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Page 1 1. 25o when measured in radians is(a) c 18 5 (b) c 24 5 (c) c 36 5 (d) none of these 2. 162o when measured in radians is
(a) c 10 7 (b) c 10 9 (c) c 3 4 (d) c 4 5 3. c 10 7 = ? (a) 272o (b) 302o (c) 288o (d) 316o 4. 11c = ? (a) 315o (b) 372o (c) 418o (d) 630o 5. 1c = ? (a) 56o27'22" (b) 57o16'22" (c) 55o18'32" (d) 57o26'32" 6. 3o 45' expressed in radians is (a) c 36 (b) c 54 (c) c 48 (d) c 96 5 7. 50o 37' 30" = ? (a) c 16 5 (b) c 18 7 (c) c 32 9 (d) c 36 11
8. In a right triangle, the difference between two acute angles is c 15
. The measure of the smallest angle is
(a) 40o (b) 45o (c) 36o (d) 39o
9. The angles of a triangle are in AP and the greatest angle is double the least. The largest angle measures
(a) 60o (b) 80o (c) 75o (d) 90o
10. The angles of a triangle are in AP and the ratio of the number of degrees in the least to the number of radians in the greatest 60 : π. The smallest angle is
(a) 15o (b) 30o (c) 45o (d) 60o
11. In a circle, the central angle of 45o intercepts an arc of length 33 cm. the radius of the circle is
(a) 21 cm (b) 35 cm (c) 42 cm (d)14 cm
12. In a circle of radius 14 cm an arc subtends an angle of 36o at the centre. The length of the arc is
(a) 6.6 cm (b) 7.7 cm (c) 8.8 cm (d) 9.1 cm
13. The minute hand of a watch is 1.4 cm long. How far does its tip move in 45 minutes? (a) 6 cm (b) 6.3 cm
(c) 6.6 cm (d) 7 cm
14. If the arcs of the same length in two circles subtend angles of 60o and 75o at their respective centres, the ratio of their radii is (a) 4:5 (b) 5:4 (c) 3:5 (d) 5:3
15. A wire of length 121 cm is bent to form an arc of a circle of radius 180 cm. the angle subtended at the centre by the arc is
(a) 36o20' (b) 34o40' (c) 38o30' (d) 39o10'
16. A horse is tied to a post by a rope. If the horse moves along a circular path, always keeping the rope tight and describes 88 m when it
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Page 2 traces 72o at the centre, then the length ofthe rope is
(a) 35 m (b) 70 m (c) 17.5 m (d) 22 m
17. A pendulum swings through an angle of 42o in describing an arc of length 55 cm. The length of the pendulum is
(a) 9π cm (b) 10π cm (c) 12π cm (d) 13.6π cm
18. The radius of a circle is 30 cm. The length of the arc of this circle whose chord is 30 cm long, is
(a) 9π cm (b) 10π cm (c) 12π cm (d) 13.6π cm
19. A wheel makes 180 revolutions in 1 minute. How many radians does it turn in 1 second? (a) (3π)c (b) (4π)c
(c) (6π)c (d) (12π)c
20. A railway train is moving on a circular curve of radius 1500 m at a speed of 90 km/hr. Through what angle has it turned in 11 seconds?
(a) 10o 30' (b) 11o 40' (c) 12o (d) 16o 30'
21. When a clock shows the time 7 : 20, what is the angle between its minute hand and the hour hand?
(a) 60o (b) 80o (c) 100o (d) 120o
22. The angle between the hour hand and the minute hand of a clock at half past three is (a) 54o (b) 63o (c) 72o (d) 75o
23. The angle between the minute hand and the hour hand of a clock when the time is 8 : 25 am, is
(a) 107o 30' (b) 105o
(c) 102o 30' (d) 92o 45'
24. The length of a pendulum is 60 cm. the angle through which it swings when its tip describes an arc of length 16.5 cm is
(a) 15o 30' (b) 15o 45' (c) 16o 15' (d) 16o 30'
25. The angles of a quadrilateral in degrees are in AP and the greatest angle is 120o. The smallest angle is (a) o 4 (b) o 3 (c) o 5 (d) o 6
26. The perimeter of a sector of a circle is equal to half the circumference of the circle. The angle of the sector is
(a) o 4 (b) o 2 (c) (π – 2)c (d) (π + 2)o 27. sin ? 3 25 (a) 2 1 (b) 2 1 (c) 2 3 (d) 2 3 28. cos ? 4 41 (a) 2 1 (b) 2 1 (c) 2 3 (d) 2 3 29. tan ? 3 16 (a) 3 (b) - 3 (c) 3 1 (d) 3 1 30. ? 4 29 (a) -1 (b) 1 (c) 3 (d) 3 1
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Page 3 31. ? 3 19 (a) -2 (b) 2 1 (c) 2 (d) 2 1 32. cosec ? 4 33 (a) 2 (b) 2 (c) 2 1 (d) 2 1 33. cos 15π = ?(a) 1 (b) -1 (c) 0 (d) none of these 34. sec 6π = ? (a) 1 (b) -1 (c) 2 (d) - 2 35. tan ? 4 5 (a) 3 (b) 3 1 (c) 1 (d) -1 36. sin (765o) = ? (a) 2 3 (b) 2 3 (c) 2 1 (d) 2 1 37. cot (-600o) = ? (a) -1 (b) 3 (c) 3 1 (d) none of these 38. If sin x = 5 6 2
and x lies in quadrant III, then cot x = ? (a) 6 2 1 (b) 6 2 1 (c) 6 2 3 (d) 6 2 3 39. If cos x = 2 4 15 and < x < π, then sin x = ? (a) 4 3 (b) 4 3 (c) 4 1 (d) 4 1 40. If sec x = - 2 and π < x < , 2 3 then sin x = ? (a) 2 3 (b) 2 3 (c) 2 1 (d) 2 1 41. If cosec x = 3 2
and x lies in quadrant IV, then tan x = ? (a) 3 1 (b) 3 1 (c) 3 (d) - 3
42. If cot θ = 5and θ does not lie in quadrant I, then the values of cosec θ and sec θ are respectively (a) 5 6 6, (b) 5 6 6, (c) 5 6 6 , (d) 5 6 6, 43. If cost θ 2 3
and θ lies in quadrant II, then (2 sin θ + tan θ) = ? (a) 0 (b) 2 3 (c) 2 3 3 (d) none of these 44. If cos 5 3 and π < θ < ? ) tan (sec ) cot (cos , ec 2 3 (a) 6 1 (b) 3 2 (c) 2 3 (d) 3 1 45. If sin θ= 2 5 3
and < θ<π, then (2sec θ – 3 cot θ) = ? (a) 2 3 (b) 2 3 (c) 2 13 (d) 2 13 46. If sec θ = 2 3 2and < θ < 2π, then ) cos cot ( ) cos tan ( ec ec 1 1 = ? (a) 2 3 (b) -1 (c) 8 3 (d) 4 3
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Page 4 47. If cos θ = 13 12 and π < θ < , 2 3 then (clot θ + cosec θ) = ? (a) 5 1 (b) 5 1 (c) 5 3 (d) 5 3 48. If cot θ = 2 5 12 and < θ < π, then ? ) cos sin ( ) cos sin ( ec 1 1 (a) 4 13 (b) 4 13 (c) 2 15 (d) 2 15 49. If sin θ= 2 5 4 and < θ < π, then ? ) sin sec cot ( ) tan cos cos ( 5 3 4 3 4 5 ec (a) 2 1 (b) 1 (c) 2 1 (d) -1 50. If sec 5 13 and θ is acute, then
) tan ( ) cot ( 4 3 3 4 =? (a) 252 55 (b) 305 44 (c) 255 54 (d) 215 33 51. Cos 135o = ? (a) 2 1 (b) 2 1 (c) 2 1 (d) 2 1 52. sec 120o = ? (a) 2 (b) - 2 (c) 2 (d) -2 53. cose 150o = ? (a) -2 (b) 2 (c) 2 (d) - 2 54. sin 315o = ? (a) 2 1 (b) 2 1 (c) 2 (d) - 2 55. cos 405o = ? (a) 2 (b) 2 1 (c) - 2 (d) 2 1 56. tan 6 11 =? (a) 3 1 (b) 3 1 (c) 3 (d) - 3 57. cot 675o = ? (a) -1 (b) 01 (c) 3 (d) 3 58. sin 3 21 =? (a) 2 1 (b) 2 1 (c) 2 3 (d) 2 3 59. cot (-600o) = ? (a) 3 (b) 3 1 (c) 3 (d) 3 1 60. cosec (-1110o) = ? (a) 3 2 (b) 3 2 (c) 2 (d) -2 61. sec 4 33 =? (a) 2 (b) 2 (c) 2 3 (d) 2 3 62. tan 3 25 =? (a) 3 (b) 3 (c) 3 1 (d) 3 1
63. The values of cot
6 4 3 cot , cot , are in
(a) AP (b) GP (c) HG (d) none of these 64. Which is smaller, sing 64o or cos 64o?
(a) sin 64o (b) cos 64o (c) both are equal (d) cannot be compared
65. Which is larger, sing 24o or cos 24o (a) sin 24o (b) cos 24o
(c) both are equal (d) cannot be compared
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Page 5 66. The extremism values of sin θ are(a) 0 and 1 (b) -1 and 0 (c) -1 and 1 (d) 2 1 2 3 and
67. The extremum values of cos θ are (a) 0 and 1 (b) -1 and 0
(c) -1 and 1 (d) 2
2 3
and
68. The value of sec θ can
(a) never be greater than 1 (b) never be less than 1 (c) never be equal to 1
(d) never lie between -1 and 1 69. tan 150o =? (a) 3 1 (b) 3 1 (c) 3 (d) 3 70. sec 150o = ? (a) 3 2 (b) 2 (c) 3 2 (d) -2 71. cot 120o = ? (a) 3 1 (b) 3 1 (c) 3 (d) 3 72. (sin 105 + cos 105o) = ? (a) 2 (b) 2 1 (c) 3 1 (d) 3 2 73. sin 15o = ? (a) 2 2 3 (b) 2 2 1 3 ) ( (c) 2 2 1 3 ) ( (d) 2 1 3 ) ( 74. cos 150o = ? (a) 21 2 1 3 ) ( (b) 2 2 1 3 ) ( (c) 2 1 3 ) ( (d) 2 1 3 ) ( 75. tan 15o =? (a) ) ( ) ( 1 3 1 3 (b) ) ( ) ( 1 3 1 3 (c) ) ( ) ( 1 2 1 2 (d) ) ( ) ( 1 2 1 2 76. sin 75o = ? (a) 2 2 1 3 ) ( (b) 2 2 1 3 ) ( (c) 2 2 1 2 ) ( (d) 2 2 1 2 ) ( 77. cos 75o= ? (a) 2 2 1 3 ) ( (b) 2 2 1 3 ) ( (c) 2 2 1 2 ) ( (d) 2 2 1 2 ) ( 78. tan 12 13 = ? (a) (2+ 3) (b) (1+ 2) (c) (2- 3) (d) ( 2-1)
79. (sin 70o cos 9o + cos 36o sin 10o) = ? (a) 2 1 (b) 2 1 (c) 2 3 (d) 2 3 80. (sin 36o cos 9o + cos 36o sin 9o) = ?
(a) 2 1 (b) 2 1 (c) 2 3 (d) 1 81. cos 80o cos 20o + sin 80o sin 20o = ?
(a) 2 1 (b) 2 3 (c) 2 1 (d) 1 82. cos 50o cos 10o – sin 50o som 10o = ?
(a) 2 1 (b) 2 3 (c) 2 1 (d) 1
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Page 6 83. sin (40o + θ) cos (10o + θ) – cos (40o + θ) sin(10o + θ) = ? (a) 2 3 (b) 2 1 (c) 2 (d) none of these 84. sin 4 12 7 4 12 7 sin cos cos =? (a) 2 (b) 2 1 (c) 2 3 (d) none of these 85 sin 12 4 12 4 sin cos cos =? (a) 2 3 (b) 2 (c) 2 1 (d) none of these 86. cos cos sin sin ?
4 3 2 4 3 2 (a) ) ( ) ( 1 3 1 3 (b) ) ( ) ( 1 3 1 3 (c) ) ( ) ( 1 2 1 2 (d) ) ( ) ( 1 2 1 2 87. sin 12 = ? (a) 2 2 1 3 ) ( (b) 2 2 1 3 ) ( (c) 2 2 1 3 ) ( (d) none these 88. 12 5 =? (a) 2 2 1 3 ) ( (b) 2 2 1 3 ) ( (c) 2 2 1 3 ) ( (d) 2 2 1 3 ) ( 89. If sin θ = 17 15 and cos , 13 12 where θ and both lie in quadrant I, then sin (θ+)=?
(a) 221 171 (b) 221 180 (c) 221 220 (d) 221 181 90. If sin 5 3 and cos 12 12
, where θ and both lie in quadrant IV, then cos (θ + )=?
(a) 65 16 (b) 65 16 (c) 65 33 (d) 65 33 91. If cos 5 4 and cos = 13 12 , where θ and both lie in quadrant IV, then cos (θ + ) = ? (a) 65 33 (b) 65 33 (c) 65 16 (d) 65 16 92. If cot θ= 2 1 and sec = 3 5 , where θ lies in quadrant III and lies in quadrant II, then than (θ+) = ? (a) 11 5 (b) 11 2 (c) 11 6 (d) 11 10 93. cos 15o – sin 15o = ? (a) 2 1 (b) 2 1 (c) 2 1 2 (d) 2 1 2 94. cot 105o – tan 105o = ? (a) 3 (b) 2 3 (c) 2 3 (d) ) ( ) ( 1 3 1 3 95. 2s sin 12 12 5 sin =? (a) 2 1 (b) 2 (c) 2 1 (d) 2 3 96. 2 cos 12 12 5 cos =? (a) 2 1 (b) 2 1 (c) 2 3 (d) 2 97. 2 sin 12 12 5 cos =? (a) 2 1 (b) 2 1 3 (c) 2 3 2 ) ( (d) 2 3
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Page 7 98. θ) θ)sin(270 θ)cosec( cos(360 θ) sin(360 θ) θ)cot(360 θ)tan(270 cos(90 θ) sin(180 o o o o o o o =? (a) 2 (b) 2 3 (c) 2 3 (d) 199. sin (40o + θ) cos (10o + θ)- cos (40o + θ) sin (10o + θ) =? (a) 2 (b) 2 1 (c) 2 3 (d) none of these 100. θ) θ)tan(180 θ)cos(270 cosec( θ) θ)sin(180 θ)sec(270 cos(90 o o o o o =? (a) cos θ (b) sec θ
(c) cot θ (d) none of these
101. cos θ+sin (270o + θ) – sin (270o - θ) + cos (180o+ θ = ?)
(a) 2 cos θ (b) 2 sin θ (c) 0 (d) none of these 102. oo oo 8 8 8 8 sin cos sin cos =?
(a) tan8o (b) tan 37o (c) tan 52o (d) none of these 103. 2 cos ) cos( ) cos( ) cos( =?
(a) -cot θ (b) cot θ (c) -tan θ (d) tan θ 104. cos x 4 +cos x 4 =? (a) 2 cos x (b) 2cos x (c) 2 sin x (d) 2sin x 105. cos x x 4 3 4 3 cos =? (a) 2sin x (b) 2 sin x
(c) 2 sin x (d) 2 1 sin x 106. x x x x 3 3 cos cos sin sin =?
(a) tan 2x (b) cot 2x (c) –tan 2x (d) –cot 2x 107. x x x x 4 6 4 6 sin sin cos cos =?
(a) cot x (b) tan x (c) –cot x (d) –tan x 108. x x x x x x 2 3 4 2 3 4 sin sin sin cos cos cos =? (a) tan 2x (b) tan 3x (c) –cot x (d) –tan x 109. x x x x 5 7 5 7 cos cos sin sin =?
(a) tan x (b) cot x (c) tan 2x (d) cot 3x 110. (sin2 6x – sin24x) = ?
(a) sin10x (b) sin 2x (c) tan 2x (d) cot 2x 111. cos 20ocos 40o cos 80o=?
(a) 16 1 (b) 8 1 (c) 8 3 (d) 16 3
112. sin 10o sin 50o sin 70o = ? (a) 4 3 (b) 8 3 (c) 8 1 (d) 16 1 113. 2 cos 45o cos 15o = ? (a) 2 3 (b) 2 1 3 ) ( (c) 2 1 3 ) ( (d) 2 3 114. 2 sin 75o sin 15o = ? (a) 2 1 (b) 3
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Page 8 (c) 2 1 3 (d) none of these 115. cos 15o – sin 15o = ? (a) 2 1 (b) 2 1 (c) 2 2 1 (d) 2 3 116. If sin x = 2 1 and x lies in quadrant III, then sin 2x = ? (a) 2 1 (b) 3 (c) 2 3 (d) 3 2 1 117. If sec x= 2 12 13 and < x < π, then cos 2x = ? (a) 169 120 (b) 169 119 (c) 119 120 (d) none of these 118. If tan 2 3 4 3 and x < x < 2π, then tan 2x = ? (a) 25 24 (b) 25 7 (c) 7 24 (d) 7 24 119. If sin x = 3 1 , then sin 3x = ? (a) 1 (b) 9 1 (c) 9 7 (d) 27 23 120. If cos x = 2 1 , then cos 3x = ? (a) 2 3 (b) 6 1 (c) -1 (d) 3 2 121. 12 12 2 2 sin cox =? (a) 2 1 (b) 2 3 (c) 2 3 (d) 2 1 122. x x x x 2 2 1 2 2 1 cos sin cos sin =? (a) tan 2x (b) tan x (c) cot 2x (d) cot x 123. If cos x = 2 5 3 and < x < π, then sin 2 x =? (a) 5 2 (b) 5 2 (c) 5 1 (d) 5 1 124. If cos x= 2 5 3 and < x < π, then cos 2 x =? (a) 5 1 (b) 5 1 (c) 5 2 (d) 5 2 125. If cos x = 5 4 and π < x < 2 3 then cos 2 x =? (a) 10 1 (b) 10 1 (c) 10 3 (d) 10 3 126. If tan x = 4 3 and π < x < 2 3 ,then tan 2 x =? (a) 3 (b) 3 1 (c) -3 (d) 3 1 127. If cos x = 3 1
and x lies in quadrant III, then tan
2 x =? (a) 2 (b) 2 (c) 3 (d) 3 128. If sin x = 2 1
and x lies in quadrant IV, then sin 2 x =? (a) 2 3 2 (b) 2 2 3 (c) 2 3 2 (d) none of these 129. x x cos cos 1 1 =? (a) tan22 x (b) cot22 x (c) sec22 x (d) cosec22 x
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Page 9 130. x x sin sin 1 1 =? (a) tan2 x (b) cot2 x (c) tan 2 4 x (d) dot 2 4 x 131. x x cos sin 1 =? (a) tan2 x (b) cot2 x (c) tan 2 4 x (d) none of these 132. cot 2 x - tan 2 x =?(a) 2 tan x (b) 2 cot x (c) 2 sin x (d) 2 cos x 133. sin 18o = ? (a) 4 1 5 ) ( (b) 4 1 5 ) ( (c) 4 1 3 ) ( (d) 2 1 3 ) ( 134. cos 18o= ? (a) 4 5 2 10 (b) 4 5 2 10 (c) 4 1 5 ) ( (d) none of these 135. cos 36o = ? (a) 4 1 5 ) ( (b) 4 1 5 ) ( (c) 2 1 3 ) ( (d) 2 1 3 ) ( 136. sin 36o = ? (a) 4 1 5 ) ( (b) 4 5 2 10 (c) 4 5 2 10 (d) none of these 137. sin 54o = ? (a) 4 1 5 ) ( (b) 4 1 5 ) ( (c) 4 5 2 10 (d) 4 5 2 10 138. cos 720 = ? (a) 4 1 5 ) ( (b) 4 1 5 ) ( (c) 3 5 2 ) ( (d) 3 5 2 ) ( 139. cos 54o = ? (a) 4 5 2 10 ( (b) 4 5 2 10 ( (c) 4 1 5 ) ( (d) 4 1 5 ) ( 140. sin 72o= ? (a) 4 5 2 10 (b) 4 5 2 10 (c) 4 1 5 ) ( (d) 4 1 5 ) ( 141. 2 sin 22 2 1 o cos 22 2 1 o = ? (a) 1 (b) 2 1 (c) 2 1 (d) 2 142. (2 cos2 15o - 1) = ? (a) 2 3 (b) 2 3 (c) 2 3 (d) 2 3 143. (3 sin 40o – 4 sin3 40o )=? (a) 2 3 (b) 2 3 (c) 3 3 (d) none of these 144. (8 cos320o – 6 cos 20o) = ? (a) 2 5 (b) 3 5 (c) 1 (d) 2 3
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Page 10 145. If tan θ =b a
, then a sin 2θ + b cos 2θ = ? (a) a (b) b (c) a + b (d) a - b
146. cot x - 2 cot 2x = ? (a) tan x (b) cos x (c) sin x (d) cos 2x 147. cos 2x + 2 sin2x=? (a) 2 (b) 2 1 (c) 1 (d) 2 3 148. x x 2 1 2 cos sin =?
(a) tan x (b) cot x (c) sec x (d) cosec x 149. x x 2 1 2 cos sin =?
(a) tan x (b) cosec x (c) sec x (d) cot x 150. x x 2 1 2 sec tan =?
(a) sin x (b) cos x (c) tan x (d) cot x 151. x x x x cos sin sin cos 2 2 1 =? (a) tan x (b) cot x (c) sec x (d) cosec x 152. ) sin ( cos x x 1 =? (a) tan 2 x (b) tan 2 4 x (c) tan 2 4 x (d) none of these
153. (sin2α cos2β + cos2α sin2β + sin2α sin2 β + cos2α cos2β) =? (a) - (b) -1 (c) 0 (d) 3 154. If x is cute, the x x sin sin 1 1 =?
(a) secx + cosec x (b) sec x + tan x (c) cosec x + cot x (d) tan x + cot x
155. (sec θ – cos θ) (cosec θ – sin θ) (cot θ + tan θ) = ?
(a) 1 (b) -1 (c) 0 (d) none of these
156. sin θ sin cos cos sin 1 1 =? (a) 1 (b) 2 (c) 3 (d) 4 157. s(1+ sin θ) 1 1 cos sin cos sin =? (a) tan θ (b) cot θ (c) sin θ (d) cos θ 158. ) cos (cot ) cos (cot 1 1 ec e =?
(a) cosec θ + cot θ (b) cosec θ - cot θ (c) 1 (d) -1 159. 2 1 1 sec tan tan sec =? (a) ) sin ( ) sin ( 1 1 (b) ) sin ( ) sin ( 1 1 (c) 1 (d) none of these
160. If x = r cos α cos β, y = r cos α sin β and z = r sin α, then x2 + y2 + z2 = ?
(a) 1 (b) r2 (c) r4 (d) none of these
161. If a tan θ = b, then cos sin cos sin a b a b = ? (a)
) ( 2 2 2 2 b a b a (b)
) ( 2 2 2 2 b a b a (c)
) ( 2 2 2 2 a b a b (d) none of these 162. If 5 cot θ = 4, then cos sin cos sin 2 3 5 =? (a) 1 (b) 4 3 (c) 14 5 (d) 14 364, CIRCULAR ROAD , LALPUR, RANCHI, MOB-7544007542/43
Page 11 (a) 2 1 (b) 2 1 (c) 2 3 (d) 3 1164. If θ lies in quadrant II, then sin sin sin sin 1 1 1 1 =?
(a) tan θ (b) 2 tan θ (c) cot θ (d) 2 cot θ 165. If π < θ < 2 3 ,then cos cos cos cos 1 1 1 1 =? (a) 2 sec θ (b) -2 sec θ (c) 2 cosec θ
(d) -2 cosec θ
166. If 7 sin2 θ + 3 cos2 θ = 4, then tan θ = ? (a) 2 1 (b) 3 1 (c) 2 1 (d) 3 1
167. If sin θ + sin2 θ = 1, then (cos2 θ + cos4 θ) = ? (a) 0 (b) 1 (c) 2 (d) none of these 168. If sec θ – tan θ =
3 2
, then which one of the following is true? (a) sec θ = , 6 5 tan θ = 2 3 (b) sec θ = , 12 13 tan θ = 12 5 (c) sec θ = , 9 8 tan θ = 5 4 (d) none of these 169. If cosec θ+cot θ=6, then which one of the
following is true? (a) cos θ = , 12 35 cot θ = 12 37 (b) cosec θ = 12 37 , cot θ , 12 35 (c) cosec θ = , 12 41 cot θ = 12 31 (d) none of these
170. If (3 sin θ + 5 cos θ) = 5, then (5 sin θ – 3 cos θ) =? (a) 4 (b) 2 (c) 1 (d) 3 171. ) tan ( ) tan ( o o 15 1 15 1 =? (a) 2 3 (b) 3 (c) 3 2 (d) 2 1 172. (3 sin 20o – 4 sin3 20o) =? (a) -1 (b) 2 1 (c) 3 (d) 2 3 173. (4cos3 15o – 3 cos 15o)= ? (a) 1 (b) -1 (c) 2 1 (d) 0 174. (2 cos 75o cos 15o) =? (a) 2 1 (b) 2 (c) 2 (d) 4 175. (sin 105o sin 75o) = ? (a) 4 3 2 ) ( (b) 4 3 2 ) ( (c) 4 1 5 ) ( (d) 4 1 5 ) ( 176. (sin 105o + cos 105o) = ? (a) 2 1 (b) 2 (c) 2 1 (d) 2 3
177. If 0o < θ < 90o and (sin θ+cos θ) = 2,then θ = ? (a) 3 (b) 4 (c) 6 (d) π
178. If 0o < θ < 90o and (sin θ + cosec θ) = 2 5 , then θ = ? (a) 3 (b) 4 (c) 6 (d) π 179. If 0o < θ < 90o and sin 2θ= 5 1
, then (sin θ + cos θ) = ? (a) 5 2 (b) 5 3 (c) 5 6 (d) 5 7
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Page 12 180. If θ is acute and sin θ = cos 2θ, then (sin θ +cos θ) =? (a) 2 1 3 ) ( (b) 2 1 3 ) ( (c) 2 2 3 ) ( (d) 2 2 3 ) (
181. If θ is acute and (cos θ-sin θ) > 0, then (cos θ+sin θ) cannot be greater than
(a) 2 1 (b) 2 1 (c) 3 1 (d) 2 182. 2 22cos4 =?
(a) 2 sin θ (b) 2 cos θ (c) sin2θ (d) cos 2θ
183. If sin 2θ = cos 3θ and θ is acute, then sin θ = ? (a) 4 1 5 ) ( (b) 4 1 5 ) ( (c) 4 2 3 ) ( (d) 4 1 2 3 ) (
184. The least value of (2 sin2 θ + 3 cos2 θ) is (a) 1 (b) 2 (c) 3 (d) 5
185. The greatest value of (sin4 θ + cos4 θ) is (a)
2 1
(b) 1 (c) 2 (d) 3 186. If cos2 θ + sec2 θ = p, then
(a) p < 1 (b) p = 1 (c) 1 < p < 2 (d) p 2 187. If sin2 θ + cos4 θ =p, then
(a) 1 p 2 (b) 4 3 p 1 (c) 16 13 4 3 p (d) 1 16 13 p
188. If 2 sin2 θ - cos θ = p, then (a) 2 p 2 (b) -1 p 3 (c) -2 p 3 (d) -2 p 4 189. 2 8 2 8 2 2 A sin A sin =? (a) 2 1 sin A (b) 2 1 sin A (c) 2 sin 8 (d) sin A
190. (cos 1o cos 2o cos 3o …… cos 178o cos 189o)= ? (a) -1 (b) 1 (c) 0 (d) 2
191. (tan 1o tan 2o tan 3o ………. Tan 89o) = ? (a) 0 (b) 1 (c)
2 1
(d) none of these 192. (tan 15o tan 25o tan 45o tan 65o tan 75o) = ?
(a) 1 (b) 2 (c) 3 (d) 3 193. 20 9 20 7 20 5 20 3 20 tan tan tan tan tan =? (a) -1 (b) 1 (c) 2 1 (d) none of these 194. The general solution of the equation sin θ = 0
is (a) θ = 2nπ, n I (b) θ = nπ, n I (c) θ = (2n+1) 2 , n I (d) θ = 2 n , n I 195. The general solution of the equation cos θ = 0
is
(a) θ = nπ, n I (b) θ = nπ, n I (c) θ =(2n+1)
2
, n I (d)none of these 196. The general solution of the equation tan θ = 0
is (a) θ = nπ, n I (b) θ = 2nπ, n I (c) θ = (2n + 1) 2 , n I (d) none of these 197. The general solution of the equation tan 3x =
0 is (a) x = 3nπ, n I (b) , 3 n x n I
64, CIRCULAR ROAD , LALPUR, RANCHI, MOB-7544007542/43
Page 13 (c) x = (2n + 1)6
, n I (d) none of these 198. The general solution of the equation cos 2x =
0 is (a) x = 2 n , n I (b) x = (2n + 1) 4 , n I (c) x = nπ, n I (d) none of these
199. The general solution of the equation sin θ = sin α is
(a) θ=α (b) θ=nπ α, n I
(c) θ = nπ + (-1)nα, n I (d) none of these 200. The general solution of the equation cos θ =
cos α is
(a) θ=α (b) θ = nπ α I (c) θ =2nπ α, n I (d) none of these
201. The general solution of the equation tan θ = tan α is
(a) θ = nπ + α, n I (b) θ = 2nπ + α, n I (c) θ = nπ + α, n I (d) θ = 2nπ α, n I 202. The general solution of the equation sin2 θ =
sin2α is
(a) θ = nπ + α, n I (b) θ = nπ α, n I (c) θ = 2nπ + α, n I (d) θ = 2nπ α, n I 203. The general solution of the equation cos2 θ =
cos2α is
(a) θ = nπ + α, n I (b) θ = 2nπ + α, n I (c) θ = nπ α, n I (d) θ = 2nπ α, n I 204. The general solution the equation tan2 θ =
tan2α is
(a) θ = nπ + α, n I (b) θ = 2nπ + α, n I (c) θ = nπ α, n I (d) θ = 2nπ α, n I 205. The general solution the equation sin
2 1 is (a) θ = nπ + 4 , n I (b) θ = 2nπ + 4 , n I (c) θ = nπ + (-1)n 4 , n I (d) none of these
206 The general solution of the equation cos
2 1 is (a) θ = nπ + , 3 n I (b) θ = 2nπ + , 3 n I (c) θ = 2nπ , 3 n I (d) none of these 207. The general solution of the equation tan
3 1 is (a) θ=nπ+ , 6 n I (b) θ=2nπ+ , 6 n I (c) θ=2nπ , 6 n I (d) none of these 208. The general solution of the equation sin
2 3 is (a) θ = nπ + , 3 n I (b) θ = 2nπ + , 3 n I (c) θ = nπ +(-1)n , 3 4 n I (d) none of these
209. The general solution of the equation cos θ = 2 1 is (a) θ = nπ , 3 2 n I (b) θ = 2nπ , 3 n I (c) θ = 2nπ , 3 2 n I (d) none of these 210. The general solution of the equation cot θ =
-3is (a) θ = nπ + , 6 5 n I (b) θ = 2nπ + , 6 5 n I (c) θ = nπ + , 3 2 n I (d) none of these
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Page 14 211. The general solution of the equation cosec θ +2= 0 is (a) θ = nπ + , 4 5 n I (b) θ = nπ + , 4 5 n I (c) θ = nπ +(-1)n , 6 5 n I (d) none of these
212. The general solution of the equation tan 3θ = - 1 is (a) θ = , 4 3 n n I (b) θ = , 4 3 2 n n I (c) θ = , 4 3 n n I (d) none of these 213. The general solution of the equation sin 2θ =
2 1 is (a) θ = , 24 4 n n I (b) ( ) , 12 7 1 2 n n n N (c) θ = , 12 2 n n I (d) none of these 214. The general solution of the equation 4 sin2 θ =
1 is (a) θ = nπ , 6 nI (b) θ = 2nπ , 6 nI (c) θ = , 24 4 n nI (d) none of these 215. The general solution of the equation 2 cos2 θ
= 1 is (a) θ = 2nπ + , 4 nI (b) θ = , 8 2 n nI (c) θ = nπ , 4 nI (d) none of these 216. The general solution of the equation cot2 θ = 3
is (a) θ = nπ + , 6 nI (b) θ = nπ , 6 nI (c) θ = 2nπ + , 6 nI (d) none of these 217. In a Δ ABC, if a = 2, b = 3, c = 4, then cos A = ?
(a) 9 2 (b) 7 5 (c) 9 6 (d) 8 7
218. In a ΔABC, ifa = 2, b = 6and c = ( 31),then A = ?
(a) 18o (b) 30o (c) 45o (d) 60o
219. In a Δ ABC, if a = 2, b = 6, c = 8,then A = ?
(a) 60o (b) 45o (c) 30o (d) 90o
220. The angles of a ΔABC are in the ratio 1 : 2 : 3. The ratio of their corresponding sides is (a) 1 : 2 : 3 (b) 2:3:1
(c) 1: 2: 3 (d) 1 : 3: 2
221. In a ΔABC, if a = ( 31), b = 2 and C = 60o, then c = ?
(a) 2 (b) 3 (c) 5 (d) 6
222. In a ΔABC, if a = 2, b = 3 and sin A = , 3 2 then B = ? (a) 30o (b) 60o (c) 90o (d) 120o
223. The angles of a ΔABC are in AP and b:c = ,
: 2
3 then C = ?
(a) 30o (b) 45o (c) 60o (d) 90o
224. In a ΔABC, if A = 30o and b:c=2: 3,then B=?
(a) 30o (b) 45o (c) 60o (d) 90o
225. In a right ΔABC, the sides are in AP, then their ratio is
(a) 2:3:4 (b) 3:4:5 (c) 4:5:6 (d) 2:3:5
226. In a ΔABC, if A = 45o , B = 60o, C=75o, then a:b:c=?
64, CIRCULAR ROAD , LALPUR, RANCHI, MOB-7544007542/43
Page 15 (a) 2: 3: 5 (b) 3:4:5(c) 2: 6:( 31) (d) none of these 227. In a ΔABC, if A 30o, C = 105o and b = 3 2,
then a = ?
(a) 2 (b) 3 (c) 2 (d) 3 2
228. In a ΔABC, if a = 5, c = 2 2and B = 45o, then b = ?
(a) 6 (b) 3 (c) 13 (d) 2 3
229. In a ΔABC, if a ( 31),B = 30o, C = 45o, then c = ?
(a) 5 (b) 4 (c) 3 (d) 2
230. In a ΔABC, b = 5, c=5 3and A = 30o, then ΔABC is
(a) isoceles (b) equilateral (c) right angled (d) scalene
231. In a ΔABC, it is given that A : B: C = 3:4:5, then a:c=?
(a) 3:5 (b) : 5
(c) 2:( 31) (d) 3:( 21)
232. In a ΔABC, if b = 20, c=15 and A = 150o, then ar(ΔABC) =?
(a) 60 sq units (b) 75 sq units (c) 90 sq units (d) 120 sq units
233. In a ΔABC, if a = 18, b = 24 and c = 30, then ar(ΔABC) =?
(a) 180 sq units (b) 210 sq units (c) 216 sq units (d) 120 sq units
234. In ΔABC, if a = 16, c=9 and B = 30o, then ar(ΔABC) = ?
(a) 36 sq units (b) 48sq units (c) 18 3 sq units (d) 72 sq units
235. In a ΔABC, if a = 15,b = 14, c = 13, then its circumradius is (a) 2 21 (b) 2 17 (c) 4 55 (d) 8 65
236. In a ΔABC, if a = 18, b = 24, c = 30, then the area of its circumcircle is
(a) 121π sq units (b) 144π sq units (c) 225π sq units (d) 256π sq units 237. In a ΔABC, if a = 4, b = 13, c = 15, then the
radius of the incircle is (a) 3 (b) 2 (c) 2 3 (d) 2 5
238. in a ΔABC, if a = 13, b = 14 and c = 15, then the area of the incircle is
(a) (16π) sq units (b) (25π) sq units (c) (36π) sq units (d) none of these 239. In an equilateral ΔABC, we have:
(a) R = 2r (b) R = 3r (c) R = 4r (d) 2R = 3r
240. In an equilateral triangle of side 2 3, the circumradius is
(a) 1 (b) 2 (c) 3 (d) 3
241. The sides of a ΔABC are in the ratio 3 : 7 : 8. Then, (R : r) = ?
(a) 7:5 (b) 8:5 (c) 7:2 (d) 7:3
242. The perimeter of a ΔABC is 27 cm and its area is 81 cm2. Its inradius is
(a) 4.5 cm (b) 6 cm (c) 7.5 cm (d) 7 cm
243. In a right ΔABC, we have: sin2A+ sin2B + sin2C = ?
(a) 1 (b) 2 (c) 3 (d) 0 244. Ina ΔABC, we have: ?
) sin( ) sin( C B C B (a) 2 2 2 a c b ) ( (b) 2 2 2 a c b ) (
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Page 16 (c) 2 2 2 2 c b c b (d) none of these245. In a ΔABC, we have: a(b cos C – c cos B) = ? (a) a2 (b) a(b2 – c2) (c) (b2 – c2) (d) 0 246. In ΔABC, we have: B C A C B A cos ) cos( cos ) cos( 1 1 =? (a) 2 2 2 2 c a b a (b) 2 2 2 2 a c c b (c) 2 2 2 2 b a a c (d) none of these 247. In a ΔABC, (a - b)2 cos22 C + (a +b)2 sin22 C =? (a) a2 (b) b2 (c) c2 (d) 2(a2 + b2)
248. In a ΔABC, (b + c) cos A + (c + a) cos B + (a + b) cos C = ?
(a) a+b+c (b) abc (c) ab+bc+ca (d) none of these
249. In a ΔABC, 2 (bccos A + cacos B+ab cos C) = ? (a) (a2 + b2 - c2) (b) (a2 + c2 - b2)
(c) (b2 + c2 - a2) (d) (a2 + b2 + c2) 250. In a ΔABC, (ac cos B – bc cos A) = ?
(a) (a2 – b2) (b) (b2 – c2) (c) (c2 – a2) (d) none of these 251. In a ΔABC, b a b a =? (a) ) sin( ) sin( B A B A (b) ) cos( ) cos( B A B A (c) 2 2 ) ( tan ) ( tan B A B A (d) none of these 252. In a ΔABC, c cos2 2 A + a cos2 2 C = ? (a) s (b) 2s (c) 3s (d) 4s 253. In a ΔABC, a c b ) ( cos2 2 A + b a c ) ( cos2 2 B + . ) ( c b a cos2 2 C =? (a) a+b+c (b) abc (c) 0 (d) none of these 254. In a ΔABC, Δ 2 2 2 C B A cot cot cot =? (a) s (b) s2 (c) 2s (d) 2s2 255. In a ΔABC, bc cos22 A + ca cos2 2 B + ab cos2 2 C = ? (a) s2 (b) (s-a)2 (c) (s-b)2 (d) (s-c)2 256. In a ΔABC, 2ab cos
2 2 2 C B A cos cos =? (a) (a + b - c) Δ (b) (b + c - a) Δ (c) (c + a - b) Δ (d) (a + b + c) Δ 257. In a ΔABC, if cos , c c b A 2 2 then (a) c2 + a2 = b2 (b) a2 + b2 = c2 (c) b2 + c2 = a2 (d) none of these 258. In a ΔABC, if cot 2 2 2 C B A cot : cot : = 3 : 5 : 7, then a:b:c = ? (a) 6:5:4 (b) 4:5:6 (c) 5:6:4 (d) 5:4:6
259. If a = 16,b = 24 and c = 20, then cos 2 B =? (a) 2 1 (b) 3 1 (c) 4 1 (d) 4 3
260. In a ΔABC, if a cos A = b cos B, then ΔABC is (a) eiter equilateral or right angled
(b) either isosceles or right angled (c) isosceles as well as right angled (d) none of these
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Page 17 Answers (EXERCISE 1)1. (c) 2. (b) 3. (c) 4. (d) 5. (b) 6. (c) 7. (c) 8. (d) 9. (b) 10 (b)
11. (c) 12. (c) 13. (c) 14. (b) 15. (c) 16. (b) 17. (c) 18. (b) 19. (c) 20. (a)
21. (c) 22. (d) 23. (c) 24. (b) 25. (b) 26. (c) 27. (c) 28. (a) 29. (b) 30. (b)
31. (c) 32. (a) 33. (b) 34. (a) 35. (c) 36. (c) 37. (c) 38. (a) 39. (c) 40. (b)
41. (d) 42. (c) 43. (a) 44. (a) 45. (a) 46. (b) 47. (b) 48. (d) 49. (c) 50. (a)
51. (b) 52. (d) 53. (b) 54. (b) 55. (b) 56. (a) 57. (a) 58. (c) 59. (b) 60. (d)
61. (b) 62. (a) 63. (b) 64. (b) 65. (b) 66. (c) 67. (c) 68. (d) 69. (b) 70. (c)
71. (s) 72. (b) 73. (c) 74. (a) 75. (b) 76. (a) 77. (b) 78. (c) 79. (c) 80. (a)
81. (a) 82. (c) 83. (b) 84. (c) 85. (a) 86. (d) 87. (a) 88. (b) 89. (c) 90. (b)
91. (a) 92. (b) 93. (b) 94. (b) 95. (c) 96. (a) 97. (c) 98. (d) 99. (b) 100. (a)
101. (c) 102. (b) 103. (a) 104. (b) 105. (c) 106. (b) 107. (a) 108. (d) 109. (a) 110. (c)
111. (b) 112. (c) 113. (c) 114. (a) 115. (b) 116. (c) 117. (b) 118. (d) 119. (d) 120. (c)
121. (b) 122. (b) 123. (b) 124. (a) 125. (b) 126. (c) 127. (b) 128. (c) 129. (b) 130. (c)
131. (a) 132. (b) 133. (a) 134 (b) 135. (b) 136. (c) 137. (a) 138. (b) 139. (b) 140. (a)
141. (c) 142. (b) 143. (a) 144. (c) 145. (b) 146. (a) 147. (c) 148. (b) 149. (a) 150. (c)
151. (a) 152. (b) 153. (a) 154. (b) 155. (a) 156. (b) 157. (d) 158. (b) 159. (a) 160. (b)
161. (c) 162. (a) 163. (b) 164. (b) 165. (d) 166. (b) 167. (b) 168. (b) 169. (b) 170. (d)
171. (b) 172. (d) 173. (c) 174. (a) 175. (b) 176. (a) 177. (b) 178. (c) 179. (c) 180. (b)
181. (d) 182. (b) 183. (a) 184. (b) 185. (b) 186. (d) 187. (b) 188. (b) 189. (a) 190. (c)
191. (b) 192. (a) 193. (b) 194. (b) 195. (c) 196. (a) 197. (b) 198. (b) 199. (b) 200. (c)
201. (a) 202. (b) 203. (c) 204. (c) 205. (c) 206. (c) 207. (a) 208. (c) 209. (c) 210. (a)
211. (c) 212. (a) 213. (b) 214. (a) 215. (c) 216. (b) 217. (d) 218. (c) 219. (c) 220. (d)
221. (d) 222. (c) 223. (b) 224. (d) 225. (b) 226. (c) 227. (b) 228. (c) 229. (d) 230. (a)
231. (c) 232. (b) 223. (c) 234. (a) 235. (d) 236. (c) 237. (c) 238. (a) 239. (a) 240. (b)
241. (c) 242. (b) 243. (b) 244. (a) 245. (c) 246. (a) 247. (c) 248. (a) 249. (d) 250. (a)
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