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

Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

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

A man is walking down a road with a basket of eggs. As he
is walking he meets someone who buys one-half of his eggs
plus one-half of an egg.
He walks a little further and meets another person who buys
one-half of his eggs plus one-half of an egg.
After proceeding further he meets another person who buys
one-half of his eggs plus one half an egg. At this point, he
has sold all of his eggs, and he never broke an egg.
How many eggs did the man have to start with?

A sundial has the fewest moving parts of any timepiece. Which has the most?

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

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

Count the number of triangles in the given picture.

If all Goats are Sheep and all Sheep are Deers, are all Deers Goats ?

Kareena is older than Katrina and younger than Karishma. Isabelle is younger than Bipasha and Karishma. Bipasha is older than Karishma. If Kareena and Isabelle are the same age, who's the youngest?