Class 11 Mathematics Trigonometric Functions MCQs Set 09

Question. Which of the following relation is correct
(a) \( \sin 1^{\circ} > \sin 1 \)
(b) \( \sin 1 > \sin 1^{\circ} \)
(c) \( \sin 1 = \sin 1^{\circ} \)
(d) \( \frac{\pi}{180} \sin 1 = \sin 1^{\circ} \)
Answer: B

Question. The radius of the circle whose arc of length 15 cm makes an angle of 3/4 radian at the centre is
(a) 10 cm
(b) 20 cm
(c) \( 11 \frac{1}{4} \text{ cm} \)
(d) \( 22 \frac{1}{2} \text{ cm} \)
Answer: B

Question. If A lies in the second quadrant and \( 3 \tan A + 4 = 0 \) then the value of \( 2 \cot A - 5 \cos A + \sin A \) is equal to
(a) \( \frac{-53}{10} \)
(b) \( \frac{-7}{10} \)
(c) \( \frac{7}{10} \)
(d) \( \frac{23}{10} \)
Answer: D

Question. \( \tan 1^{\circ} \tan 2^{\circ} \tan 3^{\circ} \tan 4^{\circ} \dots \dots \dots \dots \tan 89^{\circ} = \)
(a) 1
(b) 0
(c) \( \infty \)
(d) 1/2
Answer: A

Question. If \( \sec \theta + \tan \theta = p \), then \( \tan \theta \) is equal to
(a) \( \frac{2p}{p^2 - 1} \)
(b) \( \frac{p^2 - 1}{2p} \)
(c) \( \frac{p^2 + 1}{2p} \)
(d) \( \frac{2p}{p^2 + 1} \)
Answer: B

Question. If \( \sin \theta - \cos \theta = 1 \), then \( \sin \theta \cos \theta = \)
(a) 0
(b) 1
(c) 2
(d) 1/2
Answer: A

Question. If \( 5 \tan \theta = 4 \), then \( \frac{5 \sin \theta - 3 \cos \theta}{5 \sin \theta + 2 \cos \theta} \) equal to
(a) 0
(b) 1
(c) 1/6
(d) 6
Answer: C

Question. If \( \sin x + \sin^2 x = 1 \), then the value of \( \cos^{12} x + 3 \cos^{10} x + 3 \cos^8 x + \cos^6 x - 2 \) is equal to
(a) 0
(b) 1
(c) \( - 1 \)
(d) 2
Answer: C

Question. If \( x \sin 45^{\circ} \cos^2 60^{\circ} = \frac{\tan^2 60^{\circ} \csc 30^{\circ}}{\sec 45^{\circ} \cot^2 30^{\circ}} \), then \( x = \)
(a) 2
(b) 4
(c) 8
(d) 16
Answer: C

Question. If \( A = 130^{\circ} \) and \( x = \sin A + \cos A \), then
(a) \( x > 0 \)
(b) \( x < 0 \)
(c) \( x = 0 \)
(d) \( x \le 0 \)
Answer: A

Question. \( \frac{\cos 17^{\circ} + \sin 17^{\circ}}{\cos 17^{\circ} - \sin 17^{\circ}} \)
(a) \( \tan 62^{\circ} \)
(b) \( \tan 56^{\circ} \)
(c) \( \tan 54^{\circ} \)
(d) \( \tan 73^{\circ} \)
Answer: A

Question. \( \tan 75^{\circ} - \cot 75^{\circ} = \)
(a) \( 2\sqrt{3} \)
(b) \( 2 + \sqrt{3} \)
(c) \( 2 - \sqrt{3} \)
(d) None of these
Answer: A

Question. \( \sqrt{3} \csc 20^{\circ} - \sec 20^{\circ} = \)
(a) 2
(b) \( \frac{2 \sin 20^{\circ}}{\sin 40^{\circ}} \)
(c) 4
(d) \( \frac{4 \sin 20^{\circ}}{\sin 40^{\circ}} \)
Answer: C

Question. \( \cos^2 \alpha + \cos^2 (\alpha + 120^{\circ}) + \cos^2 (\alpha - 120^{\circ}) \) is equal to
(a) 3/2
(b) 1
(c) 1/2
(d) 0
Answer: A

Question. \( \sin 20^{\circ} \sin 40^{\circ} \sin 60^{\circ} \sin 80^{\circ} = \)
(a) -3/16
(b) 5/16
(c) 3/16
(d) -5/16
Answer: C

Question. \( \cos 20^{\circ} \cos 40^{\circ} \cos 80^{\circ} = \)
(a) 1/2
(b) 1/4
(c) 1/6
(d) 1/8
Answer: D

Question. \( 1 - 2 \sin^2 \left( \frac{\pi}{4} + \theta \right) = \)
(a) \( \cos 2\theta \)
(b) \( - \cos 2\theta \)
(c) \( \sin 2\theta \)
(d) \( - \sin 2\theta \)
Answer: D

Question. If \( \cos \alpha + \cos \beta = 0 = \sin \alpha + \sin \beta \), then \( \cos 2\alpha + \cos 2\beta = \)
(a) \( -2 \sin(\alpha + \beta) \)
(b) \( -2 \cos(\alpha + \beta) \)
(c) \( 2 \sin(\alpha + \beta) \)
(d) \( 2 \cos(\alpha + \beta) \)
Answer: B

Question. If \( \tan A = - \frac{1}{2} \) and \( \tan B = - \frac{1}{3} \), then A+B =
(a) \( \pi/4 \)
(b) \( 3\pi/4 \)
(c) \( 5\pi/4 \)
(d) None of these
Answer: B

Question. \( \frac{\sin 3\theta - \cos 3\theta}{\sin \theta + \cos \theta} + 1 = \)
(a) \( 2 \sin 2\theta \)
(b) \( 2 \cos 2\theta \)
(c) \( \tan 2\theta \)
(d) \( \cot 2\theta \)
Answer: A

Question. \( \tan 3A - \tan 2A - \tan A = \)
(a) \( \tan 3A \tan 2A \tan A \)
(b) \( - \tan 3A \tan 2A \tan A \)
(c) \( \tan A \tan 2A - \tan 2A \tan 3A - \tan 3A \tan A \)
(d) None of these
Answer: A

Question. If \( \cos A = m \cos B \), then
(a) \( \cot \frac{A+B}{2} = \frac{m+1}{m-1} \tan \frac{B-A}{2} \)
(b) \( \tan \frac{A+B}{2} = \frac{m+1}{m-1} \cot \frac{B-A}{2} \)
(c) \( \cot \frac{A+B}{2} = \frac{m+1}{m-1} \tan \frac{A-B}{2} \)
(d) None of these
Answer: A

Question. \( \tan 100^{\circ} + \tan 125^{\circ} + \tan 100^{\circ} \tan 125^{\circ} = \)
(a) 0
(b) 1/2
(c) -1
(d) 1
Answer: D

Question. If \( \sin A = \frac{1}{\sqrt{10}} \) and \( \sin B = \frac{1}{\sqrt{5}} \), where A and B are positive acute angles, then A + B =
(a) \( \pi \)
(b) \( \pi/2 \)
(c) \( \pi/3 \)
(d) \( \pi/4 \)
Answer: D

Question. \( \sin 50^{\circ} - \sin 70^{\circ} + \sin 10^{\circ} = \)
(a) 1
(b) 0
(c) 1/2
(d) 2
Answer: B

Question. \( \sin 12^{\circ} \sin 48^{\circ} \sin 54^{\circ} = \)
(a) 1/16
(b) 1/32
(c) 1/8
(d) 1/4
Answer: C

Question. \( \frac{\sin 3\theta + \sin 5\theta + \sin 7\theta + \sin 9\theta}{\cos 3\theta + \cos 5\theta + \cos 7\theta + \cos 9\theta} = \)
(a) \( \tan 3\theta \)
(b) \( \cot 3\theta \)
(c) \( \tan 6\theta \)
(d) \( \cot 6\theta \)
Answer: C

Question. \( \frac{\sin(B + A) + \cos(B - A)}{\sin(B - A) + \cos(B + A)} = \)
(a) \( \frac{\cos B + \sin B}{\cos B - \sin B} \)
(b) \( \frac{\cos A + \sin A}{\cos A - \sin A} \)
(c) \( \frac{\cos A - \sin A}{\cos A + \sin A} \)
(d) None of these
Answer: B

Question. If \( \sin 2x = n \sin 2y \), then the value of \( \frac{\tan(x + y)}{\tan(x - y)} \) is
(a) \( \frac{n+1}{n-1} \)
(b) \( \frac{n-1}{n+1} \)
(c) \( \frac{1-n}{n+1} \)
(d) \( \frac{1+n}{1-n} \)
Answer: A

Question. \( 2 \cos^2 \theta - 2 \sin^2 \theta = 1 \), then \( \theta = \)
(a) \( 15^{\circ} \)
(b) \( 30^{\circ} \)
(c) \( 45^{\circ} \)
(d) \( 60^{\circ} \)
Answer: B

Question. \( \cos^2 A(3 - 4 \cos^2 A)^2 + \sin^2 A(3 - 4 \sin^2 A)^2 = \)
(a) \( \cos 4A \)
(b) \( \sin 4A \)
(c) 1
(d) None of these
Answer: C

Question. \( \frac{3 \cos \theta + \cos 3\theta}{3 \sin \theta - \sin 3\theta} \) is equal to
(a) \( 1 + \cot^2 \theta \)
(b) \( \cot^4 \theta \)
(c) \( \cot^3 \theta \)
(d) \( 2 \cot \theta \)
Answer: C

Question. \( 2 \sin A \cos^3 A - 2 \sin^3 A \cos A = \)
(a) \( \sin 4A \)
(b) \( \frac{1}{2} \sin 4A \)
(c) \( \frac{1}{4} \sin 4A \)
(d) None of these
Answer: B

Question. If \( \cos A = \frac{3}{4} \), then \( 32 \sin \left( \frac{A}{2} \right) \sin \left( \frac{5A}{2} \right) = \)
(a) 7
(b) 8
(c) 11
(d) None of these
Answer: C

Question. If \( x = y \cos \frac{2\pi}{3} = z \cos \frac{4\pi}{3} \), then xy + yz + zx =
(a) \( - 1 \)
(b) 0
(c) 1
(d) 2
Answer: B

Question. If \( \sin \theta = - \frac{1}{\sqrt{2}} \) and \( \tan \theta = 1 \), then \( \theta \) lies in which quadrant-
(a) First
(b) Second
(c) Third
(d) Fourth
Answer: C

Question. \( \cos 24^{\circ} + \cos 5^{\circ} + \cos 175^{\circ} + \cos 204^{\circ} + \cos 300^{\circ} = \)
(a) 1/2
(b) \( - 1/2 \)
(c) \( \sqrt{3}/2 \)
(d) 1
Answer: A

Question. \( \cos^2 48^{\circ} - \sin^2 12^{\circ} = \)
(a) \( \frac{\sqrt{5} - 1}{4} \)
(b) \( \frac{\sqrt{5} + 1}{8} \)
(c) \( \frac{\sqrt{3} - 1}{4} \)
(d) \( \frac{\sqrt{3} + 1}{2\sqrt{2}} \)
Answer: B

Question. If \( \sin \alpha + \sin \beta = a \) and \( \cos \alpha - \cos \beta = b \), then \( \tan \left( \frac{\alpha - \beta}{2} \right) \) is equal to-
(a) \( - a/b \)
(b) \( - b/a \)
(c) \( \sqrt{a^2 + b^2} \)
(d) None of these
Answer: B

Question. If \( \tan \left( \frac{\alpha}{2} \right) \) and \( \tan \left( \frac{\beta}{2} \right) \) are the roots of the equation \( 8x^2 - 26x + 15 = 0 \) then \( \cos (\alpha + \beta) \) is equal to-
(a) \( - \frac{627}{725} \)
(b) \( \frac{627}{725} \)
(c) \( - \frac{725}{627} \)
(d) \( - 1 \)
Answer: A