Class 11 Mathematics Trigonometric Functions MCQs Set 03

Question. If 1+sin θ + sin² θ +…∞ = 4+2√3,0<θ <π,θ ≠π/2, , then
(a) θ =π/6
(b) θ=π/3
(c) θ =π/3 or π/6
(d) θ= π/3 or 2π/3

Answer: D

Question. General solution of tan 5θ = cot 2θ is
(a) θ = nπ/7 + π/14
(b) θ = nπ/7 + π/5
(c) θ = nπ/7 + π/2
(d) θ = nπ/7 + π/3

Answer: A

Question. If tan α =sinθ- cosθ/sin θcos θ, then sin a α is equal to
(a) ± sin θ+cos θ /√2
(b) ± sin θ-cosθ/√2
(c) ± – (sin θcos θ) q q
(d) None of the options

Answer: B

Question. The angle subtended at the centre of a circle of diameter 50 cm by an arc of length 11 cm is
(a) 25° 27′
(b) 23° 12′
(c) 25° 12′
(d) None of the options

Answer: C

Question. If sec A= a +(1/4a), then sec A + tan is equal to
(a) 2a or 1/2a
(b) a or 1/a
(c) 2a or 1/a
(d) a or 1/2a

Answer: A

Question. The value of cos⁴ π/8 + cos⁴ 3π/8 + cos⁴ 3π/8 +cos⁴ 5π/8 + cos⁴ 7π/8 is equal to
(a) 2
(b) 1/2
(c) 3/2
(d) None of the options

Answer: C

Question. The greatest value of 4 sin θ+3 cosθ + 10 is
(a) 13
(b) 15
(c) –15
(d) –13

Answer: B

Question. If cos A =-m cos B and  cot A+B/2 ∈(θ-β) b, then sin² (α- β) +-2ab cos (α- β) is equal to
(a) a² +b² 
(b) a² – b²
(c) b²-a² 
(d) – a²– b² 

Answer: A

Question. cos 2θ cos 2Φ +sin² (θ-Φ) -sin² (θ+Φ) is equal to
(a) sin 2(θ+Φ)
(b) cos 2(θ+Φ)
(c) sin 2(θ-Φ)
(d) cos 2(θ-Φ)

Answer: B

Question. If cos(θ-α) = sin (θ-β) = b, then cos ²(α-β ) +2absin (α-β) is equal to
(a) 4a²b²
(b) a²-b² 
(c) a² +b²
(d) – a² b² 

Answer: C

Question. If angle θ is divided into two parts such that the tangent of one part is K times the tangent to other and Φ is their difference, then sin θ is equal to
(a) K+1/K–1sinθ/2
(b) K+1/K–1sinΦ/2
(c) K+1/K–1sinΦ
(d) K–1/K+1sinΦ

Answer: C

Question. If tan(A – B) = 1, sec(A + B) = 2√3 , the smallest positive value of B is
(a) 25π/24
(b) 19π/24
(c) 13π/24
(d) 7π/24

Answer: D

Question. The most general value of θ satisfying the equations sin θ = sin α and cos θ = cos α is
(a) 2nπ + α
(b) 2nπ – α
(c) nπ + α
(d) nπ – α

Answer: A

Question. Solution of the equation 3 tan(θ – 15) = tan(θ + 15) is
(a) θ = nπ/2 + (–1)n π/4
(b) θ = nπ + (–1)n π/3
(c) θ = nπ – π/3
(d) θ = nπ – π/4

Answer: A

Question. If cosec θ – sin θ =a³ and sec θ – cos θ = b³,then  is a²b²(a²+b²) is equal to
(a) 2
(b) sin²/θ
(c) cos²/θ
(d) 1

Answer: D

Question. If cos² B-1=tan² A, then cosA cosB is equal to
(a) ±1/2
(b) ±1/3
(c) ±1/√2
(d) None of the options

Answer: C

Question. If√1-sin α/√1+sin α = sec α- tan α, then the quadrants in which α lies are
(a) II and III
(b) I and IV
(c) I and II
(d) III or IV

Answer: B

Question. The minimum value of 2 ^sinx+2^{cos x} is
(a) 1
(b) 2
(c) 2-1/√2
(d) 21-1/√2

Answer: D

Question. The value of sin(45°+θ)- cos (45°-θ) is
(a) 2 cos θ
(b) 2 sin θ
(c) 1
(d) 0

Answer: D

Question. The value of cos² 48° – sin² 12° sin is
(a) √5+ 1/8
(b) √5- 1/8
(c) √5+ 1/5
(d) √5+ 1/2√2

Answer: A

Question. If cos (θ+Φ) =m cos (θ-Φ), then 1-m/1+m cot Φ is equal to
(a) tan q
(b) – tan q
(c) 2 tan q
(d) None of the options

Answer: A

Question. Value of sin 10° + sin 20° + sin 30° +……+sin360° is
(a) 1
(b) 0
(c) 2
(d) 1/2

Answer: B

Question. cot²π/6 + cosec 5π/6 + 3 tan²π/6 is equal to
(a) 1
(b) 5
(c) 3
(d) 6

Answer: D

Question. If cosec θ – = cot θ = p, then the value of cosec θ is
(a) 1/2(p+1/p)
(b) 1/2(1-1/p)
(c) (1+1/p)
(d) (1-1/p)

Answer: B

Question. If sin³ θ+y cos³ θ = cos θ sin θ and x sin θ = y cos θ, then
(a) x²+y²=2
(b) x²+y² = 4
(c) x²+ y²  3
(d) x²+y²=1 

Answer: D

Question. he minimum value of 9 tan² θ+4 cot²θ is
(a) 13
(b) 9
(c) 6
(d) 12

Answer: D

Question. If tan α =(1+2^-x, tan β =(1+2 ^x+1)^-1, then α + β equals
(a) π/6
(b) π/4
(c) π/3
(d) π/2

Answer: B

Question. The value of sin 12° sin 48° sin 54° is equal to
(a) 1/16
(b) 1/32
(c) 1/8
(d) 1/4

Answer: C

Question. The value of expression sin θ + cos θ lies between
(a) –2 and 2 both inclusive
(b) 0 and √2 both inclusive
(c) – √2 and √2 both inclusive
(d) 0 and 2 both inclusive

Answer: C

Question. The minute hand of a watch is 1.5 cm long. How far does its tip move in 40 minutes? (Use π = 3.14)
(a) 2.68 cm
(b) 6.28 cm
(c) 6.82 cm
(d) 7.42 cm

Answer: B

Question. The value of the expression tanθ/1-cot +cot/1-tan θ -sec θ cosec θ is equal to
(a) -1
(b) 0
(c) 1
(d) None of the options

Answer: C

Question. If cos θ = – √3/2 and sin α= -3/5, where θ does not lie in the third quadrant and α lies in the third quadrant, then 2 tan α+√3 tan θ /cot2 θ +cos α is equal to
(a) 5/22
(b) 7/22
(c) 9/22
(d) 22/5

Answer: A

Question. The equation cos ⁴x-(a+2) cos² x-(a+3)=0 possesses a solution, if
(a) a > – 3
(b) a < – 2
(c) -3 ≤ a ≤-2
(d) a is any positive integer

Answer: C

Question. The value of sin20° sin 40° sin60° sin80° is equal to
(a) -3/16
(b) 5/16
(c) 3/16
(d) -5/16

Answer: C

Question. If cosα+ cosβ=0= sinα+ sinβ , cos2α+ cos2β equal to
(a) 2cos (α+β )
(b) -cos (α+β )
(c) 3 cos(α+β )
(d) None of the options

Answer: B

Question. If tan θ + sec θ = p, then what is the value of sec θ ?
(a) p²+1/p²
(b) p²+1/√p
(c) p²+1/2p
(d) p+1/2p

Answer: C

Question. The value of tan 19π/3 is √n . Value of ‘n’ is
(a) 1
(b) 2
(c) 3
(d) 5

Answer: C

Question. If sec² θ = 4/3, then the general value of θ is
(a) 2nπ ± π/6
(b) nπ ± π/6
(c) 2nπ ± π/3
(d) nπ ± π/3

Answer: B

Question. if cosec A + = cot A =11/2 then tanA is equal to
(a) 21/22
(b) 15/16
(c) 117/43
(d) 44/117

Answer: D

Question. The expression (sin 3x+ sinx ) sinx+ (cos 3x- cosx ) cosx is equal to
(a) 0
(b) 1
(c) –1
(d) 1

Answer: A

Question. If cos A= m cos B and cot A+B/2 =λ tan B-A/2, tan ,lthen λ is
(a) m/m – 1
(b) m+1/m
(c) m+1/m-1
(d) None of the options

Answer: C

Question. If angle θ be divided into two parts such that the tangent of one part is k times the tangent of the other and f is their difference, then sin θ is equal to
(a) k+1/k-1sin θ
(b) k-1/k+1 sinθ
(c) 2k -1/2k+1 sin θ
(d) None of the options

Answer: A

Question. Value of 2 sin² π/6 + cosec² 7π/6 · cos² π/3 is m/m–1 .The value of ‘m’ is
(a) 3
(b) 2
(c) 4
(d) None of the options

Answer: A

Question. Find x from the equation:
cosec (90° + θ) + x cos θ cot (90° + θ) = sin (90° + θ).
(a) cot θ
(b) tan θ
(c) –tan θ
(d) –cot θ

Answer: B

Question. If 3 sin θ cos θ = 5, then the value of 5θ -3 cos θ is
(a) ± 9
(b) ± 3
(c) ± 4
(d) ± 5

Answer: B

Question. If 1-tan x/1+tan x = tan y and x-y = π/6, then x and y are respectively
(a) 5π/24, π/24
(b) -7π/24,-11π/24
(c) -115π/24,-119π/24
(d) All of these

Answer: D

Question. The value of cos π/5 cos2π/5 cos 4π/5 cos 8π/5 is equal to
(a) 1/16
(b) 0
(c) -1/8
(d) -1/16

Answer: D

Question. If √3 tan 2θ + √3 tan 3θ + tan 2θ tan 3θ = 1, then the general value of θ is
(a) nπ + π/5
(b) (n + 1/6)π/5
(c) (2n ± 1/6 )π/5
(d) (n + 1/3)π/5

Answer: B

Question. cot π/20 cot 3π/20 cot 5π/20 cot 7π/20 cot 9π/20 is equal to
(a) 0
(b) -1
(c) 1
(d) None of the options

Answer: C

Question. The value of cos 12°+ cos 84°+ cos 156°+ cos 132° is
(a) 1/2
(b) 1
(c) -1/2
(d) 1/8

Answer: C

Question. If cos x + cos y + cos α = 0 and sin x + sin y + sin α = 0, then cot( x + y/2) =
(a) sin α
(b) cos α
(c) cot α
(d) sin ( x + y/2)

Answer: C

Question. Find the distance from the eye at which a coin of a diameter 1 cm be placed so as to hide the full moon, it is being given that the diameter of the moon subtends an angle of 31′ at the eye of the observer.
(a) 110 cm
(b) 108 cm
(c) 110.9 cm
(d) 112 cm

Answer: C

Question. If sinB=1/5 sin(2A+B),then tan(A+B)/tan A is equal to
(a) 2/3
(b) 3/2
(c) 3/4
(d) None of the options

Answer: B

Question. If A+ B+ C + = π and cosA= cosB cosC, then tan B tan C is equal to
(a) 1/2
(b) 2
(c) 1
(d) -1/2

Answer: B

Question. The number of values of x in the interval [0, 3π] satisfying the equation 2 sin² x + 5 sin x – 3 = 0 is
(a) 4
(b) 6
(c) 1
(d) 2

Answer: A