Inverse Trigonometric Functions VBQs Class 12 Mathematics

VBQs Inverse Trigonometric Functions Class 12 Mathematics with solutions has been provided below for standard students. We have provided chapter wise VBQ for Class 12 Mathematics with solutions. The following Inverse Trigonometric Functions Class 12 Mathematics value based questions with answers will come in your exams. Students should understand the concepts and learn the solved cased based VBQs provided below. This will help you to get better marks in class 12 examinations.

Inverse Trigonometric Functions VBQs Class 12 Mathematics

Question. A value of tan-1(sin(cos-1(√2/3))) is
(a) π/4
(b) π/2
(c) π/3
(d) π/6

Question. The trigonometric equation sin-1 x = 2sin-1 α has a solution for
(a) |α| ≤ 1/√2
(b) 1/2 < |α| < 1/√2
(c) all real values of α
(d) |α| < 1/2

A

Question.Statement I: The equation (sin–1x)3 + (cos–1x)3 – aπ3 = 0 has a solution for all a ≥ 1/32.
Statement II: For any x ∈ R, sin-1x + cos-1x + cos-1x = π/2 and 0 ≤ (sin-1x – π/4)2 ≤ 9π2/16
(a) Both statements I and II are true.
(b) Both statements I and II are false.
(c) Statement I is true and statement II is false.
(d) Statement I is false and statement II is true.

A

Question. If x, y, z are in A.P. and tan–1x, tan–1y and tan–1z are also in A.P., then
(a) x = y = z
(b) 2x = 3y = 6z
(c) 6x = 3y = 2z
(d) 6x = 4y = 3z

A

Question.

then sin x =
(a) tan2(α/2)
(b) cot2(α/2)
(c) tan α
(d) cot(α/2)

A

Question.

(a) 20/(401 + 20n)
(b) n/(n2 + 20n +1)
(c) 20/(n2 + 20n +1)
(d) n/(401+20n)

C

Question. A value of x for which sin (cot–1(1 + x)) = cos (tan–1 x), is
(a) 1/2
(b) 1
(c) 0
(d) 1/2

A

Question. If S is the sum of the first 10 terms of the series

then tan (S) is equal to:
(a) 5/6
(b) 5/11
(c) – 6/5
(d) 10/11

A

Question. If α = cos–1(3/5), β = tan-1(1/3), where 0 < α, β < π/2, then α – β is equal to :

D

Question. Let

Then a value of y is :
(a) (3x − x3) / (1+3x2)
(b) (3x + x3) / (1+3x2)
(c) (3x − x3) / (1−3x2)
(d) (3x + x3) / (1−3x2)

C

Question. A value of x satisfying the equation sin[cot–1(1 + x) ] = cos [tan–1x], is :
(a) – 1/2
(b) –1
(c) 0
(d) 1/2

Question. Considering only the principal values of inverse functions, the set

(a) contains two elements
(b) contains more than two elements
(c) is a singleton
(d) is an empty set

Question. All x satisfying the inequality (cot–1x)2 – 7 (cot–1x) + 10 > 0, lie in the interval :
(a) (-∞,cot 5)∪(cot 4,cot 2)
(b) (cot 2,∞)
(c) (-∞,cot5)∪(cot 2,∞)
(d) (cot 5, cot 4)

Question.

then x is equal to:
(a) √145/12
(b) √145/10
(c) √146/12
(d) √145/11

A

Question. If sin-1(x/5) + cosec-1(5/4) = π/2, then the values of x is
(a) 4
(b) 5
(c) 1
(d) 3

D

Question.

(a) 2 sin 2α
(b) 4
(c) 4 sin2 α
(d) – 4 sin2 α

C

Question. The value of

is equal to

A

Question. The domain of sin-1 [log3 (x/3)] is”
(a) [1, 9]
(b) [–1, 9]
(c) [–9, 1]
(d) [–9, –1]

A

Question. The value of

(a) 21/19
(b) 19/21
(c) 22/23
(d) 23/22

A

Question. If x = sin–1 (sin10) and y = cos–1 (cos10), then y – x is equal to:
(a) 0
(b) 10
(c) 7π
(d) π

D

Question.

(a) π/2
(a) 5π/4
(a) 3π/2
(a) 7π/4

C

Question.

(a) tan-1(65/156)
(b) π/2
(c) π
(d) (d) 4 tan–1(5)

C

Question. The principal value of tan-1(cot(43π/4)) is :
(a) – 3π/4
(b) 3π/4
(c) – π/4
(d) π/4

C

Question. The number of solutions of the equation sin–1 x = 2 tan–1x (in principal values) is :
(a) 1
(b) 4
(c) 2
(d) 3

A

Question. Let x ∈ (0, 1). The set of all x such that sin–1x > cos–1x, is the interval:
(a) (1/2, 1/√2)
(b) (1/√2, 1)
(c) (0, 1)
(d) (0, √3/2)

B

Question. The largest interval lying in (-π/2, π/2) for which the function, f(x) = 4−x2 + cos-1(x/2 – 1) log (cos x), is defined, is
(a) [- π/4, π/2)
(b) [0, π/2)
(c) [0,π]
(d) (- π/2, π/2)

B

Question. The value of sin−1(12/13) − sin−1(3/5) is equal to :

B

Question. If cos−1x − cos−1(y/2) = α, where −1 ≤ x ≤ 1, −2 ≤ y ≤ 2, x ≤ y/2, then for all x, y, 4x2 –4xy cosα + y2 is equal to:
(a) 4 sin2α
(b) 2 sin2α
(c) 4 sin2α – 2x2y2
(d) 4 cos2 α+ 2x2y2

A

Question. The domain of the function

(a) [1, 2]
(b) [2, 3)
(c) [1, 2]
(d) [2, 3]

B

Question. The principal value of sin-1 (–√3/2) is
(a) –2π/3
(b) –π/3
(c) 4π/3
(d) 5π/3

B

Question. A ladder 5 metre long leans against a vertical wall. The bottom of the ladder is 3 metre from the wall. If the bottom of the ladder is pulled 1 metre farther from the wall, how much does the top of the ladder slide down the wall :
(a) 1 m
(b) 7 m
(c) 2 m
(d) None of these

A

Question. From the top of a light house 60 metre high with its base at the sea level the angle of depression of a boat is 15º. The distance of the boat from the foot of the light house is:
(a) (√3–1/√3+1) 60 meter
(b) (√3+1/√3–1) 60 meter
(c) (√3+1/√3–1) meter
(d) None of these

B

Question. The principal value of sin-1[sin(2π/3)]
(a) –2π/3
(b) 2π/3
(c) 4π/3
(d) None of these

D

Question. Considering only the principal values, if tan(cos–1 x) = sin[cot–1 (1/2)]
(a) 1/√5
(b) 2/√5
(c) 3/√5
(d) √5/3

D

Question. If sin-1x + cos–1y(1/2) = π/2 then x is:
(a) 0
(b) 1/√5
(c)  2/√5
(d) √3/2

B

Question. The value of 1 sin(cot x) − is:
(a) (1+ x2)3/2
(b) (1+ x2)–3/2
(c) (1+ x2)1/2
(d) (1+ x2)–1/2

D

Question. The number of real solutions of tan−1√x(x+1) + sin-1√x2+x+1 = π/2
(a) Zero
(b) One
(c) Two
(d) Infinite

C

Question. If 1/2 < x < 1, then which of the following are real?
(a) sin−1
(b) tan−1
(c) sec−1
(d) cos−1 x

A,B,D

Question. If 6sin−1 (x2 − 6x + 8.5) =π , then:
(a) x = 1
(b) x = 2
(c) x = 3
(d) x = 4

B,D

Question. The value of tan [sin-1 (–3/5) + cos–1 (3/√13)]
(a) 6/17
(b) 6/√13
(c) √13/5
(d) 17/6

D

Question. If sin-1 (–3/5) + cos–1 (12/13) = sin-1 C, then C = ?
(a) 65/56
(b) 24/65
(c) 16/65
(d) 56/65

D

Question. If cos–1 x/2 + cos–1 y/3 = θ then 9×2 – 12xycosθ + 4y2 = ?
(a) 36sin2 θ
(b) 36cos2 θ
(c) 36 tan2 θ
(d) None of these

A

Question. The number of solutions of sin-1 x + sin-1 2x = π/3 is:
(a) 0
(b) 1
(c) 2
(d) Infinities

B

Question. 2tan-1 (cos x) = tan-1 (cosec2 x), then x = ?
(a) π/2
(b) π
(c) π/6
(d) π/3

D

Question. The solution set of the equation sin-1 x = 2tan-1 x is:
(a) {1, 2}
(b) {−1,2}
(c) {−1, 1, 0}
(d)  {1,1/2, ,0}

C

Question. If cosec−1x = sin−1(1/x) , then x may be:
(a) 1
(b)−1/2
(c) 3/2
(d)−3/2

A,C,D

Question. The value(s) of x satisfying the equation sin−1| sin x | =√sin−1 | sin x | − is/are given by: (n is any integer)
(a) nπ −1
(b) nπ
(c) nπ +1
(d) 2nπ +1

A,B,C

Question. The formula cos-1 1-x2/1+x2 = 2tan-1 x holds only for:
(a) x∈R
(b) | x |≤ 1
(c) x∈(−1,1]
(d) x∈[1,+ ∞)

D

Question. Indicate the relation which is true:
(a) tan | tan−1 x | = | x |
(b) cot | cot−1 x | = | x |
(c) tan−1 | tan x | = | x |
(d) sin | sin−1 x | = | x |

A,B,D

Question. The equation 2cos–1x + sin-1x = 11π/6 has:
(a) No solution
(b) Only one solution
(c) Two solutions
(d) Three solutions

A

Question. If sin-1x + sin-1y = 2π/3 then cos–1x + cos–1y = ?
(a) 2π/3
(b) π/3
(c) π/6
(d) π

B

Question. 2tan-1 x sin-1 2x/1+x2 is independent of x , then:
(a) x∈[1,+ ∞)
(b) x∈[−1,1]
(c) x∈(−∞,−1]
(d) None of these