# Assignments Class 11 Mathematics Trigonometric Functions

Please refer to Assignments Class 11 Mathematics Trigonometric Functions Chapter 3 with solved questions and answers. We have provided Class 11 Mathematics Assignments for all chapters on our website. These problems and solutions for Chapter 3 Trigonometric Functions Class 11 Mathematics have been prepared as per the latest syllabus and books issued for the current academic year. Learn these solved important questions to get more marks in your class tests and examinations.

## Trigonometric Functions Assignments Class 11 Mathematics

Question. Two poles standing on a hori ontal ground are of heights 5m and 10m respectively. The line oining their tops makes an angle of 15 with the ground. Then the distance (in m) between the poles, is:
(a) 5(2 + √3)
(b) 5(√3 +1)
(c) 5/2(2 + √3)
(d) 10(√3 -1)

A

Question. The value of sin 10° sin 30° sin 50° sin 70° is:
(a) 1/16
(b) 1/32
(c) 1/18
(d) 1/36

A

Question. If 0 < x < Π and cos x + sin x – 1/2 , then tan x is
(a) (1-√7) / 4
(b) (4-√7) / 3
(c) – (4+√7)/3
(d) (1+√7)/4

C

Question. Let f(x) = sin x, g(x) = x.
Statement 1: f(x) ≤ g ( x) for x in (0,∞)
Statement 2: f(x) ≤ 1 for x in (0, ∞) but g(x) → ∞ as x → ∞.
(a) Statement 1 is true, Statement 2 is false.
(b) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
(c) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
(d) Statement 1 is false, Statement 2 is true.

C

Question. A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area enclosed by the park is
(a) (3/2)x2
(b) √(x3/8)
(c) (1/2)x2
(d) Πx2

C

Question. The value of

(a) 1 / √2
(b) 1 / 2√2
(c) 1/2
(d) 1/4

B

Question. If L = sin2(Π/16) – sin2(Π/8) and M = cos2(Π/16) – sin2(Π/8), then :

D

Question. For any θ ∈ (π/4 , π/2) the expression 3(sinθ – cosθ)4 + 6(sinθ + cosθ)2 + 4sin6θ equals:
(a) 13 – 4cos2θ + 6sin2θcos2θ
(b) 13 – 4cos6θ
(c) 13 – 4cos2θ + 6cos4θ
(d) 13 – 4cos4θ + 2sin2θcos2θ

B

Question. If sin4α + 4 cos4β + 2 = 4 √2 sin α cos β ; α, β ∈ [0, Π], then cos(α + β) – cos(α – β) is equal to :
(a) 0
(b) – 1
(c) √2
(d) -√2

D

Question. Let ƒk (x) = 1/k (sink x + cosk x) for k = 1, 2, 3, … Then for all x ∈ R, the value of ƒ4 (x) – ƒ6 (x) is equal to :
(a) 1/12
(b) 1/4
(c) –1/12
(d) 5/12

A

Question. The period of the function y = sin 2x is:
(a) 2π
(b) π
(c) π/2
(d) 4π

A

Question. The function f(x) = sin πx/2 + 2cos πx/3 – tan πx/4 is periodic with period:
(a) 6
(b) 3
(c) 4
(d) 12

D

Question. The most general value of θ which will satisfy both the equations sinθ =–1/2 and tanθ = 1/√3 is:
(a) nπ + (–1)n π/6
(b) nπ + π/6
(c) 2nπ ± π/6
(d) None of these

D

Question. The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60º. If the third side is 3, the remaining fourth side is:
(a) 2
(b) 3
(c) 4
(d) 5

A

Question. The area of the circle and the area of a regular polygon of n sides and its perimeter equal to that of the circle are in the ratio of:”
(a) tan(π/n) : π/n
(b) cos(π/n) : π/n
(c) sin(π/n) : π/n
(d) cot(π/n) : π/n

A

Question. The solution of equation 5sin2 x − 7sin x cos x + 16 cos2 x = 4 is:
(a) x = nπ + tan−1 3 or x= nπ + tan−1 4
(b) x = nπ + π/6 or x= nπ + π/4
(c) x = nπ  or x= nπ + π/4
(d) None of these

A

Question. If cosθ + √3 sinθ = 2, then θ = (only principal value):
(a) π/3
(c)2π/3
(c) 4π/3
(d) 5π/3

A

Question. Principal value of tan θ = – 1is:
(a) –π/4
(c) π/4
(c) 3π/4
(d) –3π/4

A

Question. In a triangle ABC, AD is altitude from (a) Given b > c, ∠C = 23º and AD = abc/b2 − C2 then ∠B equal to:
(a) 67º
(b) 44º
(c) 113º
(d) None of these

C

Question. AD is a median of the △ABC if AE and AF are medians of the triangles ABD and ADC respectively and AD = m1.
AE = m2 , 3 AF = m3, then a2/8 is equal to:
(a) m22 + m32 − 2m12
(b) m22 + m3− 2m12
(c) m22 + m32 − 2m12
(d) None of these

A

Question. If the solutions for θ of cos pθ + cos qθ = 0, p > 0, q > 0 are in (a)P., then the numerically smallest common difference of (a)P. is:
(a) π/p+q
(c) 2π/p+q
(c) π/(p+q)
(d) 1/p+q

B

Question. If and cosθ = –1/2 and 0º< θ<360º then the values of θ are:
(a) 120º and 300º
(b) 60º and 120º
(c) 120º and 240º
(d) 60º and 240º

C

Question. In a triangle ABC, ∠B = π/3 and  ∠C = π/4 and D divides BC internally in the ratio 1 : 3. Then     C sin∠BAD/sin∠CAD is equal to:
(a) 1/3
(b) 1/√3
(c) 1/√6
(d) √(2/3)

D

Question. In a △ABC, 2ac sin(A–B+C/2) is equal to:
(a) a2 + b2 − c2
(b) c2 + a2 − b2
(c) b2 − c2 − a2
(d) c− a2 − b

B

Question. In a triangle ABC, a, b, A are given and c1,c2 are two values of third side (c) The sum of the areas of triangles with sides a, b, c1 and a, b, c2 is:
(a) 1/2a2 sin2A
(b) 1/2b2 sin2A
(c) b2 sin2A
(d) a2 sin2A

B

Question. If (cosx – sinx ) (2tanx + 1/cosx) + 2 = 0 then x =?
(a) 2nπ ± π/3
(b) nπ ± π/3
(c) 2nπ ± π/6
(d) None of these

A

Question. If sin x + cos x − 2√2 sin x cos x = 0 then the general solution of x is:
(a) x = 2nπ ± π/4
(b) x = nπ + (–1) π/6 –π/4
(c) Both (a) and (b)
(d) None of these

C

Question. If in any △ABC ; cot A/2 , cot B/2 , cot C/2 are in (a)P., then:
(a) cot A/2 cot B/2 = 4
(b) cot A/2 cot C/2 = 3
(c) cot B/2 cot C/2 = 1
(d) cot B/2 cot C/2 = 0

B

Question. In a triangle ABC, let ∠C = π/2 If r is the in radius and R is the circum-radius of the triangle, 2(r+R) then is equal to:
(a) a+b
(b) b+c
(c) c+a
(d) a+b+c

A

Question. Let fk(x) = 1/k (sink x cosk x) where x ∈ R and k ≥ 1. Then f4(x) – f6(x) equals
(a) 1/4
(b) 1/12
(c) 1/6
(d) 1/3

B

Question. The set of all possible values of θ in the interval (0, Π) for which the points (1, 2) and (sin θ, cos θ) lie on the same side of the line x + y = 1 is :
(a) (0, Π/2)
(b) (Π/4 , 3Π/4)
(c) (0, 3Π4)
(d) (0,Π/4)

A

Question. If

α, β ∈ (0, Π/2), then tan (α + 2β) is equal to _____.

1

Question. The angle of elevation of the top of a vertical tower standing on a hori ontal plane is observed to be 45o from a point A on the plane. Let B be the point 30 m vertically above the point A. If the angle of elevation of the top of the tower from B be 30o, then the distance (in m) of the foot of the tower from the point A is:
(a) 15(3 + √3)
(b) 15(5 – √3)
(c) 15(3 – √3)
(d) 15(1 + √3)

A

Question. The value of cos210° – cos10° cos50° + cos250° is :
(a) 3/4 + cos20°
(b) 3/4
(c) 3/4 (1 + cos20°)
(d) 3/2

B

Question. Let cos(α + β) = 4/5 sin (α + β) = 5/13, where 0 ≤ α, β ≤ Π/4 . Then tan 2α =
(a) 56/33
(b) 19/12
(c) 20/7
(d) 25/16

A

Question. Let A and B denote the statements
A : cos α + cos β + cos γ = 0
B : sin α + sin β + sin γ = 0
If cos (β – γ) + cos (γ – α) + cos (α – β) = – 3/2 , then :
(a) A is false and B is true
(b) both A and B are true
(c) both A and B are false
(d) A is true and B is false

B

Question. If cos (α + β) = 3/5 , sin(α – β) = 5/13 and 0 < α, β < Π/4 , then tan(2a) is equal to :
(a) 63/52
(b) 63/16
(c) 21/16
(d) 33/52

B

Question. If the equation cos4 θ + sin4 θ + λ = 0 has real solutions for θ, then λ lies in the interval :
(a) ( – 5/4 , -1)
(b) [ -1, – 1/2]
(c) (- 1/2 , – 1/4)
(d) [ – 3/2 , – 5/4]

B

Question. If 2cos θ + sin θ = 1 (θ ≠ Π/2 ), then 7 cos θ + 6 sin θ is equal to:
(a) 1/2
(b) 2
(c) 11/2
(d) 46/5

D

Question. The number of values of a in [0, 2Π] for which 2sin3α – 7 sin2 α + 7 sin α = 2, is:
(a) 6
(b) 4
(c) 3
(d) 1

C

Question. Let A = {θ : sin(θ) = tan(θ)} and B = {q : cos(θ) = 1} be two sets. Then :
(a) A = B
(b) A ⊄ B
(c) B ⊄ A
(d) A ⊂ B and B – A ≠ φ

B

Question. The value of

(a) 1/512
(b) 1/1024
(c) 1/256
(d) 1/2

A

Question. If 5(tan2x – cos2x) = 2cos 2x + 9, then the value of cos 4x is
(a) – 7/9
(b) – 3/5
(c) 1/3
(d) 2/9

A

Question. If sum of all the solutions of the equation

then k is equal to :
(a) 13/9
(b) 8/9
(c) 20/9
(d) 2/3

A

Question. The number of x ∈ [0,2Π] for which

(a) 2
(b) 6
(c) 4
(d) 8

D

Question. If m and M are the minimum and the maximum values of 4+1/2sin22x – cos4x, x ∈ R, then M – m is equal to :
(a) 9/4
(b) 15/4
(c) 7/4
(d) 1/4

B

Question. If cosec θ = p+q / p–q (p ≠ q ≠ 0) , then |cot(Π/4 + θ/2)| is equal to:
(a) √p/q
(b) √q/p
(c) √pq
(d) pq

B

Question. If A = sin2 x + cos4x, then for all real x :
(a) 13/16 ≤ A ≤1
(b) 1 ≤ A ≤ 2
(c) 3/4 ≤ A ≤ 13/16
(d) 3/4 ≤ A ≤ 1

D

Question. If p and q are positive real numbers such that p2 + q2 = 1, then the maximum value of (p + q) is
(a) 12
(b) 1/√2
(c) √2
(d) 2

C

Question. If

then the difference between the maximum and minimum values of u2 is given by
(a) (a – b)2
(b) 2√(a2 + b2)
(c) (a+b)2
(d) 2(a2 + b2)

A

Question. The number of solutions of sin 3x = cos 2x, in the interval (Π/2, Π) is
(a) 3
(b) 4
(c) 2
(d) 1

D

Question. If cos α + cos β = 3/2 and sin α + sinβ 1/2 and θ is the arithmetic mean of α and β , then sin 2θ + cos 2θ is equal to :
(a) 3/5
(b) 7/5
(c) 4/5
(d) 8/5

B

Question. Let α,β be such that Π < α – β < 3Π.
If sin α + sinβ = – 21/65 and cos α + cosβ = – 27/65, then the value of cos α-β/2
(a) -6/65
(b) 3/√130
(c) 6/65
(d) 3/√130

D

Question. The function f (x) = log(x + √x2+1), is
(a) neither an even nor an odd function
(b) an even function
(c) an odd function
(d) a periodic function

C

Question. The number of solutions of the equation sin 2x – 2 cos x + 4 sin x = 4 in the interval [0, 5Π] is :
(a) 3
(b) 5
(c) 4
(d) 6

A

Question. The number of solution of tan x + sec x = 2cos x in [0, 2 π ) is
(a) 2
(b) 3
(c) 0
(d) 1

B

Question. The period of sin2 θ is
(a) Π2
(b) Π
(c) 2Π
(d) Π/2

B

Question. Which one is not periodic?
(a) | sin3x | +sin2x
(b) cos √x + cos2x
(c) cos 4x + tan2x
(d) cos2x + sinx

B

Question. The number of distinct solutions of the equation, log½ |sin x| = 2 – log½ |cos x| in the interval [0, 2Π], is _____.

8

Question. The number of solutions of the equation

(a) 3
(b) 5
(c) 7
(d) 4

C

Question. Let S be the set of all α ∈ R such that the equation, cos 2x + α sin x = 2α –7 has a solution. Then S is equal to :
(a) R
(b) [1, 4]
(c) [3,7]
(d) [2, 6]

D

Question. If [x] denotes the greatest integer ≤ x, then the system of linear equations
[sin θ] x + [–cos θ] y = 0
[cot θ] x + y = 0
(a) have infinitely many solutions if θ ∈ (Π/2 , 2Π/3) and has a unique solution if θ ∈ (Π ,7Π/6).
(b) has a unique solution if θ ∈ (Π/2, 2Π/3) υ (Π , 7Π/6)
(c) has a unique solution if θ ∈ (/2, 2/3) and have infinitely many solutions if θ ∈ (Π ,7Π/6)
(d) have infinitely many solutions if θ ∈ (Π/2 , 2Π/3) υ (Π, 7Π/6)

A

Question. The expression (tan A / 1 – cot A) + (cot A / 1 – tan A) can be written as :
(a) sin A cos A + 1
(b) sec A cosec A + 1
(c) tan A + cot A
(d) sec A + cosec A

B

Question. The value of cos 255º + sin 195º is
(a) √3–1 / 2√2
(b) √3–1 / √2
(c) -(√3–1 / √2)
(d) √3+1 / √2

C

Question. Let S = {θ∈[–2Π, 2Π] : 2 cos2θ + 3 sinθ = 0}. Then the sum of the elements of S is:
(a) 13Π/6
(b) 5Π/3
(c) B2Π
(d) Π

C

Question. If 0 ≤ x < Π/2, then the number of values of x for which sin x – sin 2x + sin 3x = 0, is:
(a) 3
(b) 1
(c) 4
(d) 2

D

Question. If 0 ≤ x < 2Π , then the number of real values of x, which satisfy the equation cos x + cos 2x + cos 3x + cos 4x = 0 is:
(a) 7
(b) 9
(c) 3
(d) 5

A

Question. The number of values of x in the interval [0,3π] satisfying the equation 2sin2x + 5sin x – 3 = 0 is
(a) 4
(b) 6
(c) 1
(d) 2

A

Question. Statement-1: The number of common solutions of the trigonometric equations 2 sin2θ – cos2θ = 0 and 2 cos2θ – 3 sin θ = 0 in the interval [0, 2Π] is two.
Statement-2: The number of solutions of the equation, 2 cos2θ – 3 sin θ = 0 in the interval [0, Π] is two.
(a) Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for statement-1.
(b) Statement-1 is true; Statement-2 is true; Statement-2 is not a correct explanation for statement-1.
(c) Statement-1 is false; Statement-2 is true.
(d) Statement-1 is true; Statement-2 is false.

B

Question. The equation esinxe–sin– 4 = 0 has :
(a) infinite number of real roots
(b) no real roots
(c) exactly one real root
(d) exactly four real roots