Can you divide the below-given shape into four equal and identical pieces?

John drives to his office at 20km/hr. After reaching the office, he realizes that today is a holiday. He went back at an average speed of 30km/hr. Discounting the time spent in the stoppage what was the average speed of his journey?

What word is pronounced the same if you take away four of its five letters?

Can you find out the remainder when 3^300 is divided by 5?

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?

I’m tall when I’m young, and I’m short when I’m old. What am I?

Make eight squares by moving only two matchsticks.
Note- Square can be of different sizes.

A Detective reviewed the information they had on the case so far.

A lady named 'Caterina' was found shot and they already had a list of suspects - Ankit, Tarun, Harish, Manoj and Manish.
The killer is a fan of challenges him by leaving notes ad various places.
* The first was found in a toilet room.
* The second was found in an art room.
* The third was in a restroom.
* the fourth in an underwater room.
* The fifth at the no-smoking room.

All of the notes read the same thing, 'The clues are where you find the notes.' Yet, nothing was found at any place the notes were.
Detective the genius, immediately solved the case.
Who was the killer?

Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
x *
=====
* * *

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?