Which is the rope you never skip with?

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.

A detective visits his friend John just to discover that John's neighbour Dr Jacob was murdered. Dr Jacob, who is a mathematician wrote the murderer's name in a code word "Hcqtfz". There were five suspects
1. Ajit
2. Pankaj
3. Ganpat
4. Deenu
5. Hariya

The Detective was instantly able to find the murderer.
Can you?

It is a nine-letter word.
The exact opposite of the phrase "friendly and outgoing"
It contains the word "over".
It starts will a vowel.

What is it?

The first box has two white balls. The second box has two black balls. The third box has a white and a black ball.

Boxes are labeled but all labels are wrong!

You are allowed to open one box, pick one ball at random, see its colour and put it back into the box, without seeing the colour of the other ball.

How many such operations are necessary to correctly label the boxes?

Can you identify the Oscar-winning movie from the rebus below?

An office is divided into 8 cubicles. How many of the cubicles are painted if only 1/8 of the cubicles are painted?

Complete the table series riddle by finding the number that can replace "??".

Bay of Bengal is in which state?

Which is Odd One Out and why?

4377

3954

9862

8454

9831