MCQ Chapter 11 Trigonometric Functions Class 11 Mathematics

Please refer to Trigonometric Functions MCQ Questions Class 11 Mathematics below. These MCQ questions for Class 11 Mathematics with answers have been designed as per the latest NCERT, CBSE books, and syllabus issued for the current academic year. These objective questions for Trigonometric Functions will help you to prepare for the exams and get more marks.

Trigonometric Functions MCQ Questions Class 11 Mathematics

Please see solved MCQ Questions for Trigonometric Functions in Class 11 Mathematics. All questions and answers have been prepared by expert faculty of standard 11 based on the latest examination guidelines.

MCQ Questions Class 11 Mathematics Trigonometric Functions

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 these 

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 

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) 

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 these 

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 

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 these 

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 these 

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 

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 

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 

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 these 

Question:

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 

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 

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

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 these

Question:

(a) π/20
(b) π/30
(c) π/40
(d) π/60 

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 these 

Question:

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

Question:

(a) tan3θ
(b) cot3θ
(c) tan6 θ
(d) cot6 θ 

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

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

Question:

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

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 

Question:

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 

Question:

Question:

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 

Question:

Question:

(a) -171/221
(b) -21/221
(c) 21/221
(d) 171/221 

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 

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 these 

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

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 

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

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)   

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 these 

Question:

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

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 

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 

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 

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 these 

Question:

 

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 

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 

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 these 

Question:

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

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

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

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)

Question: Let sinx = 3/5 , x lies in second quadrant. 

Codes:
A B C D E
(a) 3 4 2 5 1
(b) 3 4 1 5 2
(c) 3 2 4 5 1
(d) 1 2 5 4 3

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

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

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

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

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 these

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

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

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

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

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

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

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

Question:Match the following in column-I with the given in column-II. 

Codes:
A B C D E
(a) 4 3 5 1 2
(b) 4 3 5 2 1
(c) 3 4 5 1 2
(d) 1 3 5 2 4

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

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