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

Can you fill the blank with the correct number?

6 30 870 756030 _____

Once while in his court, King Akbar asked Birbal to write something on a wall that makes one sad when read in good times and makes one happy when read in sad times.

He took only a few moment and wrote something that fit the requirements. What did he write?

Can you find the mistake in the below statement?

We have arranged an array of numbers below. What you have to do is use any kind of mathematical symbol you know excluding any symbol that contains a number like cube root. You can use any amount of symbols but you have to come up with a valid equation for all of them.

0 0 0 = 6
1 1 1 = 6
2 + 2 + 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

1. What does:
TIM JOB
represent?

2. What does:
MO_ _
represent?

If you had an infinite supply of water and 5-quart and 3-quart pails, how would you measure exactly 4 quarts? What is the least number of steps you need?

There are nine letters in the below-given diagram. You have to form a nine-letter word using these letters.

What is both possible and impossible at the same time?

A man desired to get into his work building, however he had forgotten his code.
However, he did recollect five pieces of information
* Fifth number + Third number = 14
* The fourth number is one more than the second number.
* The first number is one less than twice the second number.
* The second number and the third number equals 10.
* The sum of all five numbers is 30.

What is the code ?