Study MaterialsImportant QuestionsInverse Trigonometric Functions Class 12 Maths MCQs

Inverse Trigonometric Functions Class 12 Maths MCQs

MCQs for Class 12 Maths Chapter 2: Inverse Trigonometric Functions are provided here with correct answers and detailed solutions. These MCQs cover key concepts such as domain and range restrictions of trigonometric functions, essential for understanding their inverses and behavior graphically. They are aligned with the latest CBSE guidelines for the 2023-2024 board exams, offering valuable preparation material for Class 12 students. Access MCQs for all Class 12 Maths chapters with solutions here.

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    Inverse Trigonometric Functions Class 12 Maths MCQs Pdf

    Question 1. Solve for x : {xcos(cot-1 x) + sin(cot-1 x)}2 = \(\frac{51}{50}\)

    (a) \(\frac{1}{\sqrt{2}}\)

    (b) \(\frac{1}{5 \sqrt{2}}\)

    (c) 2√2

    (d) 5√2

    Answer: (b) \(\frac{1}{5 \sqrt{2}}\)

    Question 2.

    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q32
    Answer: (c) tan-1(15)

    Question 3.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q33
    Answer: (b) \(\sqrt{\frac{3}{76}}\)

    Question 4.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q34
    Answer: (d) \(\frac{\pi}{4}\)

    Also Refer: Areas Related to Circle Class 10 MCQs

    Question 5. If sin-1(x2 – 7x + 12) = nπ, ∀ n ∈ I, then x =

    (a) -2

    (b) 4

    (c) -3

    (d) 5

    Answer: (b) 4

    Question 6. If cos-1 x + sin-1 x = π, then the value of x is

    (a) \(\frac{3}{2}\)

    (b) \(\frac{1}{\sqrt{2}}\)

    (c) \(\frac{\sqrt{3}}{2}\)

    (d) \(\frac{2}{\sqrt{3}}\)

    Answer: (c) \(\frac{\sqrt{3}}{2}\)

    Question 7. If sin-1 x – cos-1 x = \(\frac{\pi}{6}\), then x =

    (a) \(\frac{1}{2}\)

    (b) \(\frac{\sqrt{3}}{2}\)

    (c) \(-\frac{1}{2}\)

    (d) \(-\frac{\sqrt{3}}{2}\)

    Answer: (b) \(\frac{\sqrt{3}}{2}\)

    Question 8. If tan-1 (cot θ) = 2θ, then θ is equal to

    (a) \(\frac{\pi}{3}\)

    (b) \(\frac{\pi}{4}\)

    (c) \(\frac{\pi}{6}\)

    (d) None of these

    Answer: (c) \(\frac{\pi}{6}\)

    Click Here: CBSE Class 12 Syllabus 2024

    Question 9. cot(\(\frac{\pi}{4}\) – 2cot-1 3) =

    (a) 7

    (b) 6

    (c) 5

    (d) None of these

    Answer: (a) 7

    Question 10. If tan-1 3 + tan-1 x = tan-1 8, then x =

    (a) 5\

    (b) \(\frac{1}{5}\)

    (c) \(\frac{5}{14}\)

    (d) \(\frac{14}{5}\)

    Answer: (b) \(\frac{1}{5}\)

    Question 11.

    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q1

    Answer: (d) \(-\frac{\pi}{6}\)

    Question 12.

    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q2

    Answer: (b) \(\frac{\pi}{3}\)

    Question 13.

    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q3

    Answer: (b) \(\frac{\pi}{3}\)

    Question 14.

    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q4

    Answer: (a) \(\frac{\pi}{4}\)

    Question 15.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q5
    Answer: (b) \(\frac{3 \pi}{4}\)

    Question 16.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q6
    Answer: (d) \(\frac{2 \pi}{3}\)

    Question 17.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q7
    Answer: (a) \(\tan ^{2}\left(\frac{\alpha}{2}\right)\)

    Question 18.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q8
    Answer: (b) \(\frac{6}{17}\)

    Question 19. If tan-1 (x – 1) + tan-1 x + tan-1 (x + 1) = tan-1 3x, then the values of x are

    (a) \(\pm \frac{1}{2}\)

    (b) 0, \(\frac{1}{2}\)

    (c) 0, \(-\frac{1}{2}\)

    (d) 0, \(\pm \frac{1}{2}\)

    Answer: (d) 0, \(\pm \frac{1}{2}\)

    Question 20. If 6sin-1 (x2 – 6x + 8.5) = π, then x is equal to

    (a) 1

    (b) 2

    (c) 3

    (d) 8

    Answer: (b) 2

    Question 21.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q41
    Answer: (d) \(-\frac{24}{25}\)

    Question 22. sin-1 (1 – x) – 2sin-1 x = \(\frac{\pi}{2}\)

    (a) 0

    (b) 1/2

    (c) 0, 1/2

    (d) -1/2

    Answer: (a) 0

    Question 23. 2tan-1(cos x) = tan-1(2cosec x)

    (a) 0

    (b) π/3

    (c) π/4

    (d) π/2

    Answer: (c) π/4

    Question 24.

    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q44

    Answer: (a) \(\sqrt{\frac{x^{2}+1}{x^{2}+2}}\)

    Question 25.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q45
    Answer: (a) \(\frac{3 \pi}{5}\)

    Question 26. The domain of the function defind by f(x) = \(\sin ^{-1} \sqrt{x-1}\) is

    (a) [1, 2]

    (b) [-1, 1]

    (c) [0, 1]

    (d) none of these

    Answer: (a) [1, 2]

    Question 27. The value of sin (2tan-1 (0.75)) is equal to

    (a) 0.75

    (b) 1.5

    (c) 0.96

    (d) sin 1.5

    Answer: (c) 0.96

    Question 28. The value of expression 2 sec-1 2 + sin-1(\(\frac{1}{2}\))

    (a) \(\frac{\pi}{6}\)

    (b) \(\frac{5 \pi}{6}\)

    (c) \(\frac{7 \pi}{6}\)

    (d) 1

    Answer: (b) \(\frac{5 \pi}{6}\)

    Question 29.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q49
    Answer: (c) \(\frac{24}{25}\)

    Question 30. The value of the expression \(\tan \left(\frac{1}{2} \cos ^{-1} \frac{2}{\sqrt{3}}\right)\)

    (a) 2 + √5

    (b) √5 – 2

    (c) \(\frac{\sqrt{5}+2}{2}\)

    (d) 5 + √2

    Answer: (b) √5 – 2

    Question 31.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q21
    Answer: (a) \(\frac{6}{17}\)

    Question 32.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q22
    Answer: (d) none of these

    Question 33.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q23
    Answer: (b) 0

    Question 34.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q24
    Answer: (d) \(\frac{1}{\sqrt{2}} \leq x \leq 1\)

    Question 35. cos-1[cos(2cot-1(√2 – 1))] = ______

    (a) √2 – 1

    (b) 1 + √2

    (c) \(\frac{\pi}{4}\)

    (d) \(\frac{3 \pi}{4}\)

    Answer: (d) \(\frac{3 \pi}{4}\)

    Question 36. The range of sin-1 x + cos-1 x + tan-1 x is

    (a) [0, π]

    (b) \(\left[\frac{\pi}{4}, \frac{3 \pi}{4}\right]\)

    (c) (0, π)

    (d) \(\left[0, \frac{\pi}{2}\right]\)

    Answer: (b) \(\left[\frac{\pi}{4}, \frac{3 \pi}{4}\right]\)

    Question 37.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q27
    Answer: (c) \(\frac{\pi}{4}\)

    Question 38. Find the value of sec2 (tan-1 2) + cosec2 (cot-1 3)

    (a) 12

    (b) 5

    (c) 15

    (d) 9

    Answer: (c) 15

    Question 39.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q29
    Answer: (d) \(\frac{2}{x}\)

    Question 40. The equation sin-1 x – cos-1 x = cos-1(\(\frac{\sqrt{3}}{2}\)) has

    (a) unique solution

    (b) no solution

    (c) infinitely many solution

    (d) none of these

    Answer: (a) unique solution

    Question 41. 3 tan-1 a is equal to
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q11
    Answer: (d) \(\tan ^{-1}\left(\frac{3 a-a^{3}}{1-3 a^{2}}\right)\)

    Question 42.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q12
    Answer: (d) \(\frac{1}{5}\)

    Question 43. The equation 2cos-1 x + sin-1 x = \(\frac{11 \pi}{6}\) has

    (a) no solution

    (b) only one solution

    (c) two solutions

    (d) three solutions

    Answer: (a) no solution

    Question 44.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q14
    Answer: (d) x

    Question 45. If tan-1 2x + tan-1 3x = \(\frac{\pi}{4}\), then x is

    (a) \(\frac{1}{6}\)

    (b) 1

    (c) (\(\frac{1}{6}\), -1)

    (d) none of these

    Answer: (a) \(\frac{1}{6}\)

    Question 46.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q16
    Answer: (c) \(\sqrt{\frac{x^{2}+1}{x^{2}+2}}\)

    Question 47.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q17

    Answer: (a) \(\sqrt{a b}\)

    Question 48. If tan-1 x – tan-1 y = tan-1 A, then A is equal to

    (a) x – y

    (b) x + y

    (c) \(\frac{x-y}{1+x y}\)

    (d) \(\frac{x+y}{1-x y}\)

    Answer: (c) \(\frac{x-y}{1+x y}\)

    Question 49.
    Maths MCQs for Class 12 with Answers Chapter 2 Inverse Trigonometric Functions Q19

    Answer: (c) \(\pm \sqrt{\frac{5}{2}}\)

    Question 50. The value of cot-1 9 + cosec-1(\(\frac{\sqrt{41}}{4}\)) is given by

    (a) 0

    (b) \(\frac{\pi}{4}\)

    (c) tan-1 2

    (d) \(\frac{\pi}{2}\)

    Answer: (b) \(\frac{\pi}{4}\)

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