What is wrong in the below Picture?

There is a square piece of paper with a hole that is denoted by the circle on the top right side in the given picture. You have to cut the paper in a manner that it forms two and only two separate pieces of paper and then rearrange the pieces in a manner that the holes come in the centre of the paper.

Can you fill the blank with the correct number?

6 30 870 756030 _____

Take one out and scratch my head, I am now black but once was red. What am I?

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

Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
x *
=====
* * *

I am eight letters long - "12345678"
My 1234 is an atmospheric condition.
My 34567 supports a plant.
My 4567 is too appropriate.
My 45 is a friendly thank-you.
My 678 is a man's name.

What word am I?

Imagine a box with two cogwheels, one big with 24 teeth and one small with 8 teeth. The big one is firmly attached to the center of the box which means it does not turn or move while the small one rotates around the big one.

How many times do you think that the smaller wheel will turn compared to the box when it turns once around the big one?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

A pond had 60 fish, out of which, all but 20 died.
How many fishes are now present in that pond?