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

Results

#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 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.

\(52^\circ\)

\(60^\circ\)

\(56^\circ\)

\(48^\circ\)

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

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

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

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

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

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

0

1

-1

\(\sqrt3\)

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

30°

45°

90°

0°

#6. If $ tanθ + cotθ = 5 $, then tan²θ + cot²θ is:

23

25

26

24

#7. If $\dfrac{x-x \text{ tan}^2 30}{1+\text{tan}^2 30}$ = sin² 30 + 4cot² 45 – sec² 60, then the value of $x$ is:

$\frac14$

$\frac15$

$\frac12$

$\frac{1}{\sqrt3}$

#8. If $\dfrac {sin \theta + cos \theta} { sin\theta \text{-} cos\theta} =3$ , then the value of $sin^4 \theta$ is

\(\frac 25\)

\(\frac 15\)

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

\(\frac 35\)

#9. 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

#10. If $4 sin^2 \theta -1 = 0$ 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

$\frac{17}{15}$

$\frac{13}{12}$

$\frac{11}{9}$

$\frac{12}{11}$

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

\(\sqrt3\)

2

1

0

#12. 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

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

1

\(\frac35\)

\(\frac45\)

0

#14. 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

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

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

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

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

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

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

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

#16. 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

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

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

#17. Simplify: $\dfrac{sin 25^\circ cos 65^\circ + cos 25^\circ sin 65^\circ}{tan^2 70^\circ \text{- } cosec^2 20^\circ}$

-1

0

1

2

#18. If 0° < 0 < 90° and 2 sin²θ + 3 cosθ = 3 , then the value of θ is

\(30^\circ\)

\(60^\circ\)

\(45^\circ\)

\(75^\circ\)

#19. If tan θ +cot θ = 2 , then the value of tan¹⁰⁰θ + cot¹⁰⁰θ is

2

0

1

\(\sqrt3\)

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

\(x = – y\)

\(x > y\)

\(x = y\)

\(x < y\)

#21. If cos⁴θ – sin⁴θ = 2/3, then the value of 1 – 2 sin²θ is

\(\frac43\)

0

\(\frac23\)

\(\frac13\)

#22. If 7 sin²θ + 3 cos²θ = 4 $(0^0 \leq \theta \leq 90^\circ)$ , then the value of θ is :

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

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

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

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

#23. 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

#24. 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°

#25. 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

#26. 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°

#27. 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

#28. 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

\(25\sqrt3\)

\(20\sqrt3\)

\(28\sqrt3\)

\(30\sqrt3\)

#29. 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

#30. 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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