Question

Answer the following by appropriately matching the lists based on the information given in the paragraph
Let $f(x)=\sin (\pi \cos x)$ and $g(x)=\cos (2 \pi \sin x)$ be two functions defined for $x>0$. Define the following sets whose elements are written in the increasing order :
$\mathrm{X}=\{\mathrm{x}: f(\mathrm{x})=0\}$, $\mathrm{Y}=\left\{\mathrm{x}: f^{\prime}(\mathrm{x})=0\right\}$
$\mathrm{Z}=\{\mathrm{x}: \mathrm{g}(\mathrm{x})=0\}$, $\mathrm{W}=\left\{\mathrm{x}: \mathrm{g}^{\prime}(\mathrm{x})=0\right\}$.
List-I contains the sets X,Y,Z and W. List -II contains some information regarding these sets.

| List-I | | List-II | |
| --- | --- | --- | --- |
| (I) | X | (P) | $\supseteq\left\{\frac{\pi}{2}, \frac{3 \pi}{2}, 4 \pi, 7 \pi\right\}$ |
| (II) | Y | (Q) | an arithmetic progression |
| (III) | Z | (R) | NOT an arithmetic progression |
| (IV) | W | (S) | $\supseteq\left\{\frac{\pi}{6}, \frac{7 \pi}{6}, \frac{13 \pi}{6}\right\}$ |
| | | (T) | $\supseteq\left\{\frac{\pi}{3}, \frac{2 \pi}{3}, \pi\right\}$ |
| | | (U) | $\supseteq\left\{\frac{\pi}{6}, \frac{3 \pi}{4}\right\}$ |

Which of the following is the only CORRECT combination ?

Accepted Answer

(C) (II), (Q), (T)

Answer

(A) (II), (R), (S)

Answer

(B) (I), (P), (R)

Answer

(D) (I), (Q), (U)

JEE Advanced · 2019 · 27 May 2019 · Paper 2 · Trigonometric Equations

Solution

More JEE Advanced questions on Trigonometric Equations

List-I		List-II
(I)	X	(P)	$\supseteq {\frac{π}{2}, \frac{3 π}{2}, 4 π, 7 π}$
(II)	Y	(Q)	an arithmetic progression
(III)	Z	(R)	NOT an arithmetic progression
(IV)	W	(S)	$\supseteq {\frac{π}{6}, \frac{7 π}{6}, \frac{13 π}{6}}$
		(T)	$\supseteq {\frac{π}{3}, \frac{2 π}{3}, π}$
		(U)	$\supseteq {\frac{π}{6}, \frac{3 π}{4}}$