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Question

Answer Q.15 and Q.16 by appropriately matching the lists based on the information given in the paragraph.

Let f(x)=sin(πcosx) and g(x)=cos(2πsinx) 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},.
ListI contains the sets X,Y,Z and W. ListII contains some information regarding these sets.

List IList II(I)X(P){π2,3π2,4π,7π} (II)Y(Q)an arithmetic progression (III)Z(R)NOT an arithmetic progression(IV)Z(S){π6,7π6,13π6} (T){π3,2π3,π} (U){π6,3π4}
Q.15 which of the following is the only CORRECT combination?

A
(I),(P),(R)
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B
(II),(Q),(T)
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C
(I),(Q),(U)
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D
(II),(R),(S)
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Solution

The correct option is B (II),(Q),(T)
f(x)=0sin(πcosx)=0
πcosx=n1π, n1I
cosx=1, cosx=0, cosx=1
x=n2π2, n2I
X={π2,π,3π2,2π,.....}
f(x)=0cos(πcosx)πsinx=0
sinx=0 or cos(πcosx)=0
x=n3π or πcosx=(2n4+1)π2
cosx=12,12
x=n5π±π3
Y={π3,2π3,3π3,......}
Hence, set Y elements are in arithmetic progression.

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