Can you solve below mathematical equation?

2^1234 - 2^1233

Three doctors said that Bill was their brother. Bill says he has no brothers. How many brothers does Bill actually have?

Can you identify if it's a murder or a suicide ?

Find the missing number in the image below.

Use the digits from 1 up to 9 and make 100.

Follow the rules.
=> Each digit should be used only once.
=> You can only use addition.
=> For making a number, two single digits can be combined (for example, 4 and 2 can be combined to form 42 or 24)
=> A fraction can also be made by combining the two single digits (for example, 4 and 2 can be combined to form 4/2 or 2/4)

Question: how can we do this?

I cry without having a voice.
I fly without having wings.
I bite without having teeth.
I whisper without a mouth.

Who am I?

If we tie a Sheep to one peg, a circled grass is been eaten by the Sheep. If we tie the Sheep to two pegs with a circle on its neck, then an eclipse is eaten out of the grass by the Sheep. If we want an eclipse then we put two pegs and then put a rope in between them and the other end of the rope is tied up on the Sheep's neck.

How should we tie the peg and the Sheep so that a square is eaten out from the garden grass? We only have one Sheep rope and the peg and the rings.

What 8 letter word can have a letter taken away and it still makes a word. Take another letter away and it still makes a word. Keep on doing that until you have one letter left. What is the word?

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.

Manish and Manoj play 5 games of chess.
Both Manish and Manoj win the exact same number of games. There is no tie at all.

How?