Consider the following for the next two (02) items that follow :

In the triangle ABC, 

a² + b² + c² = ac + √3 bc

If c = 8, what is the area of the triangle ?

Consider the following for the next two (02) items that follow :

Consider the function

f(x) = |x - 2| + |3 - x| + |4 - x|, where x ∈ R.

At what value of x does the function attain minimum value ?

Consider the following for the next two (02) items that follow :

Consider the function

f(x) = |x - 2| + |3 - x| + |4 - x|, where x ∈ R.

What is the minimum value of the function ?

Consider the following for the next two (02) items that follow :

Consider the sum 

S = 0! + 1! + 2! + 3! + 4! +... .+ 100!  

If the sum S is divided by 8, what is the remainder ?