What does the following BrainBat signifies?

ABCDEFGHIJKLMNOPQRSTUVWYZ

QQQQQQQQQQQQQQQQQQQQQQQQQ.

I know a nine-letter word having only one vowel.
Do you ?

A man was convicted of a minor offence in Akbar court. Akbar decided to give him a chance. He asked him to give a statement. If the statement is true, he will be killed by lions and if it is false, he will be killed by trampling of wild elephants.

The convicted person requested help from Birbal and since the crime was not a big one, Birbal decided to help him. Whatever Birbal suggested impressed Kabir and he let the convicted person go.

What did Birbal suggest to the person?

If you drop me I’m sure to crack, but give me a smile and I’ll always smile back. What am I?

A father's child, a mother's child, yet no one's son.

Who am I?

You are given 16 witch hats. The hats are divided in four different colours – red, blue, green and yellow. Every colour has been assigned to four hats. Now each of the hat will be glued with a label of an arithmetic sign – ‘+’, ‘-‘, ‘x’ or ‘/’. But you can label one sign only once on one colour. In such an arrangement, the hats can be uniquely defined by its colour and symbol.

Can you arrange all the 16 hats in a 4x4 grid in a fashion that no two rows and columns have a repetition of colour or sign?
We have arranged four hats in the below picture to assist you.

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

John is asked to stand behind Jacob and Jacob is asked to stand behind John. Both of them feel confused about it and don't know what to do?

But it is quite possible, do you know how?

Three men in a cafe order a meal the total cost of which is $15. They each contribute $5. The waiter takes the money to the chef who recognises the three as friends and asks the waiter to return $5 to the men.

The waiter is not only poor at mathematics but dishonest and instead of going to the trouble of splitting the $5 between the three he simply gives them $1 each and pockets the remaining $2 for himself.

Now, each of the men effectively paid $4, the total paid is therefore $12. Add the $2 in the waiters pocket and this comes to $14. Where has the other $1 gone from the original $15?

Which fur should we be getting from the Lion?