Class 11 Mathematics Trigonometric Functions MCQs Set D

Question. sin 12° sin 24° sin 48° sin 84° =
(a) cos 20° cos 40° cos 60° cos 80°
(b) sin 20° sin 40° sin 60° sin 80°
(c) 3/15
(d) None of these

Answer: a

Question. If x + 1/x = 2 cos θ , then x³ + 1/x³ is:
(a) 1/2 cos 3θ
(b) 2 cos 3θ 
(c) cos 3θ
(d) 1/3 cos 3θ

Answer: b

Question. The value of 4 sin α sin(α + π/3) sin(α + 2π/3) =
(a) sin 3α
(b) sin 2α
(c) sin α
(d) sin² α

Answer: a

Question. If tan θ = 1/√7 , then (cosec²θ – sec²θ/cosec²θ + sec²θ is equal to m/m+1. The value of m is
(a) 1
(b) 2
(c) 3
(d) 4

Answer: c

Question. The solution of the equation [sin x + cos x]^{1 + sin 2x} = 2, –π ≤ x ≤ π is
(a) π/2
(b) π
(c) π/4
(d) 3π/4

Answer: c

Question. Value of cot 5° cot 10° ..... cot 85° is
(a) 0
(b) –1
(c) 1
(d) 2

Answer: c

Question. cos (3π/4+x) – cos (3π/4 –x) is equal to
(a) √2 sin x
(b) –2 sin x
(c) – √2 sin x
(d) None of these

Answer: c

Question. If 1 2 3 sinθ + sinθ + sinθ = 3, then cosθ1 + cosθ2 + cosθ3 = ?
(a) 3
(b) 2
(c) 1
(d) 0

Answer: d

Question. The degree measure corresponding to the given radian [2π/15]^c
(a) 21º
(b) 22º
(c) 23º
(d) 24º

Answer: d

Question. If sin 3α = 4 sin α sin (x + α ) sin (x – α ), then x =
(a) nπ ± π/6
(b) nπ ± π/3
(c) nπ ± π/4
(d) nπ ± π/2

Answer: b

Question. If tan θ = – 1/√3 , then general solution of the equation is 
(a) 2nπ + π/6 , n ∈ I
(b) nπ + π/6 , n ∈ I
(c) 2nπ – π/6 , n ∈ I
(d) nπ – π/6 , n ∈ I

Answer: d

Question. cot x cot 2x – cot 2x cot 3x – cot 3x cot x is equal to
(a) 0
(b) 1
(c) 2
(d) 3

Answer: b

Question. sin x – sin 3x / sin² x –cos² x is equal to
(a) sin 2x
(b) cos 2x
(c) tan 2x
(d) None of these

Answer: d

Question. If sin A = 3/5 , 0 < A < π/2 and cos B = –12/13, π < B < 3π/2 , then value of sin (A – B) is
(a) –13/82
(b) –15/65
(c) –13/75
(d) –16/65

Answer: d

Question. If tan θ = –4/3 ,then sin θ is
(a) –4/5 but not 4/5
(b) –4/5 or 4/5
(c) 4/5 but not –4/5
(d) None of these

Answer: b

Question. If n is any integer, then the general solution of the equation cos x – sin x = 1/√2 is
(a) x = 2nπ – π/12 or x = 2nπ + 7π/12
(b) x = nπ ± π/12
(c) x = 2nπ + π/12 or x = 2nπ – 7π/12
(d) x = nπ + π/12 or x = nπ – 7π/12

Answer: c

Question. If 5 tan θ = 4, then 5 sinθ – 3 cosθ /5 sinθ + 2 cosθ =
(a) 0
(b) 1
(c) 1/6
(d) 6

Answer: c

Question. Number of solutions of equation, sin 5x cos 3x = sin 6x cos 2x, in the interval [0, π] is
(a) 4
(b) 2
(c) 3
(d) 5 

Answer: d

Question. If 2 tan2 θ = sec2θ, then general value of θ are
(a) nπ ± π/4 , n ∈ I
(b) nπ ± π/6 , n ∈ I
(c) 2nπ + π/4 , n ∈ I
(d) 2nπ ± π/6 , n ∈ I

Answer: a

Question. General solution of the equation tan θ tan 2θ = 1 is given by
(a) (2n + 1)π/4 ,n ∈ I
(b) nπ + π/6, n ∈ I
(c) nπ – π/6, n ∈ I
(d) nπ ± π/6, n ∈ I

Answer: d

Question. The angle subtended at the centre of radius 3 metres by the arc of length 1 metre is equal to:
(a) 20º
(b) 60º
(c) 1/3 radian
(d) 3 radian

Answer: c

Question. If sinx = 24/25 then the value of tan x is:

(a) 24/25
(b) 24/7
(c) 25/24
(d) None of these

Answer: b

Question. The angle in radian through which a pendulum swings and its length is 75 cm and tip describes an arc of length 21 cm, is
(a) 7/25
(b) 6/25
(c) 8/25
(d) 3/25

Answer: a

Question. If A + B = 45°, then (cot A – 1) (cot B – 1) is equal to 
(a) 1
(b) 1/2
(c) –1
(d) 2

Answer: d

Question. Number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, π] is
(a) 0
(b) 1
(c) 2
(d) 3

Answer: c

Question. The value of sin(–11π/3) is √3/m . Value of ‘m’ is
(a) 1
(b) 2
(c) 3
(d) 5

Answer: b

Question. If cos θ = –3/5 and π < θ < 3π/2, then the value of (cosecθ + cotθ/secθ – tanθ) is equal to 1/m . Value of m is
(a) 2
(b) 4
(c) 5
(d) 6

Answer: d

Question. If cos θ = –3/5 and π < θ < 3π/2 , then the value of (cosecθ + cotθ / secθ – tanθ) is equal to
(a) 1/3
(b) 2/3
(c) 13/2
(d) None of these

Answer: d

Question. What is the value of radian measures corresponding to the 25° measures ?
(a) 5π/36
(b) 2π/36
(c) 3π/36
(d) 4π/36

Answer: a

Question. 1/sin 10° – √3/cos 10° = 
(a) 0
(b) 1
(c) 2
(d) 4

Answer: d

Question. If sin 3θ = sinθ , then the general value of θ is:
(a) 2nπ(2n+1)π/3
(b) nπ(2n+1)π/4
(c) nπ(2n+1)π/3
(d) None of these

Answer: b

Question. If cos 7θ = cos θ – sin 4θ, then the general value of θ is
(a) nπ/4, nπ/3 + π/18
(b) nπ/3, nπ/3 + (–1)ⁿπ/18
(c) nπ/4, nπ/3 + (–1)ⁿπ/18
(d) nπ/6, nπ/3 + (–1)ⁿπ/18

Answer: c

Question. sin163º cos 347º + sin 73º sin167º = ?
(a) 0
(b) 1/2
(c) 1
(d) None of these

Answer: b

Question. If sin 2θ + sin 2Φ = 1/2 and cos 2θ + cos 2Φ = 3/2 ,then cos² (θ – Φ) = 
(a) 3/8
(b) 5/8
(c) 3/4
(d) 5/4

Answer: b

Question. The value of tan(α + β), given that cot α = 1/2, α ∈ (π, 3π/2) and sec β = –5/3 , β ∈ (π/2, π) is
(a) 1/11
(b) 2/11
(c) 5/11
(d) 3/11

Answer: b

Question. If sinα = −3/5 where π<α < 3π/2, then cos α/2 equal to:
(a) 1/√10
(b) –1/√10
(c) 3/√10
(d) –3/√10

Answer: d

Question. cot 15º –1/cot 15º +1 = ?
(a) 1/2
(b) 3/2
(c) 3√3/4
(d) √3

Answer: b

Question. If sin 2θ + sin 2Φ = 1/2, cos 2θ + cos 2Φ = 3/2, then value of cos2 (θ – Φ) is
(a) 5/8
(b) 3/8
(c) –5/8
(d) 3/5

Answer: a

Question. The most general value of θ satisfying the equation tan θ = −1 and cosθ = 1/√2 is:
(a) nπ + 7π/4
(b) nπ + (−1)ⁿ 7π/4
(c) 2nπ + 7π/4
(d) None of these

Answer: c

Question. If tan θ = 3 and θ lies in IIIrd quadrant, then the value of sin θ is
(a) 1/√10
(b) 2/√10
(c) –3/√10
(d) –5/√10

Answer: c

Question. If A + B + C = π , then cos2A + cos2B − cos2C equal to:
(a) 1− 2 sin Asin B cosC
(b) 1− 2 cos Acos B sin C
(c) 1+ 2 sin Asin B cosC
(d) 1+ 2 cos Acos B sin C

Answer: a

Question. sin 47º + sin 61º − sin11º − sin 25º = ?
(a) sin 36º
(b) sin 7º
(c) cos 36º
(d) cos 7º

Answer: d

Question. The 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 an arc at the centre of the circle is:
(a) 50º
(b) 210º
(c) 100º
(d) 60º

Answer: b

Question. If tan A + cot A = 4, then 4 4 tan A + cot A is equal to:
(a) 110
(b) 191
(c) 80
(d) 194

Answer: d

Question. If sin + cosx = 1/5 then tan 2x is:
(a) 25/17
(b) 7/25
(c) 25/7
(d) 24/7

Answer: d

Question. sin 75º = :
(a) 2–√3/2
(b) √3+1/2√2
(c) √3–1/2√2
(d) √3–1/2√2

Answer: b

Question. The minute hand of a clock is 10 cm long. How far does the tip of the hand move in 20 minutes?
(a) 10π/3
(b) 20π/3
(c) 30π/3
(d) 40π/3

Answer: b

Question. If 4 sinθ = 3cosθ then Sec2θ/4[1–tan2θ] equals to:
(a) 25/16
(b) 25/28
(c) 1/4
(d) 1

Answer: b

Question. General value of θ satisfying the equation tan²θ + sec2θ = 1 is:
(a) mπ , nπ + π/3
(b) mπ , nπ ± π/3
(c) mπ , nπ ± π/6
(d) None of these

Answer: b

Question. The value of cot 70º + 4 cos 70º is:
(a) 1/√3
(b) √3
(c) 2√3
(d) 1/2

Answer: b

Question. If sin2θ + sin 2Φ = 1/2 and cos2θ + cos2Φ =3/2 then 2 cos (θ −φ ) equal to:
(a) 3/8
(b) 5/8
(c) 3/4
(d) 5/4

Answer: b

Question. If x = ycos 2π/3 cos = zcos 4π/3 then xy + yz + zx = :
(a) −1
(b) 0
(c) 1
(d) 2

Answer: b

Question. A circular wire of radius 3 cm is cut and bent so as to lie along the circumference of a hoop whose radius is 48 cm. The angle in degrees which is subtended at the centre of hoop is
(a) 21.5°
(b) 23.5°
(c) 22.5°
(d) 24.5°

Answer: c

Question. π radian in degree measure is equal to
(a) 18°
(b) 180°
(c) 200°
(d) 360°

Answer: b

Question. sin 6θ + sin 4θ + sin 2θ = 0, then θ =
(a) nπ/4 or nπ ± π/3
(b) nπ/4 or nπ ± π/6
(c) nπ/4 or 2nπ ± π/6
(d) None of these

Answer: a

Question. Value of 2cosπ/13cos9π/13+cos3π/13+cos5π/13 is
(a) –1/2
(b) 0
(c) 1
(d) √3/2

Answer: b