Can you find a number that lies one third of the distance between 1/3 and 2/3?

Which of the following words don't belong in the group and why?
CORSET, COSTER, SECTOR, ESCORT, COURTS

I am first found in caves, now prolific online; I am a depiction, a drawing, a symbol, or sign. I will convey whichever mood you could wish; or for that matter, a fist, flask, or fish. What am I?

Why do we preferably have round manhole covers and not square ones?

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

Count the number of times the letter "F" appears in the following paragraph:

FAY FRIED FIFTY POUNDS OF
SALTED FISH AND THREE POUNDS
OF DRY FENNEL FOR DINNER FOR
FORTY MEMBERS OF HER FATHER'S FAMILY.

What came first, the chicken or the egg?

Find out the missing number in the picture attached:

I have lakes with no water, mountains with no stone and cities with no buildings. What am I?

Can you make numbers like 24, using numbers 3,3,7 & 7 with any arithmetic operator?