Check the below NCERT MCQ Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Inverse Trigonometric Functions Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.
Class 12 Maths Chapter 2 MCQ With Answers
Maths Class 12 Chapter 2 MCQs On Inverse Trigonometric Functions
Inverse Trigonometric Functions Class 12 MCQ Question 1.
sin-1 (sin\(\frac{2π}{3}\)) =
(a) \(\frac{2π}{3}\)
(b) \(\frac{π}{6}\)
(c) \(\frac{4π}{3}\)
(d) \(\frac{π}{3}\)
Answer
Answer: (d) \(\frac{π}{3}\)
Inverse Trigonometry Class 12 MCQ Question 2.
sin-1 (1 – x) – 2 sin-1 x = \(\frac{π}{2}\) then x = ?
(a) 0, \(\frac{1}{2}\)
(b) 1, \(\frac{1}{2}\)
(c) \(\frac{1}{2}\)
(d) 0
Answer
Answer: (d) 0
MCQ Of Inverse Trigonometry Class 12 Question 3.
tan-1 √3 – sec-1(-2)
(a) π
(b) –\(\frac{π}{3}\), 0
(c) \(\frac{π}{3}\)
(d) \(\frac{2π}{3}\)
Answer
Answer: (b) –\(\frac{π}{3}\), 0
Inverse Trigonometric Functions MCQ Question 4.
sin(sec-1 x + cosec-1x) =
(a) 1
(b) -1
(c) \(\frac{π}{2}\)
(d) \(\frac{π}{3}\)
Answer
Answer: (a) 1
Class 12 Maths Chapter 2 MCQ Question 5.
2 tan-1 \(\frac{1}{3}\) + tan-1 \(\frac{1}{7}\) =
(a) tan-1 \(\frac{44}{29}\)
(b) \(\frac{π}{2}\)
(c) 0
(d) \(\frac{π}{4}\)
Answer
Answer: (d) \(\frac{π}{4}\)
MCQ On Inverse Trigonometric Functions Question 6.
The principle value of sin-1 \(\frac{√3}{2}\) is
(a) \(\frac{2π}{3}\)
(b) \(\frac{π}{6}\)
(c) \(\frac{π}{4}\)
(d) \(\frac{π}{3}\)
Answer
Answer: (d) \(\frac{π}{3}\)
MCQ Inverse Trigonometry Class 12 Question 7.
The value of the expression tan-1(\(\frac{1}{2}\)cos-1\(\frac{2}{√5}\)) is
(a) 2 + √5
(b) √5 – 2
(c) \(\frac{√5+2}{4}\)
(d) √5 + 2
Answer
Answer: (d) √5 + 2
Class 12 Inverse Trigonometry MCQ Question 8.
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
Answer: (b) 3 cos-1x
Inverse Trigonometric Functions Class 12 MCQ With Solutions Question 9.
The value of tan(tan-1 \(\frac{4}{5}\) + tan-1 \(\frac{2}{3}\)) is
(a) \(\frac{6}{17}\)
(b) \(\frac{7}{16}\)
(c) \(\frac{17}{6}\)
(d) None of these
Answer
Answer: (d) None of these
MCQ On Inverse Trigonometric Functions Class 12 Question 10.
tan-1(\(\frac{x}{y}\)) – tan-1(\(\frac{x-y}{x+y}\)) is equal to
(a) \(\frac{π}{3}\)
(b) \(\frac{π}{4}\)
(c) \(\frac{π}{2}\)
(d) \(\frac{-3π}{4}\)
Answer
Answer: (b) \(\frac{π}{4}\)
Inverse Trigonometry MCQ Question 11.
The value of x for which sin |cot-1(1 – x)| = cos (tan-1 x) is
(a) \(\frac{2}{1}\)
(b) 1
(c) 0
(d) \(\frac{1}{2}\)
Answer
Answer: (d) \(\frac{1}{2}\)
Class 12 Maths Chapter 2 MCQ Questions Question 12.
Princal value of cos-1(\(\frac{-1}{√2}\))
(a) \(\frac{3π}{4}\)
(b) \(\frac{5π}{4}\)
(c) –\(\frac{π}{4}\)
(d) None of these
Answer
Answer: (a) \(\frac{3π}{4}\)
MCQ Questions For Inverse Trigonometry Class 12 With Solutions Question 13.
tan-1 √3 – sec-1 (-2) is equal to
(a) π
(b) –\(\frac{π}{3}\)
(c) \(\frac{π}{3}\)
(d) \(\frac{2π}{3}\)
Answer
Answer: (b) –\(\frac{π}{3}\)
Class 12 Maths Ch 2 MCQ Question 14.
If y = sec-1 x then
(a) 0 ≤ y ≤ π
(b) 0 ≤ y ≤ \(\frac{π}{2}\)
(c) –\(\frac{π}{2}\) < y < \(\frac{π}{2}\)
(d) None of these
Answer
Answer: (d) None of these
Ch 2 Maths Class 12 MCQ Question 15.
If x + \(\frac{1}{x}\) = 2 then the principal value of sin-1 x is x
(a) \(\frac{π}{4}\)
(b) \(\frac{π}{2}\)
(c) π
(d) \(\frac{3π}{2}\)
Answer
Answer: (d) \(\frac{3π}{2}\)
Inverse Trigonometry MCQ Class 12 Question 16.
4 tan-1 \(\frac{1}{5}\) – tan-1 \(\frac{1}{239}\)
(a) π
(b) \(\frac{π}{2}\)
(c) \(\frac{π}{3}\)
(d) \(\frac{π}{4}\)
Answer
Answer: (d) \(\frac{π}{4}\)
Inverse Trigonometric Functions MCQ Pdf Question 17.
The principle value of sin-1(sin\(\frac{2π}{3}\)) is
(a) \(\frac{2π}{3}\)
(b) \(\frac{π}{3}\)
(c) \(\frac{-π}{6}\)
(d) \(\frac{π}{6}\)
Answer
Answer: (b) \(\frac{π}{3}\)
MCQ Questions For Inverse Trigonometry Class 12 Question 18.
The value of cos-1(\(\frac{1}{2}\)) + 2sin-1(\(\frac{1}{2}\)) is equal to
(a) \(\frac{π}{4}\)
(b) \(\frac{π}{6}\)
(c) \(\frac{2π}{3}\)
(d) \(\frac{5π}{6}\)
Answer
Answer: (b) \(\frac{π}{6}\)
Chapter 2 Maths Class 12 MCQ Question 19.
Algebraic expression for sin (cot-1 x) is
(a) \(\frac{1}{1+x^2}\)
(b) \(\frac{1}{\sqrt{1+x^2}}\)
(c) \(\frac{x}{\sqrt{1+x^2}}\)
(d) None of these
Answer
Answer: (b) \(\frac{1}{\sqrt{1+x^2}}\)
Inverse Trigonometry MCQs Question 20.
If sin-1(\(\frac{2x}{1+x^2}\)) + sin-1\(\frac{2y}{1+y^2}\) = 2 tan-1 a then a is equal to
(a) \(\frac{x-y}{1+xy}\)
(b) \(\frac{y}{1+xy}\)
(c) \(\frac{y}{1-xy}\)
(d) \(\frac{x+y}{1-xy}\)
Answer
Answer: (d) \(\frac{x+y}{1-xy}\)
Question 21.
Princal value of tan-1 (-1) is
(a) \(\frac{π}{4}\)
(b) \(\frac{-π}{2}\)
(c) \(\frac{5π}{4}\)
(d) \(\frac{-π}{4}\)
Answer
Answer: (d) \(\frac{-π}{4}\)
Question 22.
tan-1(\(\frac{1}{4}\)) + tan-1(\(\frac{2}{9}\)) equal to
Answer
Answer: (d) tan-1(\(\frac{1}{2}\))
Question 23.
Principal value of sin-1(\(\frac{1}{√2}\))
(a) \(\frac{π}{4}\)
(b) \(\frac{3π}{4}\)
(c) \(\frac{5π}{4}\)
(d) None of these
Answer
Answer: (a) \(\frac{π}{4}\)
Question 24.
sin-1 x = y Then
(a) 0 ≤ y ≤ π
(b) –\(\frac{π}{2}\) ≤ y ≤ \(\frac{π}{2}\)
(c) 0 < y < π
(d) –\(\frac{π}{2}\) < y < –\(\frac{π}{2}\)
Answer
Answer: (b) –\(\frac{π}{2}\) ≤ y ≤ \(\frac{π}{2}\)
Question 25.
cos-1(cos\(\frac{7π}{6}\)) is equal to
(a) \(\frac{7π}{6}\)
(b) \(\frac{5π}{6}\)
(c) \(\frac{π}{3}\)
(d) \(\frac{π}{6}\)
Answer
Answer: (b) \(\frac{5π}{6}\)
Question 26.
sin[\(\frac{π}{3}\) – sin-1(-\(\frac{1}{2}\))] is equal to
(a) \(\frac{1}{2}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{1}{4}\)
(d) 1
Answer
Answer: (d) 1
Question 27.
tan-1\(\frac{1}{2}\) + tan-1\(\frac{2}{11}\) = tan-1 a then a = ?
(a) \(\frac{1}{4}\)
(b) \(\frac{1}{2}\)
(c) \(\frac{3}{4}\)
(d) 1
Answer
Answer: (c) \(\frac{3}{4}\)
Question 28.
tan-1\(\frac{1}{2}\) + tan-1\(\frac{1}{3}\) =
(a) \(\frac{π}{4}\)
(b) \(\frac{π}{2}\)
(c) \(\frac{π}{3}\)
(d) π
Answer
Answer: (a) \(\frac{π}{4}\)
Question 29.
If sin-1 x + sin-1 y = \(\frac{2π}{3}\) then cos-1 x + cos-1 y =
(a) \(\frac{2π}{3}\)
(b) \(\frac{π}{4}\)
(c) \(\frac{π}{3}\)
(d) \(\frac{π}{2}\)
Answer
Answer: (c) \(\frac{π}{3}\)
Question 30.
The principal value of cosec-1 (-2) is
(a) –\(\frac{2π}{3}\)
(b) \(\frac{π}{6}\)
(c) \(\frac{2π}{3}\)
(d) –\(\frac{π}{6}\)
Answer
Answer: (d) –\(\frac{π}{6}\)
Question 31.
The domain of the following f(x) = \(\sqrt{sin^{-1}x}\) is
(a) [0, 1]
(b) [-1, 1]
(c) [-, 0]
(d) [0, 1]
Answer
Answer: (a) [0, 1]
Question 32.
Which of the following is the principal value branch of cos-1 x?
(a) [\(\frac{-π}{2}\), \(\frac{π}{2}\)]
(b) (0, π)
(c) (0, π)
(d) (0, π) – {\(\frac{π}{2}\)}
Answer
Answer: (c) (0, π)
Question 33.
Which of the following is the principal value branch of cosec-1 x?
(a) (\(\frac{-π}{2}\), \(\frac{π}{2}\))
(b) (0, π) – {\(\frac{π}{2}\)}
(c) [\(\frac{-π}{2}\), \(\frac{π}{2}\)]
(d) [\(\frac{-π}{2}\), \(\frac{π}{2}\)] – [0]
Answer
Answer: (d) [\(\frac{-π}{2}\), \(\frac{π}{2}\)] – [0]
Question 34.
If 3 tan-1 x + cot-1 x = π, then x equals
(a) 0
(b) 1
(c) -1
(d) \(\frac{1}{2}\)
Answer
Answer: (b) 1
Question 35.
The value of cos-1[cos(\(\frac{33π}{5}\))] is
(a) \(\frac{3π}{5}\)
(b) \(\frac{-3π}{5}\)
(c) \(\frac{π}{10}\)
(d) –\(\frac{-π}{10}\)
Answer
Answer: (a) \(\frac{3π}{5}\)
Question 36.
The domain of the function cos-1 (2x – 1) is
(a) [0, 1]
(b) [-1, 1]
(c) [-1, -1]
(d) [0, π]
Answer
Answer: (a) [0, 1]
Question 37.
The domain of the function defined by f (x) = sin-1 \(\sqrt{x-1}\) is
(a) [1, 2]
(b) [-1, 1]
(c) [0, 1]
(d) None of these
Answer
Answer: (a) [1, 2]
Question 38.
If cos(sin-1\(\frac{2}{5}\) + cos-1 x) = 0 then x is equal to
(a) \(\frac{1}{5}\)
(b) \(\frac{2}{5}\)
(c) 0
(d) 1
Answer
Answer: (b) \(\frac{2}{5}\)
Question 39.
The value of sin (2 tan-1 (.75)) is equal to
(a) .75
(b) 1.5
(c) .96
(d) sin 1.5
Answer
Answer: (c) .96
Question 40.
The value of cos-1 (cos\(\frac{3π}{2}\)) is equal to
(a) \(\frac{π}{2}\)
(b) \(\frac{3π}{2}\)
(c) \(\frac{5π}{2}\)
(d) –\(\frac{7π}{2}\)
Answer
Answer: (a) \(\frac{π}{2}\)
Question 41.
The value of expression 2 sec-1 2 + sin-1 (\(\frac{1}{2}\)) is
(a) \(\frac{π}{6}\)
(b) \(\frac{5π}{6}\)
(c) \(\frac{7π}{6}\)
(d) 1
Answer
Answer: (b) \(\frac{5π}{6}\)
Question 42.
If tan-1 x + tan-1 y = \(\frac{4π}{5}\) then cot-1 x + cot-1 y equals
(a) \(\frac{π}{5}\)
(b) \(\frac{2π}{5}\)
(c) \(\frac{3π}{5}\)
(d) π
Answer
Answer: (a) \(\frac{π}{5}\)
Question 43.
If sin-1(\(\frac{2a}{1+a^2}\)) + cos-1(\(\frac{1-a^2}{1+a^2}\)) = tan-1(\(\frac{2x}{1-x^2}\)) where a, x ∈ |0, 1| then the value of x is
(a) 0
(b) \(\frac{a}{2}\)
(c) a
(d) \(\frac{2a}{1-a^2}\)
Answer
Answer: (d) \(\frac{2a}{1-a^2}\)
Question 44.
The value of sin [cos-1(\(\frac{7}{25}\))] is
(a) \(\frac{25}{24}\)
(b) \(\frac{25}{7}\)
(c) \(\frac{24}{25}\)
(d) \(\frac{7}{24}\)
Answer
Answer: (c) \(\frac{24}{25}\)
Question 45.
If |x| ≤ 1, then 2 tan-1 x + sin-1(\(\frac{2x}{1+x^2}\)) is equal to
(a) 4 tan-1 x
(b) \(\frac{π}{2}\)
(c) 0
(d) π
Answer
Answer: (a) 4 tan-1 x
Question 46.
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
Answer: (c) 6
Question 47.
The number of real solution of the equation is
\(\sqrt{1+cos 2x}\) = √2 cos-1(cos x) in [\(\frac{π}{2}\), π] is
(a) 0
(b) 1
(c) 2
(d) None of these
Answer
Answer: (c) 2
Question 48.
If cos-1 x > sin-1 x, then
(a) \(\frac{1}{√2}\) < x ≤ 1
(b) 0 ≤ x < \(\frac{1}{√2}\)
(c) -1 ≤ x < \(\frac{1}{√2}\) (d) x > 0
Answer
Answer: (b) 0 ≤ x < \(\frac{1}{√2}\)
Question 49.
sin-1(\(\frac{-1}{2}\))
(a) \(\frac{π}{3}\)
(b) –\(\frac{π}{3}\)
(c) \(\frac{π}{6}\)
(d) –\(\frac{π}{6}\)
Answer
Answer: (d) –\(\frac{π}{6}\)
Question 50.
sec-1(\(\frac{-2}{√3}\))
(a) \(\frac{π}{6}\)
(b) \(\frac{π}{3}\)
(c) \(\frac{5π}{6}\)
(d) –\(\frac{2π}{3}\)
Answer
Answer: (c) \(\frac{5π}{6}\)
Question 51.
cos-1(\(\frac{1}{2}\))
(a) –\(\frac{π}{3}\)
(b) \(\frac{π}{3}\)
(c) \(\frac{π}{2}\)
(d) \(\frac{2π}{3}\)
Answer
Answer: (b) \(\frac{π}{3}\)
Question 52.
cosec-1(\(\frac{-2}{√3}\))
(a) –\(\frac{π}{3}\)
(b) \(\frac{π}{3}\)
(c) \(\frac{π}{2}\)
(d) –\(\frac{π}{2}\)
Answer
Answer: (a) –\(\frac{π}{3}\)
Question 53.
cot-1(1)
(a) \(\frac{π}{3}\)
(b) \(\frac{π}{4}\)
(c) \(\frac{π}{2}\)
(d) 0
Answer
Answer: (b) \(\frac{π}{4}\)
Question 54.
cos-1(\(\frac{√3}{2}\))
(a) \(\frac{5π}{6}\)
(b) \(\frac{π}{6}\)
(c) \(\frac{4π}{9}\)
(d) \(\frac{2π}{3}\)
Answer
Answer: (a) \(\frac{5π}{6}\)
Question 55.
cosec-1(2)
(a) \(\frac{π}{6}\)
(b) \(\frac{2π}{3}\)
(c) \(\frac{5π}{6}\)
(d) 0
Answer
Answer: (a) \(\frac{π}{6}\)
Question 56.
sec-1(2)
(a) \(\frac{π}{6}\)
(b) \(\frac{π}{3}\)
(c) \(\frac{2π}{3}\)
(d) \(\frac{5π}{6}\)
Answer
Answer: (b) \(\frac{π}{3}\)
Question 57.
tan-1(√3)
(a) \(\frac{π}{6}\)
(b) \(\frac{π}{3}\)
(c) \(\frac{2π}{3}\)
(d) \(\frac{5π}{6}\)
Answer
Answer: (b) \(\frac{π}{3}\)
Question 58.
cot-1(-√3)
(a) \(\frac{5π}{6}\)
(b) \(\frac{π}{3}\)
(c) \(\frac{π}{2}\)
(d) \(\frac{π}{4}\)
Answer
Answer: (a) \(\frac{5π}{6}\)
Question 59.
tan-1 + cos-1 (\(\frac{-1}{2}\)) + sin-1 (\(\frac{-1}{2}\))
(a) \(\frac{2π}{3}\)
(b) \(\frac{3π}{4}\)
(c) \(\frac{π}{2}\)
(d) 6π
Answer
Answer: (b) \(\frac{3π}{4}\)
Question 60.
tan-1 (√3) + sec-1 (-2) – cosec-1 (\(\frac{2}{√3}\))
(a) \(\frac{5π}{6}\)
(b) \(\frac{2π}{3}\)
(c) \(\frac{π}{3}\)
(d) 0
Answer
Answer: (d) 0
Question 61.
cos-1 (\(\frac{-1}{2}\)) + 2sin-1 (\(\frac{-1}{2}\))
(a) \(\frac{π}{3}\)
(b) \(\frac{2π}{3}\)
(c) \(\frac{3π}{4}\)
(d) \(\frac{5π}{8}\)
Answer
Answer: (a) \(\frac{π}{3}\)
Question 62.
If cot-1 (\(\sqrt{cosα}\)) – tan-1 (\(\sqrt{cosα}\)) = x then sin x is equal to
(a) tan² (\(\frac{α}{2}\))
(b) cot² (\(\frac{α}{2}\))
(c) tan α
(d) cot (\(\frac{α}{2}\))
Answer
Answer: (a) tan² (\(\frac{α}{2}\))
Question 63.
4 tan-1 \(\frac{1}{5}\) – tan-1 \(\frac{1}{70}\) + tan-1 \(\frac{1}{99}\) is equal to
(a) \(\frac{π}{6}\)
(b) \(\frac{π}{4}\)
(c) \(\frac{π}{3}\)
(d) \(\frac{π}{2}\)
Answer
Answer: (b) \(\frac{π}{4}\)
Question 64.
If 6 sin-1 (x² – 6x + 8.5) = π, then x is equal to
(a) 1
(b) 2
(c) 3
(d) 8
Answer
Answer: (b) 2
Question 65.
Number of solutions of the equation
tan-1 (\(\frac{1}{2x+1}\)) + tan-1 (\(\frac{1}{4x+1}\)) = tan-1 (\(\frac{2}{x^2}\))
(a) 1
(b) 2
(c) 3
(d) 4
Answer
Answer: (b) 2
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