Can you find out which number multiplied by itself will give the output as 12345678987654321?

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

500 women soldiers are arranged in an array of ten rows and fifty columns in accordance with their respective heights. Now, the tallest woman from each row is asked to move out in the front. From them, the shortest one is labelled as Alpha. They are then asked to resume their original position.

Now, the shortest woman in each column is asked to come out in front. The tallest among them is labelled as Beta.

Can you find out if Alpha will be taller or Beta?

You visit a home for specially-abled children on the occasion of Christmas where you meet with 50 children. You have a box of chocolates containing 50 chocolates exactly.

What if you were asked to one chocolate to each child in a manner that one chocolate still remains in the box? Is it possible?

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

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

The square root of number 121 is "11". What is the square root of the number "12345678987654321."?

It spends most of its day eating white, but when it’s quick enough, it gets to eat fruit and sometimes some blue things. It’s in a dark room, where the walls are blue, it runs from a ghost that roams the halls and haunts it all the time. What is it?

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

It is always ahead of me yet I can never see it. What is it?

As shown in the picture below, we can see a boy hanging on the tree branch to save his life. There are various ways in which he can die like1. A snake hanging toward the right waiting to bite the boy.2. A roaring Lion near the tree.3. Two crocodiles are ready to attack if the boy reaches near water. The tree is chopped to some extent, so can fall as if he moves a lot. Can you give this boy an escape plan?