Quiz Tweek

Inverse Trigonometric Functions Set-1

Test your knowledge on Inverse Trigonometric Functions from Mathematics, Class 12.

60

Minutes

40

Questions

1 / -0

Marking Scheme

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Questions in this Quiz

Q1: $\text{cosec}^{-1} (-\frac{2}{\sqrt{3}})$
  • $-\pi/3$
  • $\pi/3$
  • $\pi/2$
  • $-\pi/2$
Q2: $\text{sec}^{-1} (2)$
  • $\pi/6$
  • $\pi/3$
  • $2\pi/3$
  • $5\pi/6$
Q3: Which of the following is the principal value branch of $\text{cosec}^{-1} x$?
  • $(-\pi/2, \pi/2)$
  • $(0, \pi) – \{\pi/2\}$
  • $[−\pi/2, \pi/2]$
  • $[−\pi/2, \pi/2] – \{0\}$
Q4: The value of $\sin [\text{cos}^{-1} (\frac{7}{25})]$ is
  • $25/24$
  • $25/7$
  • $24/25$
  • $7/24$
Q5: If $x + (1/x) = 2$ then the principal value of $\text{sin}^{-1} x$ is
  • $\pi/4$
  • $\pi/2$
  • $\pi$
  • $3\pi/2$
Q6: The value of $\text{cos}^{-1} [\text{cos}(\frac{33\pi}{5})]$ is
  • $3\pi/5$
  • $-3\pi/5$
  • $\pi/10$
  • $-\pi/10$
Q7: $\text{sin}^{-1} (-1/2)$
  • $\pi/3$
  • $-\pi/3$
  • $\pi/6$
  • $-\pi/6$
Q8: $\text{cot}^{-1} (1)$
  • $\pi/3$
  • $\pi/4$
  • $\pi/2$
  • 0
Q9: $\text{cos}^{-1} (-1/2) + 2\text{sin}^{-1} (-1/2)$
  • $\pi/3$
  • $2\pi/3$
  • $3\pi/4$
  • $5\pi/8$
Q10: $\text{cos}^{-1} (\sqrt{3}/2)$
  • $5\pi/6$
  • $\pi/6$
  • $4\pi/9$
  • $2\pi/3$
Q11: If $\text{sin}^{-1}(\frac{2a}{1+a^2}) + \text{cos}^{-1}(\frac{1−a^2}{1+a^2}) = \text{tan}^{-1}(\frac{2x}{1−x^2})$ where $a, x \in |0, 1|$ then the value of $x$ is
  • 0
  • $a^2$
  • $a$
  • $\frac{2a}{1−a^2}$
Q12: Which of the following is the principal value branch of $\text{cos}^{-1} x$?
  • $[−\pi/2, \pi/2]$
  • $(0, \pi)$
  • $[0, \pi]$
  • $(0, \pi) – \{\pi/2\}$
Q13: $\text{cosec}^{-1} (2)$
  • $\pi/6$
  • $2\pi/3$
  • $5\pi/6$
  • 0
Q14: $\text{sec}^{-1} (−2/\sqrt{3})$
  • $\pi/6$
  • $\pi/3$
  • $5\pi/6$
  • $-2\pi/3$
Q15: $\text{tan}^{-1} (\sqrt{3})$
  • $\pi/6$
  • $\pi/3$
  • $2\pi/3$
  • $5\pi/6$
Q16: If $\sin \{\sin^{-1} (1/2) + \cos^{-1} x\} = 1$, then the value of $x$ is
  • $1/2$
  • 0
  • 1
  • None of these
Q17: Solve for $x : \{x\cos(\cot^{-1} x) + \sin(\cot^{-1} x)\}^2 = \frac{51}{50}$
  • $\frac{1}{\sqrt{2}}$
  • $\frac{1}{5 \sqrt{2}}$
  • $2\sqrt{2}$
  • $5\sqrt{2}$
Q18: If $\text{sin}^{-1}(x^2 – 7x + 12) = n\pi, \forall n \in I$, then $x =$
  • -2
  • 4
  • -3
  • 5
Q19: If $\text{cos}^{-1} x + \text{sin}^{-1} x = \pi$, then the value of $x$ is
  • $\frac{3}{2}$
  • $\frac{1}{\sqrt{2}}$
  • $\frac{\sqrt{3}}{2}$
  • $\frac{2}{\sqrt{3}}$
Q20: If $\text{sin}^{-1} x – \text{cos}^{-1} x = \frac{\pi}{6}$, then $x =$
  • $\frac{1}{2}$
  • $\frac{\sqrt{3}}{2}$
  • $-\frac{1}{2}$
  • $-\frac{\sqrt{3}}{2}$
Q21: If $\text{tan}^{-1} (\cot \theta) = 2\theta$, then $\theta$ is equal to
  • $\frac{\pi}{3}$
  • $\frac{\pi}{4}$
  • $\frac{\pi}{6}$
  • None of these
Q22: $\cot(\frac{\pi}{4} – 2\cot^{-1} 3) =$
  • 7
  • 6
  • 5
  • None of these
Q23: If $\text{tan}^{-1} 3 + \text{tan}^{-1} x = \text{tan}^{-1} 8$, then $x =$
  • 5
  • $\frac{1}{5}$
  • $\frac{5}{14}$
  • $\frac{14}{5}$
Q24: If $\text{tan}^{-1} (x – 1) + \text{tan}^{-1} x + \text{tan}^{-1} (x + 1) = \text{tan}^{-1} 3x$, then the values of $x$ are
  • $\pm \frac{1}{2}$
  • $0, \frac{1}{2}$
  • $0, -\frac{1}{2}$
  • $0, \pm \frac{1}{2}$
Q25: If $6\text{sin}^{-1} (x^2 – 6x + 8.5) = \pi$, then $x$ is equal to
  • 1
  • 2
  • 3
  • 8
Q26: $\text{sin}^{-1} (1 – x) – 2\text{sin}^{-1} x = \frac{\pi}{2}$
  • 0
  • $1/2$
  • $0, 1/2$
  • $-1/2$
Q27: $2\text{tan}^{-1}(\cos x) = \text{tan}^{-1}(2\text{cosec } x)$
  • 0
  • $\pi/3$
  • $\pi/4$
  • $\pi/2$
Q28: The domain of the function defined by $f(x) = \text{sin}^{-1} \sqrt{x-1}$ is
  • [-1, 1]
  • none of these
Q29: The value of $\sin (2\text{tan}^{-1} (0.75))$ is equal to
  • 0.75
  • 1.5
  • 0.96
  • $\sin 1.5$
Q30: The value of expression $2 \text{sec}^{-1} 2 + \text{sin}^{-1}(\frac{1}{2})$
  • $\frac{\pi}{6}$
  • $\frac{5 \pi}{6}$
  • $\frac{7 \pi}{6}$
  • 1
Q31: The value of the expression $\tan (\frac{1}{2} \cos^{-1} \frac{2}{\sqrt{3}})$
  • $2 + \sqrt{5}$
  • $\sqrt{5} – 2$
  • $\frac{\sqrt{5}+2}{2}$
  • $5 + \sqrt{2}$
Q32: $\text{cos}^{-1}[\cos(2\cot^{-1}(\sqrt{2} – 1))] = \_\_\_\_\_\_$
  • $\sqrt{2} – 1$
  • $1 + \sqrt{2}$
  • $\frac{\pi}{4}$
  • $\frac{3 \pi}{4}$
Q33: The range of $\text{sin}^{-1} x + \text{cos}^{-1} x + \text{tan}^{-1} x$ is
  • $[0, \pi]$
  • $\left[\frac{\pi}{4}, \frac{3 \pi}{4}\right]$
  • $(0, \pi)$
  • $\left[0, \frac{\pi}{2}\right]$
Q34: Find the value of $\text{sec}^2 (\text{tan}^{-1} 2) + \text{cosec}^2 (\text{cot}^{-1} 3)$
  • 12
  • 5
  • 15
  • 9
Q35: The equation $\text{sin}^{-1} x – \text{cos}^{-1} x = \text{cos}^{-1}(\frac{\sqrt{3}}{2})$ has
  • unique solution
  • no solution
  • infinitely many solution
  • none of these
Q36: The equation $2\text{cos}^{-1} x + \text{sin}^{-1} x = \frac{11 \pi}{6}$ has
  • no solution
  • only one solution
  • two solutions
  • three solutions
Q37: If $\text{tan}^{-1} 2x + \text{tan}^{-1} 3x = \frac{\pi}{4}$, then $x$ is
  • $\frac{1}{6}$
  • 1
  • $(\frac{1}{6}, -1)$
  • none of these
Q38: If $\text{tan}^{-1} x – \text{tan}^{-1} y = \text{tan}^{-1} A$, then $A$ is equal to
  • $x – y$
  • $x + y$
  • $\frac{x-y}{1+x y}$
  • $\frac{x+y}{1-x y}$
Q39: The value of $\text{cot}^{-1} 9 + \text{cosec}^{-1}(\frac{\sqrt{41}}{4})$ is given by
  • 0
  • $\frac{\pi}{4}$
  • $\text{tan}^{-1} 2$
  • $\frac{\pi}{2}$
Q40: Which of the following is the principal value branch of $\text{cosec}^{-1} x$?
  • $(-\pi/2, \pi/2)$
  • $[0, \pi] – \{\pi/2\}$
  • $[-\pi/2, \pi/2]$
  • $[-\pi/2, \pi/2] – \{0\}$