Let f x = sin ⁡ π cos ⁡ x and g x = cos ⁡ 2 π sin ⁡ x be two functions defined for x > 0 . Define the following sets whose elements are written in the increasing order: X = x : f x = 0 , Y = x : f ' x = 0 Z = x : g x = 0 , W = x : g ' x = 0 List- I contains the sets X , Y , Z and W . List- I I contains some information regarding these sets. List- I List- II I X P ⊇

Step-by-step solution

I f x = sin ⁡ π cos ⁡ x   and X = x : f x = 0 f x = 0 ⇒ sin ⁡ π cos ⁡ x = 0 ⇒ π cos ⁡ x = m π ,   m ∈ I ⇒ cos ⁡ x = m cos ⁡ x = 0 ,   1 ,   - 1 ⇒ x = n π 2 ⇒ X = n π 2 ,   n ∈ I ⇒ X = ± π 2 ,   ± π , ± 3 π 2 , ±   2 π … … I - P ,   Q I I   g x = cos ⁡ 2 π sin ⁡ x and Z = x : g x = 0 co