Do you need some help in preparing for your upcoming Maths exam? We’ve compiled a list of MCQ Questions for Class 12 Maths with Answers to get you started with the subject, Inverse Trigonometric Functions Class 12 MCQs Questions with Answers. You can download NCERT MCQ Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions with Answers Pdf free download and learn how smart students improve problem-solving skills well ahead. So, ace up your preparation with Class 12 Maths Chapter 2 Inverse Trigonometric Functions Objective Questions.
Inverse Trigonometric Functions Class 12 MCQs Questions with Answers
Don’t forget to practice the multitude of MCQ Questions on Inverse Trigonometric Functions Class 12 with answers so you can apply your skills during the exam.
Question 1.
If sin-1 x + sin-1 y = \(\frac { 2π }{3}\), then the value of cos-1 x + cos-1 y is
(a) \(\frac { 2π }{3}\)
(b) \(\frac { π }{3}\)
(c) \(\frac { π }{2}\)
(d) π
Answer
Answer: (b) \(\frac { π }{3}\)
Question 2.
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) –\(\frac { π }{3}\)
Question 3.
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 4.
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 5.
tan-1 √3 – cot-1(-√3) is equal to
(a) π
(b) –\(\frac { π }{2}\)
(c) 0
(d) 2√3
Answer
Answer: (b) –\(\frac { π }{2}\)
Question 6.
sin (tan-1 x), |x| < 1, is equal to
(a) \(\frac { x }{\sqrt{1-x^2}}\)
(b) \(\frac { 1 }{\sqrt{1-x^2}}\)
(c) \(\frac { x }{\sqrt{1+x^2}}\)
(d) \(\frac { x }{\sqrt{1+x^2}}\)
Answer
Answer: (d) \(\frac { x }{\sqrt{1+x^2}}\)
Question 7.
sin-1 (1 – x) – 2 sin-1 x = \(\frac { π }{2}\), then x is equal to
(a) 0, \(\frac { 1 }{2}\)
(b) 1, \(\frac { 1 }{2}\)
(c) 0
(d) \(\frac { 1 }{2}\)
Answer
Answer: (c) 0
Question 8.
tan-1 (\(\frac { x }{y}\)) – tan-1 \(\frac { x-y }{x+y}\) is equal to
(a) \(\frac { π }{2}\)
(b) \(\frac { π }{3}\)
(c) \(\frac { π }{4}\)
(d) –\(\frac { 3π }{4}\)
Answer
Answer: (c) \(\frac { π }{4}\)
Question 9.
The value of sin-1(cos(\(\frac { 43π }{5}\))) is
(a) \(\frac { 3π }{5}\)
(b) \(\frac { -7π }{5}\)
(c) \(\frac { π }{10}\)
(d) –\(\frac { -π }{10}\)
Answer
Answer: (d) –\(\frac { -π }{10}\)
Question 10.
The principal value of the expression
cos-1 [cos (-680°)] is
(a) \(\frac { 2π }{9}\)
(b) \(\frac { -2π }{9}\)
(c) \(\frac {34π }{9}\)
(d) –\(\frac { π }{9}\)
Answer
Answer: (a) \(\frac { 2π }{9}\)
Question 11.
The value of cot (sin-1x) is
(a) \(\frac { \sqrt{1+x^2} }{x}\)
(b) \(\frac { x }{\sqrt{1+x^2}}\)
(c) \(\frac {1}{x}\)
(d) \(\frac { \sqrt{1-x^2} }{x}\)
Answer
Answer: (d) \(\frac { \sqrt{1-x^2} }{x}\)
Question 12.
The domain of sin-1 2x is
(a) [0, 1]
(b) [-1, 1]
(c) [\(\frac {-1}{2}\), \(\frac {1}{2}\)]
(d) [-2, 2]
Answer
Answer: (c) [\(\frac {-1}{2}\), \(\frac {1}{2}\)]
Question 13.
The greatest and least values of (sin-1 x)² + (cos-1x)² are respectively
(a) \(\frac { 5π^2 }{4}\) and \(\frac { π^2 }{8}\)
(b) \(\frac { π }{2}\) and \(\frac { -π }{2}\)
(c) \(\frac { π^2 }{4}\) and \(\frac { -π^2 }{4}\)
(d) –\(\frac { π^2 }{4}\) and 0
Answer
Answer: (a) \(\frac { 5π^2 }{4}\) and \(\frac { π^2 }{8}\)
Question 14.
If cos-1 x – cos-1 — = α, then 4x² – 4xy cos α + y² is equal to:
(a) 4
(b) 2 sin² α
(c) -4 sin² α
(d) 4 sin² α.
Answer
Answer: (d) 4 sin² α.
Hint:
Squaring, 4x² + y² cos² α – 4xy cos α
= 4 sin² α – y² sin² α
⇒ 4x² – 4xy cos α + y² = 4 sin² α.
Question 15.
If sin-1 (\(\frac {5}{4}\)) = \(\frac {π}{2}\), then the value of x is
(a) 3
(b) 4
(c) 5
(d) 1
Answer
Answer: (a) 3
Hint:
Question 16.
The value of cot (cosec-1\(\frac {5}{3}\) + tan-1\(\frac {2}{3}\)) is
(a) \(\frac { 5 }{17}\)
(b) \(\frac { 6 }{17}\)
(c) \(\frac { 3 }{17}\)
(d) \(\frac { 4 }{17}\)
Answer
Answer: (b) \(\frac { 6 }{17}\)
Hint:
Question 17.
If tan-1 y = tan-1 x + tan-1(\(\frac { 2x }{1-x^2}\)) when |x| < \(\frac { 1 }{√3}\), then the value of y is:
(a) \(\frac { 3x-x^3 }{1-3x^2}\)
(b) \(\frac { 3x+x^3 }{1-3x^2}\)
(c) \(\frac { 3x-x^3 }{1+3x^2}\)
(d) \(\frac { 3x+x^3 }{1+3x^2}\)
Answer
Answer: (a) \(\frac { 3x-x^3 }{1-3x^2}\)
Hint:
Fill in the blanks
Question 1.
Principal value of sin-1 (-\(\frac {1}{2}\)) is ………………
Answer
Answer: –\(\frac {π}{6}\)
Question 2.
Principal value of sin-1 (-\(\frac {1}{√2}\)) is ……………….
Answer
Answer: \(\frac {-π}{4}\)
Question 3.
Principal value of cos-1 (\(\frac {-1}{2}\)) is ………………
Answer
Answer: \(\frac {2π}{3}\)
Question 4.
Principal value of tan-1 (-√3) is …………………
Answer
Answer: –\(\frac {π}{3}\)
Question 5.
Principal value of tan-1 (-1) is ……………..
Answer
Answer: –\(\frac {π}{4}\)
Question 6.
Principal value of cot-1 (√3) is ……………….
Answer
Answer: \(\frac {π}{6}\)
Question 7.
Principal value of cosec-1 (-√2) is ……………..
Answer
Answer: –\(\frac {π}{4}\)
Question 8.
sin-1 x + cos-1 x = ………………
Answer
Answer: \(\frac {π}{2}\)
Question 9.
tan-1 x + cot-1 x = ………………..
Answer
Answer: \(\frac {π}{2}\)
Question 10.
sec-1 x + cosec-1 x = ……………….
Answer
Answer: \(\frac {π}{2}\)
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