I am quite hot but become too cold if you remove the first two letters. What am I?

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

I was speeding and ran through a stop sign, yet two traffic officers who were there do nothing about it.

why?

Considering the below equation:

V + II - VI = 10
IV - X + VIII = 20
IV - VII + VI = 30

Then, I + II + III = ?

Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.
They need to guess their own hat colour by writing it on a piece of paper, or they can write 'pass'.
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
What is the best strategy?

Manish has to secure 40% marks to pass his B.tech final exams.
He got just 40 marks and failed by 40-marks.

What is the maximum marks?

What is common among 11, 69, and 88?

What jumps when it walks and sits when it stands?

If you remove one from eleven, it becomes ten. If you remove one from nine, it becomes ten.

How is this possible?

I am the black child of a white father, a wingless bird, flying even to the clouds of heaven. I give birth to tears of mourning in pupils that meet me, even though there is no cause for grief, and at once on my birth, I am dissolved into air. What am I?