Let f(x) = sin(π cos x) and g(x) = cos(2π sin x) be two functions defined for x > 0. Define, in increasing order, X = {x : f(x) = 0}, Y = {x : f′(x) = 0}, Z = {x : g(x) = 0}, and W = {x : g′(x) = 0}. List-I contains (I) X, (II) Y, (III) Z, (IV) W. List-II contains (P) ⊇ {π/2, 3π/2, 4π, 7π}; (Q) an arithmetic progression; (R) NOT an arithmetic progression; (S) ⊇ {π/6, 7π/6, 13π/6}; (T) ⊇ {π/3, 2π/3, π}; (U) ⊇ {π/6, 3π/4}.
Which of the following is the only CORRECT combination?