What work can one never finish?

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?

I am thinking of a five-digit number such that:
The first and last digits are the same, their submission is an even number and multiplication is an odd number and is equal to the fourth number. Subtract five from it and we obtain the second number. Then divide into exact halves and we get the 3rd number.

What number I am thinking of?

They came out at night, without being called.
They lost at day, without being stolen.
Who are they?

If a boy blows 18 bubbles,
Then pops 6 eats 7 and then
He pops 5 and blows 1.
How many are left?

Queen Elizabeth organised a royal party.

To Avoid uninvited guest royal family set a password.
Jack (an uninvited person) plan to enter the party. He stand nearby the door.

First guest comes, the security person said 'twelve' and guest replied with six.
Second guest comes , the security person said 'six' and guest replied with 'three'.

Jack thought is enough and he walked to the entry point. The security person said 'eight' , Jack replied smilingly 'four'.
He was immediately thrown out of the party. why ?

Name a key which is hardest to turn.

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

You have four chains. Each chain has three links in it. Although it is difficult to cut the links, you wish to make a single loop with all 12 links. What is the fewest number of cuts you must make to accomplish this task?

Sachin bought a car with a strange 5 digit numbered plate.The water image of the number is 78633 more than my car number. All the digits of car number are distinct.

What is the original number on number plate?