JEE MATH APEX

Trigonometry-JEE-Main-PYQ’s

Mathematics Questions

Let f(\theta) = 3 \left( \sin^4 \left( \frac{3\pi}{2} - \theta \right) + \sin^4 (3\pi + \theta) \right) - 2 (1 - \sin^2 2\theta) and S = \left\lbrace \theta \in [0, \pi] : f'(\theta) = -\frac{\sqrt{3}}{2} \right\rbrace. If 4\beta = \sum_{\theta \in S} \theta, then f(\beta) is equal to:
(A) \frac{9}{8}
(B) \frac{3}{2}
(C) \frac{5}{4}
(D) \frac{11}{8}
Click to View Answer
Correct Answer: [ ]
2 \sin \left( \frac{\pi}{22} \right) \sin \left( \frac{3\pi}{22} \right) \sin \left( \frac{5\pi}{22} \right) \sin \left( \frac{7\pi}{22} \right) \sin \left( \frac{9\pi}{22} \right) = \, ?
(A) \dfrac{3}{16}
(B) \dfrac{1}{16}
(C) \dfrac{1}{32}
(D) \dfrac{9}{32}
Click to View Answer
Correct Answer: [ ]
If \cot \alpha = 1 and \sec \beta = -\frac{5}{3}, where \pi < \alpha < \frac{3\pi}{2} and \frac{\pi}{2} < \beta < \pi, then the value of \tan (\alpha + \beta) and the quadrant in which \alpha + \beta lies, respectively are:
(A) -\frac{1}{7} and IVth quadrant
(B) 7 and Ist quadrant
(C) -7 and IVth quadrant
(D) \frac{1}{7} and Ist quadrant
Click to View Answer
Correct Answer: [ ]
\alpha = \sin 36^\circ is a root of which of the following equation?
(A) 16x^4 - 10x^2 - 5 = 0
(B) 16x^4 + 20x^2 - 5 = 0
(C) 16x^4 - 20x^2 + 5 = 0
(D) 4x^4 - 10x^2 + 5 = 0
Click to View Answer
Correct Answer: [ ]
The value of \cos\left(\frac{2\pi}{7}\right) + \cos\left(\frac{4\pi}{7}\right) + \cos\left(\frac{6\pi}{7}\right) is equal to:
(A) -1
(B) -\frac{1}{2}
(C) -\frac{1}{3}
(D) -\frac{1}{4}
Click to View Answer
Correct Answer: [ ]
Find the value of: 16 \sin(20^\circ) \sin(40^\circ) \sin(80^\circ)
(A) \sqrt{3}
(B) 2\sqrt{3}
(C) 3
(D) 4\sqrt{3}
Click to View Answer
Correct Answer: [ ]
The value of 2 \sin(12^\circ) - \sin(72^\circ) is:
(A) \dfrac{\sqrt{5}(1 - \sqrt{3})}{4}
(B) \dfrac{1 - \sqrt{5}}{8}
(C) \dfrac{\sqrt{3}(1 - \sqrt{5})}{2}
(D) \dfrac{\sqrt{3}(1 - \sqrt{5})}{4}
Click to View Answer
Correct Answer: [ ]
The value of 2 \sin \left( \frac{\pi}{8} \right) \sin \left( \frac{2\pi}{8} \right) \sin \left( \frac{3\pi}{8} \right) \sin \left( \frac{5\pi}{8} \right) \sin \left( \frac{6\pi}{8} \right) \sin \left( \frac{7\pi}{8} \right) is:
(A) \dfrac{1}{4\sqrt{2}}
(B) \dfrac{1}{4}
(C) \dfrac{1}{8}
(D) \dfrac{1}{8\sqrt{2}}
Click to View Answer
Correct Answer: [ ]
If \tan\left(\frac{\pi}{9}\right),\ x,\ \tan\left(\frac{7\pi}{18}\right) are in arithmetic progression and \tan\left(\frac{\pi}{9}\right),\ y,\ \tan\left(\frac{5\pi}{18}\right) are also in arithmetic progression, then |x - 2y| is equal to:
(A) 4
(B) 3
(C) 0
(D) 1
Click to View Answer
Correct Answer: [ ]
If \sin \theta + \cos \theta = \frac{1}{2}, then 16(\sin(2\theta) + \cos(4\theta) + \sin(6\theta)) is equal to:
(A) 23
(B) -27
(C) -23
(D) 27
Click to View Answer
Correct Answer: [ ]

Pages: 1 2 3 4 5 6 7

Comments

Leave a comment