I have branches, but no fruit, trunk or leaves. What am I?

Solve the mathematical equation in the picture below.

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?

Consider this about a word: The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?

If you drop a 15 kg iron bar and a 5 kg bag of cotton from a height of 50 meters which will reach the ground first?

Solve the below puzzle by replacing the question mark with the correct number.

3 6 12

4 8 16

5 10 ?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

Can you solve this amazing hard number series problem?
7, 8, 10, 12, 16, 18 ?

John is selling fruits.
He sells grapes at $30, Dates $25, and a Wolfberry $45.
At what price does he sell fig?

PS: Logical Thinking

Some friends went on a vacation to a resort. It was raining heavily and it kept raining for thirteen days.

When it rained in the morning, the afternoon was beautiful and when it rained in the afternoon, the day was blessed with a clear morning.

Overall, the friends experienced eleven nice mornings and twelve nice afternoons. Can you find out the number of days they spent on vacation?