Trigonometry Questions for SSC CGL

Trigonometry Questions with Solution for SSC CGL, CHSL, CPO Competitive Exams. Mock Test for free online practice – All type from previous year papers.

Quiz : Trigonometry MCQs
Subject : Mathematics
Important Questions with Solutions

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#1. If $0 \leq\theta\leq\frac{\pi}{2}$ and $sec^2\theta + tan^2\theta = 7$ then $\theta$ is

\(\frac{5\pi}{12}\) radian

\(\frac{\pi}{3}\) radian

\(\frac{\pi}{5}\) radian

\(\frac{\pi}{6}\) radian

#2. If $0 \leq\theta\leq\frac{\pi}{2}$ and $sec^2\theta + tan^2\theta = 7$ then $\theta$ is

\(\frac{5\pi}{12}\) radian

\(\frac{\pi}{3}\) radian

\(\frac{\pi}{5}\) radian

\(\frac{\pi}{6}\) radian

#3. If the sum and difference of two angles are $\frac{22}{9}$ radian and 36° respectively, then the value of smaller angle in degree taking the value of $\pi$ as $\frac{22}{7}$ is.

\(52^\circ\)

\(60^\circ\)

\(56^\circ\)

\(48^\circ\)

#4. If the sum and difference of two angles are $\frac{22}{9}$ radian and 36° respectively, then the value of smaller angle in degree taking the value of $\pi$ as $\frac{22}{7}$ is.

\(52^\circ\)

\(60^\circ\)

\(56^\circ\)

\(48^\circ\)

#5. In circular measure, the value of the angle $11^\circ$ 15′ is

\(\frac{\pi^c}{16}\)

\(\frac{\pi^c}{8}\)

\(\frac{\pi^c}{4}\)

\(\frac{\pi^c}{12}\)

#6. In circular measure, the value of the angle $11^\circ$ 15′ is

\(\frac{\pi^c}{16}\)

\(\frac{\pi^c}{8}\)

\(\frac{\pi^c}{4}\)

\(\frac{\pi^c}{12}\)

#7. Solve cot $9^\circ$ cot $27^\circ$ cot $63^\circ$ cot $81^\circ$

0

1

-1

\(\sqrt3\)

#8. Solve cot $9^\circ$ cot $27^\circ$ cot $63^\circ$ cot $81^\circ$

0

1

-1

\(\sqrt3\)

#9. If tan θ − tan 30° tan 60° and θ is an acute angle, then 2θ is equal to

30°

45°

90°

0°

#10. If $tan\:θ + cot\:θ = 5$ , then $\tan^2\:θ + cot^2\:θ$ is

23

25

26

24

#11. If $tan\:θ + cot\:θ = 5$ , then $\tan^2\:θ + cot^2\:θ$ is

23

25

26

24

#12. If $\frac{x – x\:tan^2 30^\circ}{1 + tan^2 30^\circ} = sin^2 30^\circ + 4\:cot^2 45 ^\circ – sec^2 60^\circ$ , then the value of $x$ is

\(\frac14\)

\(\frac15\)

\(\frac12\)

\(\frac{1}{\sqrt3}\)

#13. If $\frac{x – x\:tan^2 30^\circ}{1 + tan^2 30^\circ} = sin^2 30^\circ + 4\:cot^2 45 ^\circ – sec^2 60^\circ$ , then the value of $x$ is

\(\frac14\)

\(\frac15\)

\(\frac12\)

\(\frac{1}{\sqrt3}\)

#14. If $\frac{ sin\theta + cos\theta}{sin\theta – cos\theta} = 3$ , then the value of $sin^4 \theta$ is

\(\frac 25\)

\(\frac 15\)

\(\frac {16}{25}\)

\(\frac 35\)

#15. If $\frac{ sin\theta + cos\theta}{sin\theta – cos\theta} = 3$ , then the value of $sin^4 \theta$ is

\(\frac 25\)

\(\frac 15\)

\(\frac {16}{25}\)

\(\frac 35\)

#16. If $sin A + sin^2 A = 1$ , then the value of $cos^2 A + cos^4 A$ is

2

\(1\frac{2}{3}\)

\(1\frac{1}{2}\)

1

#17. If $4sin^2 \theta – 1 = 0$ and the angle $\theta$ is less than 90°, then the value of $cos^2 \theta + \tan^2 \theta$ $(take\: 0^\circ <\theta< 90^\circ)$ is

\(\frac{17}{15}\)

\(\frac{13}{12}\)

\(\frac{11}{9}\)

\(\frac{12}{11}\)

#18. If $4sin^2 \theta – 1 = 0$ and the angle $\theta$ is less than 90°, then the value of $cos^2 \theta + \tan^2 \theta$ $(take\: 0^\circ <\theta< 90^\circ)$ is

\(\frac{17}{15}\)

\(\frac{13}{12}\)

\(\frac{11}{9}\)

\(\frac{12}{11}\)

#19. If $sec\:x + cos\:x = 2$ , then the value of $sec^{16}\:x + cos^{16} \:x$ will be.

\(\sqrt3\)

2

1

0

#20. If $sec\:x + cos\:x = 2$ , then the value of $sec^{16}\:x + cos^{16} \:x$ will be.

\(\sqrt3\)

2

1

0

#21. If $cos\:x + cos^2\:x = 1$ , then $sin^8\: x + 2 sin^6 \:x + sin^4\:x$ is equal to

0

3

2

1

#22. If $cos\:x + cos^2\:x = 1$ , then $sin^8\: x + 2 sin^6 \:x + sin^4\:x$ is equal to

0

3

2

1

#23. If A is an acute angle and cot A + cosec A = 3, then the value of sin A is :

1

\(\frac35\)

\(\frac45\)

0

#24. If tan $9^\circ = \frac {p}{q}$ , then the value of $\frac{sec^2\: 81^\circ}{1 + cot^2\: 81^\circ}$ is

\(\frac {q}{p}\)

1

\(\frac {p^2}{q^2}\)

\(\frac {q^2}{p^2}\)

#25. If tan $9^\circ = \frac {p}{q}$ , then the value of $\frac{sec^2\: 81^\circ}{1 + cot^2\: 81^\circ}$ is

\(\frac {q}{p}\)

1

\(\frac {p^2}{q^2}\)

\(\frac {q^2}{p^2}\)

#26. If $\sin θ =\frac {3}{5}$ , then the value of $\frac {tan\:\theta + cos\: \theta}{cot\:\theta + cosec\: \theta}$ is equal to

\(\frac{29}{60}\)

\(\frac{31}{60}\)

\(\frac{34}{60}\)

\(\frac{37}{60}\)

#27. If $\sin θ =\frac {3}{5}$ , then the value of $\frac {tan\:\theta + cos\: \theta}{cot\:\theta + cosec\: \theta}$ is equal to

\(\frac{29}{60}\)

\(\frac{31}{60}\)

\(\frac{34}{60}\)

\(\frac{37}{60}\)

#28. If α and β are positive acute angles, then sin (4α – β) = 1 and cos (2α + β) = $\frac12$ , then the value of sin (α + 2β) is

0

1

\(\frac{\sqrt3}{2}\)

\(\frac{1}{\sqrt2}\)

#29. If α and β are positive acute angles, then sin (4α – β) = 1 and cos (2α + β) = $\frac12$ , then the value of sin (α + 2β) is

0

1

\(\frac{\sqrt3}{2}\)

\(\frac{1}{\sqrt2}\)

#30. Simplify: $\frac{sin\:25^\circ cos\: 65^\circ + cos \:25^\circ sin \:65^\circ}{tan^2\: 70^\circ – cosec^2 \:20^\circ}$

-1

0

1

2

#31. Simplify: $\frac{sin\:25^\circ cos\: 65^\circ + cos \:25^\circ sin \:65^\circ}{tan^2\: 70^\circ – cosec^2 \:20^\circ}$

-1

0

1

2

#32. If $0° < 0 < 90°$ and $2 sin^2\: θ + 3 cos\:θ = 3$ , then the value of θ is

\(30^\circ\)

\(60^\circ\)

\(45^\circ\)

\(75^\circ\)

#33. If $0° < 0 < 90°$ and $2 sin^2\: θ + 3 cos\:θ = 3$ , then the value of θ is

\(30^\circ\)

\(60^\circ\)

\(45^\circ\)

\(75^\circ\)

#34. If $tan θ +cot θ = 2$ , then the value of $tan^{100}\: \theta + cot^{100} \theta$ is

2

0

1

\(\sqrt3\)

#35. If $tan θ +cot θ = 2$ , then the value of $tan^{100}\: \theta + cot^{100} \theta$ is

2

0

1

\(\sqrt3\)

#36. The equation $cos^2 \: \theta = \frac {(x+y)^2}{4xy}$ is only possible when

\(x = – y\)

\(x > y\)

\(x = y\)

\(x < y\)

#37. The equation $cos^2 \: \theta = \frac {(x+y)^2}{4xy}$ is only possible when

\(x = – y\)

\(x > y\)

\(x = y\)

\(x < y\)

#38. If $cos ^4\: \theta – sin^ 4\: \theta = \frac {2}{3}$ , then the value of 1 – 2 $sin^2\:\theta$ is

\(\frac43\)

0

\(\frac23\)

\(\frac13\)

#39. If $cos ^4\: \theta – sin^ 4\: \theta = \frac {2}{3}$ , then the value of 1 – 2 $sin^2\:\theta$ is

\(\frac43\)

0

\(\frac23\)

\(\frac13\)

#40. If $7 sin^2\: \theta + 3 \:cos^2\: \theta = 4 (0° \leq \: \theta\: \leq 90^\circ)$ , then the value of θ is :

\(\frac{\pi}{2}\)

\(\frac{\pi}{3}\)

\(\frac{\pi}{6}\)

\(\frac{\pi}{4}\)

#41. If $7 sin^2\: \theta + 3 \:cos^2\: \theta = 4 (0° \leq \: \theta\: \leq 90^\circ)$ , then the value of θ is :

\(\frac{\pi}{2}\)

\(\frac{\pi}{3}\)

\(\frac{\pi}{6}\)

\(\frac{\pi}{4}\)

#42. If A = tan 11° tan 29°, B = 2 cot 61° cot 79°, then which of the following is correct?

A = 2B

A = – 2B

2A = B

2A = –B

#43. The measure of the angles of a triangle is in the ratio 2 : 7 : 11. The measures of angle are

16°, 56°, 88°

18°, 63°, 99°

20°, 70°, 90°

25°, 175°, 105°

#44. A 10 metre long ladder is placed against a wall. It is inclined at an angle of 30° to the ground. The distance (in m) of the foot of the ladder from the wall is (Given = $\sqrt3 =1.732)$

8.16

7.32

8.26

8.660

#45. A 10 metre long ladder is placed against a wall. It is inclined at an angle of 30° to the ground. The distance (in m) of the foot of the ladder from the wall is (Given = $\sqrt3 =1.732)$

8.16

7.32

8.26

8.660

#46. If a 48 m tall building has a shadow of 48 $\sqrt3$ m, then the angle of elevation of the sun is

15°

60°

45°

30°

#47. If a 48 m tall building has a shadow of 48 $\sqrt3$ m, then the angle of elevation of the sun is

15°

60°

45°

30°

#48. The angle of elevation of sun changes from 30° to 45°, the length of the shadow of a pole decreases by 4 metres, the height of the pole is (Assume $\sqrt3 =1.732$ )

1.464 m

9.464 m

3.648 cm

5.464 m

#49. The angle of elevation of sun changes from 30° to 45°, the length of the shadow of a pole decreases by 4 metres, the height of the pole is (Assume $\sqrt3 =1.732$ )

1.464 m

9.464 m

3.648 cm

5.464 m

#50. Two poles of equal height are standing opposite to each other on either side of a road which is 100 m wide. From a point between them on road, the angles of elevation of their tops are 30° and 60° The height of each pole (in metre) is

\(25\sqrt3\)

\(20\sqrt3\)

\(28\sqrt3\)

\(30\sqrt3\)

#51. The angle of depression of a point situated at a distance of 70 m from the base of a tower is 60° The height of the tower is :

\(35\sqrt3\) m

\(70\sqrt3\)m

\(\frac{70\sqrt3}{3}\) m

70 m

#52. From a tower 125 metres high, the angle of depression of two objects, which are in horizontal line through the base of the tower are 45° and 30° and they are on the same side of the tower. The distance (in metres) between the objects is

\(125\sqrt3\)

\(125(\sqrt3 – 1)\)

\(125/(\sqrt3 – 1)\)

\(125/(\sqrt3 + 1)\)

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