Can you find a pattern and the missing number in the series given below?

100, 155, 258,? , 584, 819.

In my garden, I have many trees but only one of them is the mango tree. In these mango trees, there are some mangoes(as expected).

But after a strong wind, there are neither mangoes on the tree nor on the ground. Explain?

Sweet & very intelligent katty has 8 puppets(Jane Bird Barbie Angel Colleen Nora Lass Missy).
All puppets are of different size. She arrange all puppets to face towards the guest and tell the guess the following clues :

* Jane has three puppets bigger on its left side
* Bird has two puppets smaller on its left side
* Barbie has one puppet bigger on its right side
* Angel has two puppets smaller on its right side
* Colleen has one puppet bigger on its left side
* Nora has one puppet smaller on its left side
* Lass has four puppets bigger on its right side
* Missy has three puppets smaller on its right side

Also some puppets are inside the bigger puppets.

Assuming you are the guest , can you tell the katty how the puppets are arranged ?

Can you fill the blank with the correct number?

6 30 870 756030 _____

Irene killed hundreds of people mercilessly and yet the police were not able to put her behind the bars. Why?

Can you count the number of triangles in the given figure?

Spot what is wrong here in below Picture?

What is a word made up of 4 letters, yet is also made up of 3. Sometimes is written with 9 letters, and then with 4. Rarely consists of 6, and never is written with 5.

In the given figure, move three matchsticks so that the resulting figure contains two rectangles.

You can take four of the five letters out of this word, but the pronunciation never changes. What is the word?