CBSE Class 12 Maths – MCQ and Online Tests – Unit 2 – Inverse Trigonometric Functions
Every year CBSE conducts board exams for 12th standard. These exams are very competitive to all the students. So our website provides online tests for all the 12th subjects. These tests are also very effective and useful for those who preparing for competitive exams like NEET, JEE, CA etc. It can boost their preparation level and confidence level by attempting these chapter wise online tests.
These online tests are based on latest CBSE Class 12 syllabus. While attempting these our students can identify the weak lessons and continuously practice those lessons for attaining high marks. It also helps to revise the NCERT textbooks thoroughly.
CBSE Class 12 Maths – MCQ and Online Tests – Unit 2 – Inverse Trigonometric Functions
Question 1.
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 2.
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 3.
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 4.
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 5.
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 6.
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 7.
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 8.
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 9.
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 10.
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 11.
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 12.
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 13.
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) \(\frac{3π}{2}\)
Question 14.
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) \(\frac{π}{3}\)
Question 15.
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) \(\frac{1}{\sqrt{1+x^2}}\)
Question 16.
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
Question 17.
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) \(\frac{3π}{4}\)
Question 18.
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) \(\frac{π}{4}\)
Question 19.
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) \(\frac{1}{2}\)
Question 20.
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
Question 21.
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) \(\frac{π}{4}\)
Question 22.
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) \(\frac{π}{3}\)
Question 23.
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
Question 24.
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
Question 25.
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 26.
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 27.
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 28.
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 29.
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 30.
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 31.
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 32.
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 33.
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
Question .34
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 35.
cot-1(-√3)
(a) \(\frac{5π}{6}\)
(b) \(\frac{π}{3}\)
(c) \(\frac{π}{2}\)
(d) \(\frac{π}{4}\)
Answer
Answer: (a) \(\frac{5π}{6}\)
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