Class 10th Objective Question Chapter 8 Trigonometry MCQ
1. यदि \(\tan \theta = \frac{4}{3}\), तब \(\sin \theta + \cos \theta = ?\) [2021AII]
A) \(\frac{7}{3}\) B) \(\frac{7}{4}\) C) \(\frac{7}{5}\) D) \(\frac{5}{7}\) उत्तर देखेंAnswer- (C) \(\frac{7}{5}\)
2. यदि \(\tan \theta = \sqrt{3}\), तब \(\sec \theta \) होगा [2021AII]
A) \(\frac{2}{\sqrt{3}}\) B) \(\frac{\sqrt{3}}{2}\) C) \(\frac{1}{2}\) D) 2 उत्तर देखेंAnswer- (D) 2
3. यदि \(4 \tan \theta = 4\) तो \(\theta \) का मान है [2021AII]
A) \(0^\circ\) B) \(30^\circ\) C) \(45^\circ\) D) \(60^\circ\) उत्तर देखेंAnswer- (C) \(45^\circ\)
4. एक घड़ी के मिनट की सुई द्वारा 60 मिनट में बनाया गया कोण है [2021AII]
A) 60° B) 120° C) 180° D) 360° उत्तर देखेंAnswer- (D) 360°
5. \(\frac{2(1 – \sin^2 A)}{\cos^2 A} = \) [2021AII]
A) 1 B) -2 C) 2 D) 0 उत्तर देखेंAnswer- (C) 2
6. यदि \(\theta = 90^\circ\) तो \(\sin \theta – \cos \theta = ?\) [2021AII]
A) 0 B) 1 C) 2 D) \(\frac{1}{2}\) उत्तर देखेंAnswer- (B) 1
7. दिए गए समकोण \(\Delta ABC\) में, \(\frac{AB}{AC} =?\) [2021AII]
A) \(\sin a\) B) \(\cos a\) C) \(\sec a\) D) \(cosec a\) उत्तर देखेंAnswer- (B) \(\cos a\)
8. \(\sec \theta + \tan \theta (1 – \sin \theta) = ?\) [2021AII]
A) \(\sin \theta\) B) \(cosec \theta\) C) \(\cos \theta\) D) \(\sec \theta\) उत्तर देखेंAnswer- (D) \(\sec \theta\)
9. \(\tan 50^\circ + \cot 40^\circ = ?\) [2021AII]
A) 1 B) \(\cot 40^\circ\) C) \(\tan 50^\circ\) D) \(2 \tan 50^\circ\) उत्तर देखेंAnswer- (D) \(2 \tan 50^\circ\)
10. यदि \(cosec \theta = \frac{17}{8}\) तो \(\tan \theta =\) [2021AII]
A) \(\frac{8}{17}\) B) \(\frac{8}{15}\) C) \(\frac{15}{8}\) D) \(\frac{15}{17}\) उत्तर देखेंAnswer- (B) \(\frac{8}{15}\)
11. यदि \(cosec \theta = \frac{b}{a}\) तो \(\sec \theta\) का मान है [2021AII]
A) \(\frac{b}{\sqrt{b^2 – a^2}}\) B) \(\frac{\sqrt{b^2 – a^2}}{b}\) C) \(\frac{a}{\sqrt{b^2 – a^2}}\) D) \(\frac{b}{a}\) उत्तर देखेंAnswer- (A) \(\frac{b}{\sqrt{b^2 – a^2}}\)
12. निम्नलिखित में से कौन \(cosec \theta\) के बराबर है? [2020AI]
A) \(\frac{\cos \theta}{\sin \theta}\) B) \(\frac{1}{\sec \theta}\) C) \(\frac{1}{\sin \theta}\) D) \(\frac{\sin \theta}{\cos \theta}\) उत्तर देखेंAnswer- (C) \(\frac{1}{\sin \theta}\)
13. यदि \(2 \sin \theta = 1\), \((3x \cot^2 \theta + 3)\) का मान होगा [2020AI]
A) 12 B) 15 C) 9 D) 8 उत्तर देखेंAnswer- (A) 12
14. यदि \(\sec\theta = \frac{13}{12} \) हो, तो \(\cot\theta\) बराबर हैं [2020AI]
A) \(\frac{5}{12}\) B) \(\frac{5}{13}\) C) \(\frac{12}{5}\) D) \(\frac{13}{5}\) उत्तर देखेंAnswer- (C) \(\frac{12}{5}\)
15. \(1 + \tan^2 \theta\) का मान है : [2015AI, 2017AI, 2020AI, 2022AI]
A) \(\sec^2 \theta\) B) \(cosec^2 \theta\) C) \(\tan^2 \theta\) D) \(\cot^2 \theta\) उत्तर देखेंAnswer- (A) \(\sec^2 \theta\)
16. यदि \(\tan \theta = \frac{8}{15}\) हो तो \(cosec \theta\) का मान है : [2020AI]
A) \(\frac{17}{8}\) B) \(\frac{8}{17}\) C) \(\frac{15}{17}\) D) \(\frac{17}{15}\) उत्तर देखेंAnswer- (A) \(\frac{17}{8}\)
17. यदि \(cosec \theta = \sqrt{10}\) हो, तो \(\sec \theta =\) ? [2020AII]
A) \(\frac{3}{\sqrt{10}}\) B) \(\frac{\sqrt{10}}{3}\) C) \(\frac{1}{\sqrt{10}}\) D) \(\frac{2}{10}\) उत्तर देखेंAnswer- (B) \(\frac{\sqrt{10}}{3}\)
18. \(\sec \theta\) = ? [2020AII]
A) \(\frac{\cos \theta}{\sin \theta}\) B) \(\frac{1}{\cos \theta}\) C) \(\frac{1}{\sin \theta}\) D) \(\frac{\sin \theta}{\cos \theta}\) उत्तर देखेंAnswer- (B) \(\frac{1}{\cos \theta}\)
19. \(3 \cos \theta = 2\) हो तो \(2 \sec^2 \theta + 2 \tan^2 \theta – 7\) का मान होगा : [2020AII]
A) 0 B) 1 C) 3 D) 4 उत्तर देखेंAnswer- (A) 0
20. यदि \(\sin A = \frac{8}{17}\) हो तो \(\cot A\) का मान होगा : [2020AII]
A) \(\frac{8}{15}\) B) \(\frac{17}{15}\) C) \(\frac{15}{8}\) D) \(\frac{8}{17}\) उत्तर देखेंAnswer- (C) \(\frac{15}{8}\)
21. निम्नलिखित में से कौन \(\cot \theta\) के बराबर है ? [2019AI]
A) \(\frac{\sin \theta}{\cos \theta}\) B) \(\frac{\cos \theta}{\sin \theta}\) C) \(\frac{1}{\sec \theta}\) D) \(\frac{1}{\sin \theta}\) उत्तर देखेंAnswer- (B) \(\frac{\cos \theta}{\sin \theta}\)
22. यदि \(5 \cos \theta = 3\) तो \(3 \tan \theta\) का मान होगा : [2019AI]
A) 3 B) 5 C) 4 D) 7 उत्तर देखेंAnswer- (C) 4
23. \(\sin^2 \theta + \cos^2 \theta =\) [2017C, 2019AI]
A) 1 B) 2 C) 0 D) -1 उत्तर देखेंAnswer- (A) 1
24. यदि \(\tan \theta = \frac{3}{4}\) हो तो \(\sin \theta\) का मान है : [2019A]
A) \(\frac{4}{5}\) B) \(\frac{2}{3}\) C) \(\frac{4}{3}\) D) \(\frac{3}{5}\) उत्तर देखेंAnswer- (D) \(\frac{3}{5}\)
25. यदि \(15 \cot A = 8\) तो \(\sin A\) का मान होगा : [2019AII]
A) \(\frac{15}{17}\) B) \(\frac{17}{15}\) C) \(\frac{15}{8}\) D) \(\frac{3}{5}\) उत्तर देखेंAnswer- (A) \(\frac{15}{17}\)
26. यदि \(\cos A = \frac{1}{2}\) हो तो \(1 – 2 \cos^2 A\) का मान है : [2019AII]
A) \(\frac{1}{2}\) B) \(\frac{2}{3}\) C) \(\frac{1}{4}\) D) \(\frac{1}{3}\) उत्तर देखेंAnswer- (A) \(\frac{1}{2}\)
27. \(\tan^2 \theta – \sec^2 \theta\) का मान किसके बराबर है – [2019AII]
A) 1 B) 0 C) 2 D) -1 उत्तर देखेंAnswer- (D) -1
28. निम्न में से कौन \(\cos \theta\) के बराबर है ? [2019AII]
A) \(\sqrt{\sin^2 \theta – 1}\) B) \(\sqrt{1 – \sin^2 \theta}\) C) \(\sqrt{1 + \sin^2 \theta}\) D) \(\sqrt{1 – \cos^2 \theta}\) उत्तर देखेंAnswer- (B) \(\sqrt{1 – \sin^2 \theta}\)
29. यदि \(\sqrt{3} \tan \theta = 3 \sin \theta\) तब \(\sin^2 \theta – \cos^2 \theta\) का मान बराबर है; [2018AII]
A) \(\sqrt{3}\) B) \(\frac{2}{3}\) C) \(\frac{1}{3}\) D) \(\frac{1}{\sqrt{3}}\) उत्तर देखेंAnswer- (C) \(\frac{1}{3}\)
30. \(7 \sin^2 \theta + 3 \cos^2 \theta = 4\) तब \(\sec \theta + cosec \theta\) बराबर है: [2018AII]
A) \(\frac{2}{\sqrt{3}} – 2\) B) \(\frac{2}{\sqrt{3}} + 2\) C) \(\frac{2}{\sqrt{3}}\) D) \(\frac{\sqrt{3}}{2}\) उत्तर देखेंAnswer- (B) \(\frac{2}{\sqrt{3}} + 2\)
31. यदि \(5 \cot \theta = 3\) तब \(\frac{5 \sin \theta – 3 \cos \theta}{4 \sin \theta + 3 \cos \theta}\) बराबर है : [2018AII]
A) \(\frac{11}{8}\) B) \(\frac{16}{29}\) C) \(\frac{14}{27}\) D) \(\frac{11}{29}\) उत्तर देखेंAnswer- (B) \(\frac{16}{29}\)
32. \(1 + \cot^2 \theta\) का मान होगा : [2017AII]
A) \(\sec^2 \theta\) B) \(cosec^2 \theta\) C) \(\tan^2 \theta\) D) \(\cot^2 \theta\) उत्तर देखेंAnswer- (B) \(cosec^2 \theta\)
33. \(\sec^2 \theta – 1\) का मान हैं [2016AII]
A) \(cosec^2 \theta\) B) \(\sin^2 \theta\) C) \(\tan^2 \theta\) D) \(\cot^2 \theta\) उत्तर देखेंAnswer- (C) \(\tan^2 \theta\)
34. \(\sin \theta\) बराबर है : [2016C]
A) \(1 + \tan^2 \theta\) B) \(\frac{1}{cosec \theta}\) C) \(\frac{1}{\cos \theta}\) D) \(\sec^2 \theta – 1\) उत्तर देखेंAnswer- (B) \(\frac{1}{cosec \theta}\)
35. सही विकल्प चुनिए: \(9 \sec^2 A – 9 \tan^2 A\) बराबर है : [2013A, 2015AI]
A) 1 B) 9 C) 8 D) 0 उत्तर देखेंAnswer- (B) 9
36. यदि \(\sin \theta = \frac{3}{5}\) हो तो \(\cos \theta\) का मान होगा : [2013C]
A) \(\frac{4}{5}\) B) \(\frac{4}{3}\) C) \(\frac{5}{6}\) D) \(\frac{3}{5}\) उत्तर देखेंAnswer- (A) \(\frac{4}{5}\)
37. \(\sin A = \frac{3}{4}\cos A\) का मान होगा – [2011AI]
A) \(\frac{4}{3}\) B) \(\frac{\sqrt{3}}{4}\) C) \(\frac{\sqrt{4}}{3}\) D) \(\frac{\sqrt{7}}{4}\) उत्तर देखेंAnswer- (D) \(\frac{\sqrt{7}}{4}\)
38. यदि \(\cos \theta = p\) तो \(\tan \theta\) का मान होगा – [2022AI]
A) \(\frac{\sqrt{1 – p^2}}{p}\) B) \(\frac{1}{p}\) C) \(\frac{p}{\sqrt{1 – p^2}}\) D) \(\frac{\sqrt{1 + p^2}}{p}\) उत्तर देखेंAnswer- (A) \(\frac{\sqrt{1 – p^2}}{p}\)
39. \(\frac{1}{\sin \theta}\) = [2022AI]
A) \(\cos \theta\) B) \(cosec \theta\) C) \(\sec \theta\) D) \(\cot \theta\) उत्तर देखेंAnswer- (B) \(cosec \theta\)
40. \(\sec B \times \cos B =\)` [2022AII]
A) 2 B) -1 C) 0 D) 1 उत्तर देखेंAnswer- (D) 1
41. यदि \(\cot \theta = \frac{1}{\sqrt{3}}\) तो \(\sec \theta\) का मान है – [2022AII]
A) \(\sqrt{3}\) B) \(\frac{1}{2}\) C) 2 D) \(\frac{1}{\sqrt{3}}\) उत्तर देखेंAnswer- (C) 2
42. \(\frac{\sin 30^\circ}{\cos 30^\circ} \times \cot 30^\circ =\) [2022AII]
A) 0 B) 2 C) 3 D) 1 उत्तर देखेंAnswer- (D) 1
43. \(\frac{1 – \tan^2 45^\circ}{1 – \tan^2 45^\circ} = \) [2022AII]
A) \(\sin 90^\circ\) B) \(\sin 0^\circ\) C) \(\tan 90^\circ\) D) \(\sin 45^\circ\) उत्तर देखेंAnswer- (B) \(\sin 0^\circ\)
44. यदि \(\tan \theta = \frac{12}{5}\) तो \(\sin \theta\) का मान होगा- [2022AII]
A) \(\frac{5}{12}\) B) \(\frac{12}{13}\) C) \(\frac{5}{13}\) D) \(\frac{12}{5}\) उत्तर देखेंAnswer- (B) \(\frac{12}{13}\)
45. यदि \(\tan \theta = \frac{p}{q}\) तो \(\frac{p \sin \theta – q \cos \theta}{p \sin \theta + q \cos \theta}\) का मान होगा- [2022AII]
A) \(p^2 – q^2\) B) \(\frac{p^2 + q^2}{p^2 – q^2}\) C) \(\frac{p^2 + q^2}{2}\) D) \(\frac{p^2 – q^2}{p^2 + q^2}\) उत्तर देखेंAnswer- (D) \(\frac{p^2 – q^2}{p^2 + q^2}\)
46. \(\sin(45^\circ + \theta) – \cos(45^\circ – \theta) = ?\) [2021AI]
A) \(2 \sin \theta\) B) \(2 \cos \theta\) C) 0 D) 1 उत्तर देखेंAnswer- (C) 0
47. \(\cos 60^\circ \cos 30^\circ – \sin 60^\circ \sin 30^\circ\) का मान होगा- [2021AI]
A) 1 B) 2 C) 0 D) -1 उत्तर देखेंAnswer- (C) 0
48. \(\sin(90^\circ – \theta) = ?\) [2020AI]
A) \(\sin \theta\) B) \(-\sin \theta\) C) \(\cos \theta\) D) \(-\cos \theta\) उत्तर देखेंAnswer- (C) \(\cos \theta\)
49. \(2 \cos^2 60^\circ\) का मान है – [2020AI]
A) \(\frac{1}{3}\) B) \(\frac{1}{4}\) C) 1 D) \(\frac{1}{2}\) उत्तर देखेंAnswer- (D) \(\frac{1}{2}\)
50. \(\Delta ABC\) एक समकोण त्रिभुज है जिसमें \(\angle C = 90^\circ\) है तो \(\cos (A + B)\) का मान है – [2020AI]
A) 0 B) 1 C) \(\frac{1}{2}\) D) \(\frac{\sqrt{3}}{2}\) उत्तर देखेंAnswer- (A) 0
51. \(\sec^2 60^\circ – 1\) का मान है : [2020AII]
A) 2 B) 3 C) 4 D) 0 उत्तर देखेंAnswer- (B) 3
52. \(\tan 30^\circ \cdot \sin 30^\circ \cdot \cot 60^\circ \cdot cosec 30^\circ = \) [2020AII]
A) \(\frac{1}{2}\) B) \(\frac{1}{3}\) C) \(\frac{1}{4}\) D) 1 उत्तर देखेंAnswer- (B) \(\frac{1}{3}\)
53. यदि \(A\) और \(B\) दो ऐसे न्यूनकोण हों कि \(\sin A = \cos B\), तब \((A + B) = ?\) [2020AII]
A) \(45^\circ\) B) \(60^\circ\) C) \(90^\circ\) D) \(30^\circ\) उत्तर देखेंAnswer- (C) \(90^\circ\)
54. \(\cos(90^\circ – A) = ?\) [2019AII]
A) \(\cot A\) B) \(\sin A\) C) \(\tan A\) D) \(\sec A\) उत्तर देखेंAnswer- (B) \(\sin A\)
55. यदि \(A\), \(B\), \(C\) किसी त्रिभुज के कोण हों तो \(\sin \frac{B + C}{2}\) बराबर है : [2019AII]
A) \(\tan \frac{A}{2}\) B) \(\sin \frac{A}{2}\) C) \(\cos \frac{A}{2}\) D) \(\sec \frac{A}{2}\) उत्तर देखेंAnswer- (C) \(\cos \frac{A}{2}\)
56. \(\tan^2 60^\circ\) का मान है – [2018AII]
A) 1 B) 3 C) \(\frac{1}{\sqrt{3}}\) D) \(\frac{1}{3}\) उत्तर देखेंAnswer- (B) 3
57. \(\cot(90^\circ – 0)\) बराबर है : [2019AII]
A) \(cosec 0\) B) \(\tan 0\) C) \(\sec 0\) D) \(\cos 0\) उत्तर देखेंAnswer- (B) \(\tan 0\)
58. \(cosec 15^\circ\) के मान है : [2019AII]
A) 2 B) \(\frac{1}{\sqrt{2}}\) C) \(\sqrt{2}\) D) \(\frac{1}{\sqrt{2}}\) उत्तर देखेंAnswer- (C) \(\sqrt{2}\)
59. \(\frac{2 \tan 30^\circ}{1 + \tan^2 30^\circ}\) का मान है : [2018AI]
A) \(\sin 60^\circ\) B) \(\cos 60^\circ\) C) \(\tan 60^\circ\) D) \(\sec 60^\circ\) उत्तर देखेंAnswer- (A) \(\sin 60^\circ\)
60. \(\cos \frac{\pi}{3}\) का मान होगा : [2017AII]
A) \(\frac{1}{2}\) B) \(\frac{1}{\sqrt{3}}\) C) \(\frac{\sqrt{3}}{2}\) D) \(\sqrt{3}\) उत्तर देखेंAnswer- (A) \(\frac{1}{2}\)
61. \(\frac{1}{\sqrt{3}}\) बराबर है : [2016AII]
A) \(\tan 60^\circ\) B) \(\cos 45^\circ\) C) \(\tan 30^\circ\) D) \(\sin 30^\circ\) उत्तर देखेंAnswer- (C) \(\tan 30^\circ\)
62. \(\tan \frac{\pi}{2}\) का मान होगा : [2016AII]
A) 0 B) \(\sqrt{3}\) C) \(\frac{1}{\sqrt{3}}\) D) \(\infty\) उत्तर देखेंAnswer- (D) \(\infty\)
63. \(\sin \frac{\pi}{4} – \cos \frac{\pi}{4}\) का मान होगा – [2016AII]
A) 2 B) 0 C) -1 D) 1 उत्तर देखेंAnswer- (B) 0
64. निम्न में किसका मान के बराबर है 0? [2016C]
A) \(\sin 90^\circ\) B) \(\cos 90^\circ\) C) \(\sin 30^\circ\) D) \(\tan 30^\circ\) उत्तर देखेंAnswer- (B) \(\cos 90^\circ\)
65. निम्नलिखित में से \(\sqrt{2}\) किसके बराबर है ? [2015AI]
A) \(\tan 60^\circ\) B) \(\cos 45^\circ\) C) \(\sin 30^\circ\) D) \(\frac{1}{\sin 45^\circ}\) उत्तर देखेंAnswer- (D) \(\frac{1}{\sin 45^\circ}\)
66. \(\frac{1}{\sqrt{3}}\) किसका मान है ? [2015AI]
A) \(\tan 60^\circ\) B) \(\cos 45^\circ\) C) \(\sin 30^\circ\) D) \(\tan 30^\circ\) उत्तर देखेंAnswer- (C) \(\sin 30^\circ\)
67. यदि \(30 = 90^\circ\) तो \(\cos 0 = ?\) [2015C]
A) \(\frac{1}{2}\) B) \(\frac{\sqrt{3}}{2}\) C) \(\frac{1}{\sqrt{2}}\) D) \(\frac{2}{\sqrt{3}}\) उत्तर देखेंAnswer- (B) \(\frac{\sqrt{3}}{2}\)
68. यदि \(\sqrt{2} \cos 0 = 1\) हो तो \(\theta\) का मान है : [2014AI]
A) \(60^\circ\) B) \(45^\circ\) C) \(30^\circ\) D) \(90^\circ\) उत्तर देखेंAnswer- (B) \(45^\circ\)
69. यदि \(\sqrt{3} \sec 0 = 2\) हो, तो \(\theta\) मान है : [2014C, 2014AI]
A) \(0^\circ\) B) \(30^\circ\) C) \(45^\circ\) D) \(60^\circ\) उत्तर देखेंAnswer- (B) \(30^\circ\)
70. यदि \(2 \cos \theta = \sqrt{3}\) हो, तो \(\theta\) मान है : [2013C]
A) \(45^\circ\) B) \(60^\circ\) C) \(30^\circ\) D) \(60^\circ\) उत्तर देखेंAnswer- (C) \(30^\circ\)
71. यदि \(\tan \theta = \sqrt{3}\) हो, तो \(\theta\) मान है [2012A]
A) \(90^\circ\) B) \(45^\circ\) C) \(30^\circ\) D) \(60^\circ\) उत्तर देखेंAnswer- (D) \(60^\circ\)
72. \(\frac{\cos 60^\circ +1}{\cos 60^\circ -1}\) का मान है : [2012A]
A) -2 B) -3 C) 3 D) 2 उत्तर देखेंAnswer- (B) -3
73. \(\tan A = ?\) [2011A]
A) \(\cot(90^\circ – A)\) B) \(\sec (90^\circ – A)\) C) \(cosec (90^\circ – A)\) D) \(\cos(90^\circ – A)\) उत्तर देखेंAnswer- (A) \(\cot(90^\circ – A)\)
74. यदि \(A = 45^\circ\) तो \(\sin A + \cos A\) = [2022AI]
A) \(\sqrt{2}\) B) \(\frac{1}{\sqrt{2}}\) C) \(\frac{1}{2}\) D) 1 उत्तर देखेंAnswer- (A) \(\sqrt{2}\)
75. यदि \(2 \sin \alpha = 2\) तो \(\alpha =\) [2022AI]
A) \(0^\circ\) B) \(45^\circ\) C) \(60^\circ\) D) \(90^\circ\) उत्तर देखेंAnswer- (D) \(90^\circ\)
76. \(\tan 45^\circ : \tan 60^\circ =\) [2022AII]
A) 1 : 2 B) 3 : 1 C) 1 : \(\sqrt{3}\) D) \(\sqrt{3}\) : 1 उत्तर देखेंAnswer- (C) 1 : \(\sqrt{3}\)
77. \(\frac{1}{\sqrt{3}}\) किसका मान है ? [2022AII]
A) \(\sin 30^\circ\) B) \(\tan 30^\circ\) C) \(\cos 60^\circ\) D) \(\tan 45^\circ\) उत्तर देखेंAnswer- (B) \(\tan 30^\circ\)
78. \(\cos(90^\circ – 0) =\) [2022AII]
A) \(\cos 90^\circ + \cos 0\) B) \(\sin 0\) C) \(-\sin 0\) D) \(-\cos \theta\) उत्तर देखेंAnswer- (B) \(\sin 0\)
79. यदि \(\theta = 45^\circ \) तो \( \cos^2 \theta – \sin^2 \theta\) का मान होगा- [2022AII]
A) 1 B) \(\frac{1}{2}\) C) 0 D) \(\frac{3}{2}\) उत्तर देखेंAnswer- (C) 0
80. निम्नलिखित में किसका मान \(\sqrt{2}\) के बराबर है? [2022AII]
A) \( \tan 60^\circ \) B) \( \cos 45^\circ \) C) \( \sin 30^\circ \) D) \( cosec 45^\circ \) उत्तर देखेंAnswer- (D) \( cosec 45^\circ \)
81. यदि \(\theta = 45^\circ \) तो \( \tan^2 \theta + \frac{1}{\sin^2 \theta}\) का मान क्या होगा? [2022AII]
A) 1 B) 2 C) 3 D) 4 उत्तर देखेंAnswer- (C) 3
82. \(\frac{\sec 11^\circ}{cosec 79^\circ}\) का मान होगा- [2017AII]
A) 1 B) 0 C) 2 D) -1 उत्तर देखेंAnswer- (A) 1
83. \(cosec^2 57^\circ – \tan^2 33^\circ =?\) [2015AII]
A) 0 B) 1 C) -1 D) 2 उत्तर देखेंAnswer- (B) 1
84. \(\sec^2 10^\circ – \cot^2 80^\circ\) का मान होगा [2018AII]
A) 1 B) 0 C) \(\frac{3}{2}\) D) \(\frac{1}{2}\) उत्तर देखेंAnswer- (A) 1
85. \( \tan 1^\circ \cdot \tan 2^\circ \cdot \tan 3^\circ \cdot \ldots \cdot \tan 89^\circ =\) [2018AI]
A) 0 B) 1 C) \(\frac{1}{2}\) D) 2 उत्तर देखेंAnswer- (B) 1
86. \(\frac{2 \cos 37^\circ}{\sin 53^\circ} =\) [2017AI]
A) 0 B) -1 C) 1 D) 2 उत्तर देखेंAnswer- (D) 2
87. \(\frac{\sin 63^\circ}{\cos 27^\circ} =\) [2022AII]
A) \(\sqrt{3}\) B) 1 C) 1 D) 2 उत्तर देखेंAnswer- (B) 1
88. \(\cot(90^\circ – A) =?\) [2011AI]
A) \(\cot A\) B) \(\tan A\) C) \(\sin A\) D) इनमें से कोई नहीं उत्तर देखेंAnswer- (B) \(\tan A\)
89. \(\tan 10^\circ \tan 15^\circ \tan 75^\circ \tan 80^\circ =?\) [2021AI]
A) \(\sqrt{3}\) B) \(\frac{1}{\sqrt{3}}\) C) -1 D) 1 उत्तर देखेंAnswer- (D) 1
90. \(\frac{\tan 49^\circ}{\cot 41^\circ} =?\) [2021AI]
A) 3 B) 2 C) 1 D) 6 उत्तर देखेंAnswer- (C) 1
91. \(\cos 1^\circ \cdot \cos 2^\circ \cdot \cos 3^\circ \cdot \ldots \cdot \cos 90^\circ =\) [2021AI]
A) 0 B) 1 C) -1 D) \(\sqrt{2}\) उत्तर देखेंAnswer- (B) 1
92. यदि \(\sin \theta = \cos \theta\) तो \(\theta\) किसके बराबर है? [2019AI]
A) \(45^\circ\) B) \(30^\circ\) C) \(90^\circ\) D) \(60^\circ\) उत्तर देखेंAnswer- (A) \(45^\circ\)
93. \(\frac{\sin 18^\circ}{\cos 72^\circ} =\) [2021AI]
A) 0 B) 1 C) -1 D) \(\infty\) उत्तर देखेंAnswer- (B) 1
94. \(\frac{\tan 65^\circ}{\cot 25^\circ}\) का मान है [2021AI]
A) 1 B) -1 C) 0 D) \(\frac{1}{2}\) उत्तर देखेंAnswer- (A) 1
95. \(cosec(90^\circ – 0)\) किसके बराबर है? [2021AII]
A) 1 B) -1 C) 0 D) \(\frac{1}{2}\) उत्तर देखेंAnswer- (C) 0
96. यदि \(\sec A = cosec B = \frac{13}{12}\) तब (A + B) का मान है [2021AII]
A) 0 B) > \(90^\circ\) C) \(90^\circ\) D) < \(90^\circ\) उत्तर देखेंAnswer- (B) > \(90^\circ\)
97. यदि \(\tan(\alpha + \beta) = \sqrt{3}\) और \(\tan \alpha = \frac{1}{\sqrt{3}}\) तब \(\tan \beta\) का मान है- [2021AI]
A) \(\frac{1}{6}\) B) \(\frac{1}{7}\) C) \(\frac{1}{3}\) D) \(\frac{7}{6}\) उत्तर देखेंAnswer- (D) \(\frac{7}{6}\)
98. यदि किसी \(\Delta ABC\) में \(\angle A\) तथा \(\angle B\) पूरक है तो \(\cot C\) का मान है- [2020AI]
A) \(\frac{1}{\sqrt{3}}\) B) 0 C) 1 D) \(\sqrt{3}\) उत्तर देखेंAnswer- (D) \(\sqrt{3}\)
99. \(\tan 15^\circ \cdot \tan 20^\circ \cdot \tan 70^\circ \cdot \tan 75^\circ\) का मान होगा: [2020AII]
A) -1 B) 2 C) 0 D) 1 उत्तर देखेंAnswer- (B) 2
100. यदि \(\sin x^\circ = \sin \alpha\) तब \(\alpha\) है – [2019AI]
A) \(\frac{180}{\pi}\) B) \(\frac{\pi}{270}\) C) \(\frac{270}{\pi}\) D) \(\frac{\pi}{180}\) उत्तर देखेंAnswer- (B) \(\frac{\pi}{270}\)
101. \(\frac{\sin 50^\circ}{\cos 40^\circ}\) का मान होगा [2019AII]
A) 2 B) 1 C) 0 D) 4 उत्तर देखेंAnswer- (B) 1
102. यदि \(A + B = 90^\circ\) तो \(\cos A\) बराबर होगा [2018AII]
A) \(\cos B\) B) \(\sin A\) C) \(\sin B\) D) \(\cos A\) उत्तर देखेंAnswer- (C) \(\sin B\)
103. \(\frac{\tan 21^\circ}{\cot 60^\circ} =\) [2017AI]
A) 0 B) 1 C) -1 D) \(\frac{1}{2}\) उत्तर देखेंAnswer- (B) 1
104. यदि \(\theta \) तथा \(\phi \) पूरक कोण हैं तो – [2022AI]
A) \(\cos \theta = \cos \phi\) B) \(\sec \theta = cosec \phi\) C) \(\sin \theta = \sin \phi\) D) \(\tan \theta = \tan \phi\) उत्तर देखेंAnswer- (B) \(\sec \theta = cosec \phi\)
105. \(\sin^2 75^\circ + \sin^2 15^\circ =\) [2013AI]
A) 0 B) 1 C) -1 D) 2 उत्तर देखेंAnswer- (B) 1
106. \(2(\sin^2 \alpha + \cos^2 \alpha) =\) [2015AII]
A) 1 B) 0 C) 2 D) -1 उत्तर देखेंAnswer- (C) 2
107. \((5 cosec^2 \theta – 5 \cot^2 \theta) =\) [2022AI]
A) 1 B) 0 C) 2 D) -1 उत्तर देखेंAnswer- (B) 0
108. यदि \(3 \alpha = 180^\circ\) तो \(\cos \alpha\) [2022AI]
A) 0 B) 1 C) \(\frac{1}{2}\) D) \(\frac{1}{\sqrt{2}}\) उत्तर देखेंAnswer- (C) \(\frac{1}{2}\)
109. यदि \(a \sin \theta = 1\) और \(b \cos \theta = 1\) तो \(\tan \theta =\) [2022AII]
A) \(\frac{a}{b}\) B) \(\frac{b}{a}\) C) 1 D) \(\frac{a}{b^2}\) उत्तर देखेंAnswer- (B) \(\frac{b}{a}\)
110. यदि \(\cos 32^\circ = x\) और \(\cos 58^\circ = y\) तो निम्नलिखित में से कौन-सा सत्य है? [2022AII]
A) \(x > y\) B) \(x = y\) C) \(x < y\) D) इनमें से कोई नहीं उत्तर देखेंAnswer- (A) \(x > y\)
111. यदि \(\sin 42^\circ = p\) तो \(\sin 48^\circ\) का मान निम्नलिखित में कौन-सा होगा? [2022011]
A) \(p\) B) \(-p\) C) \(\sqrt{1 – p^2}\) D) \(\frac{p}{\sqrt{1 – p^2}}\) उत्तर देखेंAnswer- (C) \(\sqrt{1 – p^2}\)
112. \(\frac{\sec 30^\circ}{cosec 60^\circ} = [2022A11]\)
A) \(\frac{2}{\sqrt{2}}\) B) \(\frac{\sqrt{3}}{2}\) C) \(\sqrt{3}\) D) 1 उत्तर देखेंAnswer- (D) 1
113. यदि \(\cos(\alpha + \beta) = 0\) तो \(\sin(\alpha – \beta) = [2022011]\)
A) \(\sin \alpha\) B) \(\cos \beta\) C) \(\sin 2\alpha\) D) \(\cos 2\beta\) उत्तर देखेंAnswer- (D) \(\cos 2\beta\)
114. \(\frac{2\sin^2 63^\circ + 1 + 2 \sin^2 27^\circ}{3\cos^2 17^\circ – 2 + 3 \cos^2 73^\circ} = [2022A11]\)
A) \(\frac{3}{2}\) B) \(\frac{2}{3}\) C) 2 D) 3 उत्तर देखेंAnswer- (D) 3
115. \((cosec \theta – \cot \theta)^2 = ?\) [2021AI]
A) \(\frac{1 + \cos \theta}{1 – \cos \theta}\) B) \(\frac{1 – \cos \theta}{1 + \cos \theta}\) C) \(\frac{1 + \sin \theta}{1 – \sin \theta}\) D) \(\sin \theta \cdot \cos \theta\) उत्तर देखेंAnswer- (B) \(\frac{1 – \cos \theta}{1 + \cos \theta}\)
116. \((1 + \tan \theta + \sec \theta)(1 + \cot \theta – cosec \theta) = ?\) [2020AI]
A) \(-1\) B) 0 C) 1 D) 2 उत्तर देखेंAnswer- (D) 2
117. \((1 – \cos^2 \theta)(1 + \cot^2 \theta) = ?\) [2020AII]
A) 0 B) -1 C) \(\frac{1}{2}\) D) 1 उत्तर देखेंAnswer- (D) 1
118. \(\frac{1 + \tan^2 A}{1 + \cot^2 A} = ?\) [2020AI]
A) \(-1\) B) \(\sec^2 A\) C) \(\cot^2 A\) D) \(\tan^2 A\) उत्तर देखेंAnswer- (D) \(\tan^2 A\)
119. \(\frac{1 + \cot^2 A}{1 + \tan^2 A}\) बराबर है- [2020AII]
A) \(\sec^2 A\) B) \(cosec^2 A\) C) \(\cot^2 A\) D) \(\tan^2 A\) उत्तर देखेंAnswer- (C) \(\cot^2 A\)
120. \(\frac{\sec^2 A}{1 + \cot^2 A}\) बराबर है- [2020AII, 2019AII]
A) \(\sec^2 A\) B) \(cosec^2 A\) C) \(\cot^2 A\) D) \(\tan^2 A\) उत्तर देखेंAnswer- (D) \(\tan^2 A\)
121. \(\frac{1 + \tan^2 A}{cosec^2 A}\) बराबर है- [2020AII, 2019AII]
A) \(\sec^2 A\) B) \(cosec^2 A\) C) \(\cot^2 A\) D) \(\tan^2 A\) उत्तर देखेंAnswer- (D) \(\tan^2 A\)
122. यदि \(\sec \theta + \tan \theta = x\) तो \(\tan \theta =\) [2022AI]
A) \(\frac{x^2 + 1}{2x}\) B) \(\frac{x^2 – 1}{2x}\) C) \(\frac{x}{x^2 + 1}\) D) \(\frac{x^2 – 1}{x}\) उत्तर देखेंAnswer- (B) \(\frac{x^2 – 1}{2x}\)
123. \(\sin^2 \phi + \frac{1}{1 + \tan^2 \phi} =\) [2022AII]
A) 1 B) 0 C) \(\sin \phi\) D) \(\frac{1}{2}\) उत्तर देखेंAnswer- (A) 1
124. \((1 + \cot^2 \theta)(1 – \cos^2 \theta) = [2022AII]\)
A) \(\sec^2 A\) B) \(\tan^2 A\) C) \(\cos^2 A\) D) 1 उत्तर देखेंAnswer- (D) 1
125. \(\sqrt{\frac{1 – \cos \theta}{1 + \cos \theta}} =\)
A) \(\sec \theta – \tan \theta\) B) \(\cos \theta – \sin \theta\) C) \(cosec \theta – \cot \theta\) D) \(\tan \theta – \cot \theta\) उत्तर देखेंAnswer- (C) \(cosec \theta – \cot \theta\)