Match each entry in List-I to the correct entry in List-II and choose the correct option. | List-I | List-II | |--------|--------| | (P) The number of elements in the set $\left\{\mathrm{x} \in[-\pi, \pi]: \sin ^{6} \mathrm{x}+\cos ^{4} \mathrm{x}=1\right\}$ | (1) is 1 | | (Q) The number of elements in the set $\left\{\mathrm{x} \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]: \sin ^{2} \mathrm{x}+\cos ^{6} \mathrm{x}=1\right\}$ | (2) is 2 | | (R) The number of elements in the set $\left\{\mathrm{x} \in[-\pi, \pi]: \cos ^{2}\left(\frac{\mathrm{x}}{2}\right)-\sin ^{2} \mathrm{x}=\frac{1}{2}\right\}$ | (3) is 3 | | (S) The number of elements in the set $\left\{x \in[-2 \pi, 2 \pi]: 6 \sin ^{2}\left(\frac{x}{2}\right)-\cos 3 x=3\right\}$ | (4) is 4 | | | (5) is 5 |

(B) (P)→(5), (Q)→(3), (R)→(2), (S)→(4)

(A) (P)→(2), (Q)→(5), (R)→(3), (S)→(4)

(C) (P)→(5), (Q)→(4), (R)→(1), (S)→(3)

(D) (P)→(4), (Q)→(3), (R)→(2), (S)→(5)

JEE Advanced · 2026 · 17 May 2026 · Paper 1 · Trigonometric Equations

Match each entry in List-I to the correct entry in List-II and choose the correct option.

List-I	List-II
(P) The number of elements in the set ${x \in [- π, π] : sin^{6} x + cos^{4} x = 1}$	(1) is 1
(Q) The number of elements in the set ${x \in [- \frac{π}{2}, \frac{π}{2}] : sin^{2} x + cos^{6} x = 1}$	(2) is 2
(R) The number of elements in the set ${x \in [- π, π] : cos^{2} (\frac{x}{2}) - sin^{2} x = \frac{1}{2}}$	(3) is 3
(S) The number of elements in the set ${x \in [- 2 π, 2 π] : 6 sin^{2} (\frac{x}{2}) - cos 3 x = 3}$	(4) is 4
	(5) is 5

Answer: (B)

(P)

sin^{6} x + cos^{4} x = 1

requires

sin^{6} x = sin^{2} x

and

cos^{4} x = cos^{2} x

, giving

sin^{2} x \in {0, 1}

and

cos^{2} x \in {0, 1}

. Solutions:

x = - π, - π /2, 0, π /2, π

. P→5.

(Q)

sin^{2} x + cos^{6} x = 1

gives solutions

x = - π /2, 0, π /2

. Q→3.

(R) Simplifying gives

2 cos^{2} x + cos x - 2 = 0

, with

cos x = \frac{- 1 + 17}{4}

. In

[- π, π]

, 2 solutions. R→2.

(S) Simplifying gives

4 cos^{3} x = 0

, so

x = \pm π /2, \pm 3 π /2

. In

[- 2 π, 2 π]

, 4 solutions. S→4.

Answer: (B).

JEE Advanced · 2026 · 17 May 2026 · Paper 1 · Single correct option