class 12

Missing

JEE Advanced

Let f(x)= $sin(πcosx)$ and g(x)=$cos(1πsinx)$ e two function defined for $x>0$ define the following sets whose elements are written in increasing order.

$X={x:f(x)=0},Y={x:f_{′}(x)=0}$

$Z={x:g(x)=0},W={x:g_{′}(x)=0}$

$List I(I) X(II) Y(III) Z(IV)W List II(P) ⊇{2π ,23π ,4π,7π}(Q)an arithmetic progression(R)not an arithmetic progression(S) ⊇{6π ,67π ,613π }(T) ⊇{3π ,32π ,π}(U) ⊇{6π ,43π } $

Q.