MCQ On Class 12 Maths Chapter 2 Inverse Trigonometric Functions

(1) tan^-1 (√3) + sec^-1 (-2) – cosec^-1 (2/√3)

[A] 5/π

[B] 2π/3

[C] π/3

[D] 0

Answer: 0

(2) The principle value of sin-1(sin2π/3)is

[A] 2π/3

[B] π/3

[C] -π/6

[D] π/6

Answer: π/3

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(3) Algebraic expression for sin (cot^-1 x) is

[A] 1/1+x²

[B]

[C]

[D] None of these

Answer:

(4) cos^-1(cos7π/6) is equal to

[A] 7π/6

[B] 5π/6

[C] π/3

[D] π/6

Answer: 5π/6

(5) cosec^-1(2)

[A] π/6

[B] 2π/3

[C] 5π/6

[D] 0

Answer: π/6

(6) If 6 sin^-1 (x² – 6x + 8.5) = π, then x is equal to

[A] 1

[B] 2

[C] 3

[D] 8

Answer: 2

(7) tan^-1 √3 – sec^-1(-2)

[A] π

[B] –π/3, 0

[C] π/3

[D] 2π/3

Answer: –π/3, 0

(8) sin(sec^-1 x + cosec^-1x) =

[A] 1

[B] -1

[C] π/2

[D] π/3

Answer: 1

(9) sin^-1 (1 – x) – 2 sin^-1 x = π/2 then x = ?

[A] 0, 1/2

[B] 1, 1/2

[C] 1/2

[D] 0

Answer: 0

(10) The value of x for which sin |cot^-1(1 – x)| = cos (tan^-1 x) is

[A] 2/1

[B] 1

[C] 0

[D] 1/2

Answer: 1/2

(11) Simplified form of cos^-1 (4x³ – 3x)

[A] 3 sin^-1x

[B] 3 cos^-1x

[C] π – 3 sin^-1x

[D] None of these

Answer: 3 cos^-1x

(12) 4 tan^-1 15 – tan^-1 1/239

[A] π

[B] π/2

[C] π/3

[D] π/4

Answer: π/4

(13) Principal value of sin^-1(1√2)

[A] π/4

[B] 3π/4

[C] 5π/4

[D] None of these

Answer: π/4

(14) The principal value of cosec^-1 (-2) is

[A] –2π/3

[B] π/6

[C] 2π/3

[D] –π/6

Answer: –π/6

(15) Which of the following is the principal value branch of cos^-1 x?

[A] [−π/2, π/2]

[B] (0, π)

[C] (0, π)

[D] (0, π) – {π/2}

Answer: (0, π)

(16) If 3 tan^-1 x + cot^-1 x = π, then x equals

[A] 0

[B] 1

[C] -1

[D] 1/2

Answer: 1

(17) The domain of the function cos^-1 (2x – 1) is

[A] [0, 1]

[B] [-1, 1]

[C] [-1, -1]

[D] [0, π]

Answer: [0, 1]

(18) If tan^-1 x + tan^-1 y = 4π5 then cot^-1 x + cot^-1 y equals

[A] π/5

[B] 2π/5

[C] 3π/5

[D] π

Answer: π/5

(19) If cos^-1 α + cos^-1 β + cos^-1 γ = 3π, then α(β + γ) + β (γ + α) + γ(α + β) equals

[A] 0

[B] 1

[C] 6

[D] 12

Answer: 6

(20) If cos^-1 x > sin^-1 x, then

[A] 1/√2 < x ≤ 1

[B] 0 ≤ x < 1/√2

[C] -1 ≤ x < 1/√2

[D] x > 0

Answer: 0 ≤ x < 1/√2

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