Name one eight-letter word with 'kst' in the middle, 'in' the beginning, 'and' at the end.?

Rectify the following equality 101 - 102 = 1 by moving just one digit.

Detective Rockford was jogging near the beach at 4:30 am.
He hears a sound near the shack "No Michael, Please Do not shoot me".
Next instance he heard the sound of gunfire. Rockford rushes to the shack where he finds women lying dead and a gun in close proximity of three "Doctore Lawyer and a Teacher".

Rockford immediately knew that the Lawyer has committed the crime. How?

What has one eye, but can’t see?

You stand in front of two doors. A guard stands next to each door. You know the following things: one path leads to paradise, the other leads to death. You cannot distinguish between the two doors. You also know that one of the two guards always tells the truth and the other always lies. You have permission to ask one guard one question to discover which door leads to paradise. What one question would you ask to guarantee you enter the door to paradise?

I am Huge on Sunday and Saturday.
I am small from Tuesday to Thursday.
I do not exist on Monday and Friday.
Who am I?

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

Replace the 'X' with any mathematical symbol to make the expression equal to 111.

18 X 12 X 2 X 3 = 111

Using the clues below, what four numbers am I thinking of?

The sum of all the numbers is 31.
One number is odd.
The highest number minus the lowest number is 7.
If you subtract the middle two numbers, it equals two.
There are no duplicate numbers.

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

Who am I?