your money?

A word I know,
Six letters contain,
Subtract just one,
And twelve is what remains.

The following question it puts forth you:

25 - 55 + (85 + 65) = ?

Then, you are told that even though you might think it's wrong, the correct answer is actually 5!

Whats your reaction to it? How can this be true?