Final Lap Test Series-6

FINAL LAP TEST SERIES-6

TRIGONOMETRY

12 INFOMATHS/MCA/MATHS/

1. The period of sin2q is

(a) p2 (b) p (c) 2p (d)

2. then sin x =

(a) tan2(a/2) (b) cot2(a/2)

3. If then

(a) (b)

(a) tan 55° (b) cot 55°

5. If then x =

(a) (b)

6. If then general value of q is

(a) (b)

7. If tan (A + B) = p, tan (A – B) = q, then the value of tan 2A is :

(a) (b)

8. If tan A + cot A = 4, then

tan4A + cot4A is equal to

(a) 110 (b) 191 (c) 80 (d) 194 (e) 195

9. If then is equal to

(a) cos q (b) sin q (c) sec q (d) cos 2q (e) tan q

10. If the angle of elevation of the top of a tower at a distance 500 m from its foot is 30°, then height of the tower is

(a) (b) (c) (d) (e)

11. In triangle ABC,

a2 cos(B – C) + b2 cos (C – A) + c2 cos (A – B) is equal to

(a) abc (b) a + b + c

(e) 0

12. The measures of the sides of a triangle are 3, 5 and 7, then the greatest angle is

(a) 60° (b) 100° (c) 90° (d) 120° (e) 140°

13. If tan (A – B) = 1, then smallest positive value of B is

(a) (b) (c) (d)

14. If tan-1x + tan-1y + tan-1z = p, then x + y + z is equal to

(a) xyz (b) 0

(e) x2 + y2 + z2

15. If q = sin-1 [sin(-600°)] then one of the possible value of q is

(a) (b) (c) (d) (e) 0

16. If then x =

(a) 2 (b) 4 (c) 8 (d) 16 (e) 32

17. If then the value of q is

(a) (b) 1 (c) (d)

18. If then the value of x is

(a) 0 (b) - 2 (c) 1 (d) 2

19. The acute angle in radians between the minute and the hour hands of a clock when the time is 4 hours 20 minutes is

(a) (b) q (c) (d)

20. The value of is

(a) (b)

21. If then the largest angle of a triangle whose sides are 1, sin x, cos x is

(a) (b) (c) x (d)

22. The general solution of the equation sinq+cosq = 1 is

(a)

(b)

(c)

(d)

23. If cos and where ‘P’ and ‘Q’ both are acute angles. Then the value of P – Q is :

(a) 30° (b) 60° (c) 45° (d) 75°

24. The equation 3 cos x + 4 sin x = 6 has …… solution

(a) finite (b) infinite

25. If sec-1x = cosec-1y, then

(a) p (b) (c) (d)

26. If then the value of is ….

(a) but ¹ (b) or

27. If C = 2 cos q, then the value of the determinant IS

(a) (b)

28. If in two circles, arcs of the same length subtend angles of 60° and 75° at the centre, then the ratio of their radii is

(a) 4 : 5 (b) 5 : 4

29. sec50° + tan 50° is equal to

(a) tan 20° + tan 50° (b) 2 tan 20°+ tan 50°

30. The ranges of tan-1x is

(a) (b)

31. The value of sin-1x + cos-1x is

(a) (b) p (c) (d) - p

32. If then x equals

(a) (b)

33. The sum S = sin q + sin2q + … + sin nq, equals

(a)

(b)

(c)

(d)

34. If then a + b equals

(a) (b) (c) (d)

35. The solution of the equation

(a) (b)

36. If the sum of the infinite series

(a) (b) (c) (d)

37. If tan q + sec q = ex, then cos q equals

(a) (b)

38. cosh 2x =

(a) cosh2x + sinh2x (b) 2 cosh2x – 1

39. If tan-1 (a + ib) = x + iy, then x =

(a) (b)

40. cosh-1x =

(a) (b)

41. The sum of the radii of inscribed and circumscribed circles for n sided regular polygon of side a, is

(a) (b)

42. The upper th portion of a vertical pole subtends an angle at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is

(a) 80 m (b) 20 m

43. In a triangle ABC, medians AD and BE are drawn. If AD = 4, ÐDAB and ABE , then the area of the DABC is

(a) (b) (c) (d)

44. If in a triangle ABC, then the sides a, b and c

(a) satisfy a + b = c (b) are in A.P.

45. The trigonometric equation sin-1x = 2 sin-1a, has a solution for

(a) (b)

46. The number of sides of two regular polygons are in the ratio 5 : 4. The difference between their angles is 9°. Which of the following is correct?

(a) one of them is a pentagon and the other is a rectangle

(b) one of them must be a hexagon.

(d) one of them has 20 sides and the other has 16 sides.

47. The value of

tan31°.tan32°.tan33° …. tan59° is equal to

(a) – 1 (b) 0 (c) 1 (d) 2.

48. The numbers and

are in

(a) A.P. (b) G.P. (c) H.P. (d) None of these

49. The correct value of the parameter ‘t’ of the identity 2(sin6x + cos6x) + t(sin4x + cos4x) = - 1 is

(a) 0 (b) – 1

50. If w = x + y + z, then

sin x + sin y + sin z – sin w is equal to

(a)

(b)

(c)

(d)

51. To derive the tangent formula, the following steps are given:

(1)

(2)

(3)

(4)

Their correct and proper sequential form to derive the formula is

(a) 2, 4, 3, 1 (b) 1, 2, 3, 4

52. If then is equal to

(a) (b)

53. Consider the following :

(1) If cot q = x, then

(2) If then

(3) If x = p sec q and y = q tan q, then x2q2 – y2p2 = p2q2

(4) The maximum value of is 3.

Which of the these are correct?

(a) 1 and 2 (b) 2 and 3

54. The expression

is equal to

(a) sin2a + sin3a (b) 3

55. A person at the top of a hill observes that the angles of depression of two consecutive kilometer stones on a road leading to the foot of the hill are 30° and 60°. The height of the hill is

(a) km (b) km

56. The value of is

(a) 6/17 (b) 7/16

57. For a triangleABC,

1 + cos 2A + cos 2B + cos 2C = 0, then the triangle must be

(a) equilateral (b) isosceles

58. The lines 4x + 4y = 1, 8x – 3y = 2 and y = 0 are

(a) sides of an isosceles triangle

(b) concurrent

(d) sides of an equilateral triangle.

59. The line 3x + 4y – 24 = 0 cuts the x-axis at A and y-axis at B. The incentre of the triangle OAB, where O is the origin, is at

(a) (2, 3) (b) (3, 3) (c) (4, 3) (d) (3, 4)

60. If then B =

(a) (b)

61. If sin6q = 32cos5q sin q - 32cos3q sinq +3x, then x =

(a) cos q (b) cos 2 q

62. The period of the function

(a) 3p (b) 6p (c) 9p (d) 12p

63. cos a. sin (b - g) + cos b . sin (g - a) + cos g . sin (a - b) =

(a) 0 (b) 1/2

64. sin47° - sin25° + sin 60° - sin 11° =

(a) cos 7° (b) sin7°

65. If A + B + C = 270°, then cos2A + cos2B + cos2C + 4sinA sinB sinC =

(a) 0 (b) 1 (c) 2 (d) 3

66. The solution set of (5 + 4 cos q) (2 cos q + 1) = 0 in the interval [0, 2p] is

(a) (b)

67.

(a) (b) 0 (c) (d)

68. In a DABC if then cos C =

(a) 5/7 (b) 7/5 (c) 16/17 (d) 1736

69. cos1° + cos2° + cos3° + …. + cos 180°=

(a) 1 (b) 0 (c) 2 (d) – 1

70. The value of

(a) 2 (b) 1 (c) 0 (d) 3

71. If cos-1x + cos-1y + cos-1z = 3p, then xy + yz + zx =

(a) 1 (b) 0 (c) – 3 (d) 3

72.

(a) (b)

73. The general solution of the equation tan 2q tan q = 1 for n Î Z is, q =

(a) (b)

74. The maximum of 4sin2x + 3 cos2x is

(a) 4 (b) 3 (c) 7 (d) 5

75. If then

(a) A = 0 for all q

(b) A is odd function of q

(d) A is independent of q.

76. The value of cot 70° + 4 cos 70° is

(a) (b) (c) (d)

77. If q = sin-1x + cos-1x – tan-1x, x ³ 0, then the smallest interval in which q lies is

(a) (b)

78. Let A, B and D are the angles of a plain triangle and Then is equals to

(a) 7/9 (b) 2/9 (c) 1/3 (d) 2/3

79. If a, b (a ¹ b), satisfies the equation a cos q + b sin q = c, then value of is

(a) (b) (c) (d)

80. Which one of the following is true?

(a) sin (cos-1x) = cos (sin-1x)

(b) sec (tan-1x) = tan (sec-1x)

(d) tan (sin-1x) = sin (tan-1x)

(e) All of these.

81. If tan-1a + tan-1b = sin-11 – tan-1c, then

(a) a + b + c = abc

(b) ab + bc + ca = abc

(c)

(d) ab + bc + ca = a + b + c

(e) None of these

82. The number of values of q in the interval [-p, p] satisfying the equation cos q + sin2q = 0 is

(a) 1 (b) 2 (c) 3 (d) 4 (e) Many

83. For any angle q, the expression is equal to

(a) (2 cos q + 1) (2 cos 2q + 1) (2 cos 4q + 1)

(b) (cos q - 1) (cos 2q - 1) (cos 4q - 1)

(d) (2 cos q + 1) (2 cos 2q + 1) (2 cos 4q + 1)

(e) (2 cos q - 1) (2 cos 2q - 1) (2 cos 4q + 1)

84. If m tan (q - 30°) = n tan(q + 120°), then cos 26 equals

(a) (b)

(e)

85. is equal to

(a) (b) (c) (d) (e)

86. For the principal value branch of the graph of the function y = sin-1x, - 1 £ x £ 1, which among the following is a true statement?

(a) graph is symmetric about the x-axis

(b) graph is symmetric about the y-axis

(d) the line x = 1 is a tangent

(e) the line y = 1 is a tangent.

87. If sec q + tan q = k, cos q =

(a) (b) (c) (d) (e) N.O.T

88. Let and then AB = 0 if

(a)

(b)

(c)

(d)