I travel all around the world but always stay in the corner. What am I?

Remove two matchsticks to make the below equation correct.

I never stop running even when I standstill. If I am formed by joining two identical bodies together, can you guess who I am?

When I go in I might cause pain. I cause you to spit and ask you not to swallow. I can fill your hole. What am I?

I sleep during the day and fly at night, but I have no feathers to aid my flight. What am I?

How can you make the following equation true by drawing only one straight line: 5+5+5=550 ?

You find yourself in a strange place guarded by two guards.One of the guard always say truth while other always lies.You don't know the identity of the two.You can ask only one question to go out from there. What should you ask?

Replace the question mark with the correct number below.

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?

A professor thinks of two consecutive numbers between 1 and 10.
'A' knows the 1st number and 'B' knows the second number

A: I do not know your number.
B: Nor do I know your number.
A: Now I know.

What are the four solutions for this?