Which is the smallest number that you can write using all the vowels exactly once?

Can you fill the blank with the correct number?

6 30 870 756030 _____

John is found dead in a bare field. Nobody killed John,
John did not commit suicide.

Inspector Jacob found a bag just a few meters away from John which could save his life. What was in the bag?

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

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.

One is to three as three is to five and five is to four and four is the magic number.
What is the pattern?

A man is found dead with a knife in his back When the investigation is done. A chair lays beside him and the forensic team finds moisture around the body.

If he committed suicide, how did he do it?

You have a basket containing ten apples. You have ten friends, who each desire an apple. You give each of your friends one apple.
Now all your friends have one apple each, yet there is an apple remaining in the basket.
How?

Baseball bat and ball cost $100. If the bat cost $99 more than the ball, what is the cost of each?

What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first two, and the last is three times the second?