Mathematics Inverse Trigonometric Functions Online Test

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Question 1

1. If sin 6 θ + sin 4 θ + sin 2 θ = 0, then θ =

Answer

nπ/4 or nπ ± π/6

Answer

None of these

Answer

nπ/4 or nπ ± π/3

Answer

nπ/4 or 2nπ ± π/6

Question 2

2. The solution of the equation cos² θ + sin θ + 1 = 0 lies in the interval

Answer

(5π/4, 7π/4)

Answer

(π/4, 3π/4)

Answer

(3π/4, 5π/4)

Answer

(- π/4, π/4)

Question 3

3. One root of the equation cos x – x + ½ = 0 lies in the interval

Answer

(π/2, π)

Answer

(– π/2, 0)

Answer

(π, 3π/2)

Question 4

4. Tan⁻¹ A + Tan⁻¹ (1–A/1+A)

Question 5

5. Tan⁻¹(1) =

Answer

None of these

Question 6

6. The principal tangent function is

Answer

None of these

Answer

One – to – one

Question 7

7. Tan⁻¹ A – Tan⁻¹ B =

Answer

Tan⁻¹(1+AB/A – B)

Answer

Tan⁻¹(1–AB/A+B)

Answer

Tan⁻¹(A + B/1 – AB)

Answer

Tan⁻¹(A – B/1+AB)

Question 8

8. If (1 + tan θ)(1 + tan Ø) = 2, then θ + Ø =

Question 9

9. The equation 2 cos²(x/2) sin²x = x² + 1/x² 0 ≤ x ≤ π/2 has

Answer

None of these

Answer

More than one real solution

Answer

No solution

Answer

One real solution

Question 10

10. Sin⁻¹{2A√1 – A²}

Answer

Sin⁻¹{2A² – 1}

Answer

Sin⁻¹{A² – 2}

Answer

Sin⁻¹{A² – 2}

Answer

Sin⁻¹{2A² – 1}

Question 11

11. Tan⁻¹ 1/3 + Tan⁻¹ 1/5 + Tan⁻¹ 1/7 + Tan⁻¹ 1/8

Question 12

12. The domain of the function y = cos⁻¹ x is

Answer

0 ≤ x ≤ 1

Answer

– 2 ≤ x ≤ 2

Answer

– 1 ≤ x ≤ 1

Answer

– 1 ≤ x ≤ 2

Question 13

13. The value of sin [arc cos (- ½ )]is

Answer

None of these

Question 14

14. Tan⁻¹ 1/7+ Tan⁻¹ 1/13 =

Answer

Tan⁻¹ 2/9

Answer

Tan⁻¹ 2/9

Answer

Tan⁻¹ 3/46

Answer

Tan⁻¹ 9/2

Question 15

15. If sin⁻¹ x = π/5 for some x ϵ (-1,1), then the value of cos⁻¹x is

Question 16

16. Tan⁻¹ 1/7 + Tan⁻¹ 1/13 =

Answer

Tan⁻¹ 3/46

Answer

Tan⁻¹ 2/9

Answer

Tan⁻¹ 9/2

Answer

Tan⁻¹ 2/9

Question 17

17. Tan⁻¹(3A – A³/1 – 3A²)

Answer

2Tan⁻¹ A

Answer

3 Tan⁻¹ A

Answer

Tan⁻¹ 3A

Answer

Tan⁻¹ 2A

Question 18

18. The values of θ satisfying sin 7 θ = sin 4 θ – sin θ and 0 < θ < π/2 are

Answer

π/6, π/9

Answer

π/3, π/9

Answer

π/9, π/4

Answer

π/3, π/4

Question 19

19. For n ϵ Z, the general solution of the equation (√3 – 1)sin θ + (√3 + 1) cos θ = 2 is

Answer

θ = nπ +(-1)ⁿ π/4 + π/12

Answer

None of these

Answer

θ = 2nπ ± π/4 - π/12

Answer

θ = 2nπ ± π/4 + π/12

Question 20

20. Tan⁻¹(x – 1/x – 2) + Tan (x + 1/x + 2) =

Answer

Tan⁻¹(2x² – 3/2x²– 4)

Answer

Tan⁻¹(2x² + 3/2x²+ 4)

Answer

Tan⁻¹(2x² + 4/2x²+ 3)

Answer

Tan⁻¹(2x² – 4/2x²– 3)

Question 21

21. The principal cosine function is

Answer

One – to – one

Question 22

22. Tan⁻¹ A + Tan⁻¹ B + Tan⁻¹ C =

Answer

Tan⁻¹(A–B/1+AB)

Answer

Tan⁻¹(A+B+C–ABC/1–AB–BC–CA)

Answer

Tan⁻¹(A+B/1–AB)

Answer

Tan⁻¹(1–AB–BC–CA/A+B+C–ABC)

Question 23

23. The set of values of x for which tan3x–tan2x/1+tan3xtan2x = 1 is

Answer

nπ + π/4 n = 1,2,3,……

Answer

2nπ + π/4 n = 1,2,3,……

Question 24

24. 2Cos⁻¹ A =

Answer

Sin⁻¹{A² – 2}

Answer

Sin⁻¹{A² – 2}

Answer

Sin⁻¹{2A² – 1}

Answer

Sin⁻¹{2A² – 1}

Question 25

25. The value of sin (Cos⁻¹√3/2) is

Answer

None of these

Question 26

26. Tan⁻¹ A + Tan⁻¹ B =

Answer

Tan⁻¹(1+AB/A – B)

Answer

Tan⁻¹(A + B/1 – AB)

Answer

Tan⁻¹(1–AB/A+B)

Answer

Tan⁻¹(A – B/1+AB)

Question 27

27. The number of values of x in the interval [0, 5π] satisfying the equation 3 sin² x – 7 sinx + 2 = 0 is

Question 28

28. The value of cos [cos⁻¹ (- √3/2) + π/6] is

Answer

None of these

Question 29

29. The smallest positive root of the equation tan x – x = 0 lies on

Answer

(3π/2, 2π)

Answer

(π/2, π)

Answer

(π, 3π/2)

Question 30

30. Inverse of sin function is written as

Answer

(sin x)⁻¹

Answer

Sin x⁻¹

Question 31

31.

Question 32

32. The number of solutions of the equation tan x + sec x = 2 cos lying the interval [0, 2π] is

Question 33

33. Tan⁻¹ ½ + Tan⁻¹ 1/13 =

Question 34

34. If 4 sin² θ = 1, then values of θ are

Answer

2nπ ± π/6

Answer

nπ ± π/6

Answer

nπ ± π/3

Answer

2nπ ± π/3

Question 35

35. If 5 cos 2 θ + 2 cos² θ/2 + 1 = 0, - π < θ < π, then θ =

Answer

π/3, cos⁻¹ (3/5)

Answer

cos – 1 3/5

Answer

± π/3, π – cos⁻¹ 3/5

Question 36

36. The domain of principal sine function is

Answer

[–π/2, π/2]

Answer

[0, 3π/2]

Question 37

37. The graph of y = sin⁻¹ x is along the

Answer

Y – axis

Answer

X – axis

Answer

Both and b

Question 38

38. Range of Tan⁻¹ x is

Answer

[– π/2, π/2]

Answer

[π/2, π/2]

Question 39

39.

Question 40

40. General solution of tan 5 θ = cot 2 θ is

Answer

θ = nπ/7 + π/2

Answer

θ = nπ/7 + π/14 where n ϵ Z

Answer

nπ/7 + π/14

Answer

θ = nπ/7 + π/3

Question 41

41. If sin A = sin B, cos A = cos B, then the value of A in terms of B is

Answer

nπ + (– 1)ⁿ B

Answer

2nπ – B

Question 42

42.

Question 43

43. The domain of principal cosine function is

Answer

[0, 3π/2]

Question 44

44. tan⁻¹(1/4) + tan⁻¹(2/9) is equal to

Answer

½ sin⁻¹ (3/5)

Answer

½ tan⁻¹ (3/5)

Answer

½ cos⁻¹ (3/5)

Answer

tan⁻¹ ½

Question 45

45.

Question 46

46.

Question 47

47. Which of the following is solution of cos 3x = ½ = ?

Answer

1/3 arc cos ½

Answer

Arc cos 1/6

Question 48

48. Tan⁻¹(– 1) =

Question 49

49. Tan⁻¹ (2A/1 – A²) =

Answer

2 Tan⁻¹ A

Answer

Tan⁻¹(2/A) =

Answer

Tan⁻¹(A/2) =

Answer

Tan⁻¹ A

Question 50

50. cot θ = sin 2 θ (θ ≠ nπ, n integer) if θ =

Answer

π/4, π/3

Answer

π/4, π/2

Question 51

51. Range of cosec⁻¹x is

Answer

None of these

Answer

[– π/2, π/2]

Question 52

52. The general solution of tan 3x = 1 is

Answer

nπ + π/4

Answer

nπ/3 + π/12

Answer

nπ ± π/4

Question 53

53. The solution set of the system of equation: x – y = 2π/3, cos x + cos y = 2/3, where x and y are real in:

Answer

a fine non-empty set

Answer

None of these

Question 54

54. The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is

Answer

nπ/2 + π/8

Answer

nπ + π/8

Answer

(-1)ⁿ nπ/2 + π/8

Answer

2nπ + cos⁻¹ (3/4)

Question 55

55. If 2 tan⁻¹ (cos x) = tan⁻¹ (cosec² x), then x is equal to

Question 56

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Total Questions:	55
Time Allowed:	20 Minutes
Total Marks:	55
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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