Multiple Choice Trigonometry and Trigonometry Ratio Sample Paper:
Ques. If cos x + cos2 x = 1, then the value of sin2 x + sin4 x is
(a) 1
(b) – 1
(c) 0
(d) 2
Ques. If tan A + cot A = 4, then tan4 A + cot4 A is equal to
(a) 110
(b) 191
(c) 80
(d) 194
Ques. A circular wire of radius 7 cm is cut and bend again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is
(a) 50°
(b) 210°
(c) 100°
(d) 60°
Ques. If sin x + sin2 x = 1, then cos8 x + 2 cos6 x + cos4 x =
(a) 0
(b) – 1
(c) 2
(d) 1
Ques. If A = 130o and x = sin A + cos A, then
(a) x > 0
(b) x < 0
(c) x = 0
(d) None of these
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Ques. The value of tan (–945o) is
(a) – 1
(b) – 2
(c) – 3
(d) – 4
Ques. If tan A = 1/2, tan B = 1/3, then cos 2A =
(a) sin B
(b) sin 2B
(c) sin 3B
(d) None of these
Ques. cos 1o . cos 2o . cos 3o … cos 179o =
(a) 0
(b) 1
(c) 2
(d) 1/2
Ques. Which of the following is correct?
(a) tan 1 > tan 2
(b) tan 1 = tan 2
(c) tan 1 < tan 2
(d) tan 1 = 1
Ques. If sin x = –24/25, then the value of tan x is
(a) 24/25
(b) –24/7
(c) 25/24
(d) None of these
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Ques. If A lies in the second quadrant and 3tan A + 4 = 0, the value of 2 cot A – 5 cos A + sin A is equal to
(a) –53/10
(b) –7/10
(c) 7/10
(d) 23/10
Ques. If sin A, cos A and tan A are in G.P., then cos3 A + cos2 A is equal to
(a) 1
(b) 2
(c) 4
(d) None of these
Ques. The expression cos(45o – A) cos(45o – B) – sin(45o – A) sin(45o – B) is equal to
(a) cos(A + B)
(b) sin(A + B)
(c) cos(A – B)
(d) sin(A – B)
Ques. In a triangle ABC, A is an abtuse angle, sin A = 3/5, cos B = 12/13 . Then sin C=
(a) 16/ 65
(b) 5 / 13
(c) 36/65
(d) 20 / 65
Ques. If 8 tan A = – 15, 25 sin B = – 7 and neither A nor B is in the 4th quadrant, then sin (A + B) =
(a) 304/ 425
(b) – 304 / 425
(c) 403/425
(d) – 403 / 425
Related: Hybridization questions
Ques. The value of sin 130o cos 140o + cos 130o sin 140o is
(a) 1
(b) –1
(c) 0
(d) ½
Ques. The value of sin(n + 1)A sin(n + 2)A + cos(n + 1)A cos(n + 2)A is equal to
(a) sin A
(b) –cos A
(c) cos A
(d) sin 2A
Ques. If cos x + cos2 x = 1 then sin12 x+ 3 sin10 x + 3 sin8 x + sin6 x =
(a) 12
(b) 1
(c) –10
(d) 8
Ques. If (1/8) sec 3 (– 300) – (4/3) cos 330o +(4/3)sin 840o + 3tan2 210o = k, then k =
(a) – 2
(b) 0
(c) 3
(d) 2
Ques. The value of (cos 80o/sin 10o) + cos 59o cosec 31o =
(a) 2
(b) 0
(c) 1
(d) none of these
Related: Circular motion questions
Ques. A railway train is travelling on a circular curve of 1500 m radius at the rate of 66 k.m. per hour. In 10 seconds the angle it has turned is
(a) 7°
(b) 6°
(c) 8°
(d) none of these
Ques. If the length of the pendulum is 75 cm and the tip describes an arc of 15 cm, then the angle through which is pendulum swings is
(a) 126/11 degrees
(b) 125/11 degrees
(c) 136/11 degrees
(d) none of these
Ques. The value of tan 616o tan 194o – cos (–505o) cos755o + sin 395o sin 145o is
(a) 1
(b) –1
(c) 2
(d) –2
Ques. A wheel is making 20 resolution per minute, then time taken to make 30o is
(a) 1 second
(b) 1/2 second
(c) 1/3 second
(d) 1/4second
Ques. A horse trots uniformly along a circular track of radius 27 m. The angle subtended at the centre of the track by the arc passed over by the horse in 3 seconds is 70o,then the distance will the horse pass over in 1/2 minute is (approx.)
(a) 331 m
(b) 330 m
(c) 335 m
(d) 332 m
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Ques. In a circle of diameter 60m, the length of a chord is 30m. Then the length of the major arc is
(a) 150.1 m
(b) 157.1 m
(c) 152.1 m
(d) 154.1 m
Ques. A circular wire of radius 15 cm is cut and bent so as to lie along the circumference of a loop of radius 120 cm. The angle subtended by it at the centre is
(a) 30°
(b) 45°
(c) 60°
(d) none of these
Ques. The wheel of a railway carriage is 4ft in diameter and makes 6 revolutions per second, then the velocity of the train is
(a) 51. 38 mile/hour
(b) 50.38 mile/hour
(c) 45.32 mile/hour
(d) none of these
Ques. Two arcs of two different circles are of equal lengths. If these arcs subtends angles of 45o and 60o at the centres of the circle, then the ratio of the radii of the two circles is
(a) 3 : 4
(b) 2 : 3
(c) 4 : 3
(d) 3 : 2
Ques. An arc AB of a circle subtends an angle x radians at the centre O of the circle. Given that the area of the sector AOB is equal to the square of the length of the arc AB, then the value of x is
(a) 3/2
(b) 1/4
(c) 1/2
(d) ¾
Related: problems on LCM and HCF
Ques. The value of k, for which (cos x + sin x)2 + k sin x cos x – 1 = 0 is an identity, is
(a) – 1
(b) – 2
(c) 0
(d) 1
Ques. The ratio of the greatest value of 2 – cos x + sin2 x is to its least value is
(a) 7/4
(b) 11/4
(c) 13/4
(d) none of these
Ques. Which one is True?
(a) sin 1 > sin 2 > sin 3
(b) sin 1 < sin 2 < sin 3
(c) sin 1 < sin 3 < sin 2
(d) sin 3 < sin 1 < sin 2
Ques. sin (2 sin–1 0.8) =
(a) 0.96
(b) 0.48
(c) 0.64
(d) None of these
Ques. If sin x + sin2 x = 1, then the value of cos12 x + 3 cos10 x + 3 cos8 x + cos6 x – 2 is equal to
(a) 0
(b) 1
(c) – 1
(d) 2
Ques. If sin x + sin y = 3 (cos y – cos x), then the value of sin 3x / sin 3y is
(a) 1
(b) – 1
(c) 0
(d) None of these
Related: quadrilateral question
Ques. If cosec A + cot A = 11/2, then tan A =
(a) 21/22
(b) 15/16
(c) 44/117
(d) 117/43
Ques. sin 15° + cos 105° =
(a) 0
(b) 2 sin 15°
(c) cos 15° + sin 15°
(d) sin 15° – cos 15°
Ques. If (sec A + tan (a) (sec B + tan (b) (sec C + tan (c) = (sec A – tan (a) (sec B – tan (b) (sec C – tan (c) then each side is equal to
(a) 1
(b) – 1
(c) 0
(d) None of these
Ques. The value of sin 10o + sin 20o + sin 30o + …+ sin 360o is
(a) 1
(b) 0
(c) – 1
(d) None of these
Related: Mathematical Induction questions
Ques. The angle subtended at the centre of a circle of radius 3 metres by an arc of length 1 metre is equal to
(a) 20°
(b) 60°
(c) 1/3 radian
(d) 3 radians
Ques. cos A + sin (270o + A) – sin (270o – A) + cos (180o + A) =
(a) – 1
(b) 0
(c) 1
(d) None of these
Ques. cos 1o + cos 2o + cos 3o + … + cos 180o =
(a) 0
(b) 1
(c) – 1
(d) 2
Related: Matrices questions
Ques. (sec A + tan A – 1) (sec A – tan A + 1) – 2 tan A =
(a) sec A
(b) 2 sec A
(c) 0
(d) 1
Ques. 1 + sinA – cos A / 1 + sin A + cos A =
(a) sin A/2
(b) cos A/2
(c) tan A/2
(d) cot A/2
Ques. tan A + cot (180o + A) + cot (90o + A) + cot (360o – A)
(a) 0
(b) 2 tan A
(c) 2 cot A
(d) 2 (tan A – cot A)
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