Q 2703023848.     Consider a quadratic function `f(x) = ax^2 + bx + c, (a, b, c in R, a ne 0)` and satisfying the following
conditions

(i) `f(x-4) = f(2-x) ∀ x in R` and `f(x) ge x ∀ x in R`

(ii) `f(x) le ((x+1)/2)^2 ∀ x in (0 , 2)`

(iii) The minimum value of `f(x)` is zero
The value of the leading coefficient of the quadratic polynomial is

A

`1/4`

B

`1/3`

C

`1/2`

D

`1`

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