This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions – Quiz 2 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 2 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. What is the principal value of Arctan $\sqrt{3}$ A) $\frac{\pi}{2}$. B) $\pi$. C) $\frac{4\pi}{3}$. D) $\frac{\pi}{3}$. Show Answer Correct Answer: D) $\frac{\pi}{3}$. 2. $\int\\frac{x^2dx}{\sqrt{1-x^6}}$ A) $-\frac{1}{3}\arcsin x^3+C$. B) $\frac{1}{3}\arccos x^3+C$. C) $\frac{1}{3}\arcsin x^3+C$. D) $-\frac{1}{3}\arccos x^3+C$. Show Answer Correct Answer: C) $\frac{1}{3}\arcsin x^3+C$. 3. I. Find the slope, the tangent and normal lines to the given curves at the points indicated. What is the first step in solving this problem? A) Calculate the derivative of the curve at the given point. B) Draw the curve on a graph. C) Estimate the slope visually. D) Find the y-intercept of the curve. Show Answer Correct Answer: A) Calculate the derivative of the curve at the given point. 4. Use a calculator to approximate the value of expression, if possible:$\arctan\left(-3.5\right)$ A) -1.12925. B) Not possible. C) 3.1416. D) 1.1659. Show Answer Correct Answer: A) -1.12925. 5. $\tan^{-1}\left(-\sqrt[]{3}\right)$ A) $\frac{\pi}{3}$. B) $-\frac{\pi}{6}$. C) $-\frac{\pi}{3}$. D) $-\frac{\pi}{4}$. Show Answer Correct Answer: C) $-\frac{\pi}{3}$. 6. Find the y' of the given implicit function:$2. xy^2 = tan(x+1)^2 + 1$ A) Dy/dx = $[2 sec^2(x+1)] / [2y]$. B) Dy/dx = $[tan(x+1) sec^2(x+1)] / [xy^2]$. C) Dy/dx = [2 tan(x+1)] / [xy]. D) Dy/dx = $[2 tan(x+1) sec^2(x+1)] / [2xy]$. Show Answer Correct Answer: D) Dy/dx = $[2 tan(x+1) sec^2(x+1)] / [2xy]$. 7. Complete the Sum Formula:tan(x + y) = ..... A) (tan x + tan y) / (1-tan x tan y). B) (tan x + tan y) / (1 + tan x tan y). C) (tan x-tan y) / (1-tan x tan y). D) (tan x-tan y) / (1 + tan x tan y). Show Answer Correct Answer: A) (tan x + tan y) / (1-tan x tan y). 8. Which of the following functions is even? A) $y=\sin^{-1}x$. B) $y=\cos^{-1}x$. C) $y=\tan^{-1}x$. D) None of the choices. Show Answer Correct Answer: D) None of the choices. 9. When $\theta = 35^\circ$ $\frac{d\theta}{dt} = 0.33$ $\frac{dx}{dt}$ A) -1.002 km/sec. B) -0.502 km/sec. C) 0.502 km/sec. D) 0.102 km/sec. Show Answer Correct Answer: B) -0.502 km/sec. 10. Express cot(x) in terms of sin and cos. A) Cot(x) = sin(x) * cos(x). B) Cot(x) = sin(x) / cos(x). C) Cot(x) = cos(x) / sin(x). D) Cot(x) = 1 / tan(x). Show Answer Correct Answer: C) Cot(x) = cos(x) / sin(x). 11. $\sin^{-1}\left(-\frac{\sqrt[]{2}}{2}\right)$ A) $\frac{\pi}{4}$. B) $-\frac{\pi}{6}$. C) $-\frac{\pi}{4}$. D) $0$. Show Answer Correct Answer: C) $-\frac{\pi}{4}$. 12. Which of the following is true about the inverse functions? A) The inverse function can be obtained by interchanging the x and y axes. B) The inverse of a function is always defined. C) The inverse function has the same range as the original function. D) The inverse function is always one-one. Show Answer Correct Answer: A) The inverse function can be obtained by interchanging the x and y axes. 13. $\cos\left(\sin^{-1}\left(\frac{1}{2}\right)\right)$ A) $\frac{\pi}{6}$. B) $\frac{\sqrt{2}}{2}$. C) $\frac{1}{2}$. D) $\frac{\sqrt{3}}{2}$. Show Answer Correct Answer: D) $\frac{\sqrt{3}}{2}$. 14. Fill in the blank for the Double Angle Formula:sin 2x = ..... A) $2 \sin^2 x$. B) $sin^2 x + cos^2 x$. C) 2 sin x cos x. D) Sin x + cos x. Show Answer Correct Answer: C) 2 sin x cos x. 15. Cos(arcsin(12/13)) A) 13/5. B) -13/12. C) 5/13. D) 13/12. Show Answer Correct Answer: C) 5/13. 16. What does $\tan^{-1}\left(\tan\left(45^{\circ}\right)\right)$ A) 0. B) $45^{\circ}$. C) $\tan\left(45^{\circ}\right)$. D) $\tan^{-1}\left(45\right)$. Show Answer Correct Answer: B) $45^{\circ}$. 17. Evaluate $\sin^{-1}(0)$ A) $\pi$. B) $\frac{\pi}{2}$. C) $\frac{\pi}{4}$. D) $0$. Show Answer Correct Answer: D) $0$. 18. Find the exact value of the expression:$\cos\left(\tan^{-1}2\right)$ A) $\frac{2\sqrt[]{5}}{5}$. B) $\sqrt[]{5}$. C) $\frac{1}{\sqrt[]{5}}$. D) $\frac{\sqrt[]{5}}{5}$. Show Answer Correct Answer: D) $\frac{\sqrt[]{5}}{5}$. 19. The integral $\int_{ }^{ }\frac{dx}{\sqrt{2x-x^2}}$ A) $\arccos\left(x-1\right)+c$. B) $\frac{1}{2}\arcsin\left(x-1\right)+c$. C) $\frac{1}{2}\arccos\left(x-1\right)+c$. D) $\arcsin\left(x-1\right)+c$. Show Answer Correct Answer: D) $\arcsin\left(x-1\right)+c$. 20. For the curve y = $sin^2(x)$ $\frac{\pi}{4}$ $\frac{1}{2}$ A) -1. B) 2. C) 1. D) 0. Show Answer Correct Answer: C) 1. 21. Which expression equals d/dx (arccot x)? A) $\frac{1}{1 + x^2}$. B) $\frac{1}{\sqrt{1-x^2}}$. C) $-\frac{1}{(1+x^2)}$. D) $-\frac{x}{(1+x^2)}$. Show Answer Correct Answer: C) $-\frac{1}{(1+x^2)}$. 22. A boy is flying a kite at a height of 50 meters. The kite is moving horizontally away from the boy, find the rate of the kite moving when the angle of elevation of the kite is 50$^\circ$ and changing at a rate of 1.25 rad/sec. What is the rate at which the kite is moving horizontally away from the boy? A) 60.0 m/sec. B) 32.1 m/sec. C) 75.0 m/sec. D) 48.0 m/sec. Show Answer Correct Answer: C) 75.0 m/sec. 23. Sin$^{-1 }$(1/2)= A) 30. B) 90. C) 1. D) 0. Show Answer Correct Answer: A) 30. 24. What is the relationship between arctan(x) and tan(arctan(x))? A) Arctan(x) = x. B) Tan(arctan(x)) = x. C) Arctan(tan(x)) = x. D) Tan(arctan(x)) = 1. Show Answer Correct Answer: B) Tan(arctan(x)) = x. 25. Identify the domain of $y=\arcsin\left(x\right)+1$ A) $0\le x\le\pi$. B) $-1\le x\le1$. C) $0\le x\le2$. D) $-\infty Show Answer Correct Answer: B) $-1\le x\le1$. 26. By the derivative of a quotient, if y = cot(u) = cos(u)/sin(u), what is dy/du? A) $sin^2(u)-\frac{cos^2(u)}{sin^2(u)}$. B) $-sin^2(u)-\frac{cos^2(u)}{sin^2(u)}$. C) $sin^2(u) + cos^2(u) / sin^2(u)$. D) $cos^2(u)-sin^2(u) / sin^2(u)$. Show Answer Correct Answer: B) $-sin^2(u)-\frac{cos^2(u)}{sin^2(u)}$. 27. For a function to have an inverse it must ..... A) Pass the vertical line test. B) Pass the horizontal line test. C) All the above. D) None of the above. Show Answer Correct Answer: B) Pass the horizontal line test. 28. If tan(x) = 3, find x using the inverse function. A) X = arctan(3). B) X = tan(1). C) X = sin(3). D) X = cos(3). Show Answer Correct Answer: A) X = arctan(3). 29. Find each value. Write angle measures in degrees and radians. $Arc\cos\left(-\frac{1}{2}\right)$ A) 90$^\circ$ or $\frac{\pi}{2}$. B) 120$^\circ$ or $\frac{2\pi}{3}$. C) 150$^\circ$ or $\frac{5\pi}{6}$. D) 60$^\circ$ or $\frac{\pi}{3}$. Show Answer Correct Answer: B) 120$^\circ$ or $\frac{2\pi}{3}$. 30. What is the inverse of the points (1, 3)(2, 4)(6, 8) A) (-3, -1)(-4, -2)(-8, -6). B) (-1, -3)(-2, -4)(-6, -8). C) (3, 1)(4, 2)(8, 6). D) (1, 3)(2, 4)(6, 8). Show Answer Correct Answer: C) (3, 1)(4, 2)(8, 6). 31. Arctan( $-\frac{\sqrt{3}}{3}$ A) $\frac{\pi}{6}$. B) $\frac{\pi}{3}$. C) $\frac{11\pi}{6}$. D) $-\frac{\pi}{6}$. Show Answer Correct Answer: D) $-\frac{\pi}{6}$. 32. Refer to the graph shown. Which trigonometric function does this graph represent? A) Y = cos x. B) Y = sin x. C) Y = csc x. D) Y = sec x. Show Answer Correct Answer: D) Y = sec x. 33. Evaluate $\cos^{-1}(-1)$ A) $\pi$. B) $0$. C) $\frac{\pi}{2}$. D) $\frac{3\pi}{2}$. Show Answer Correct Answer: A) $\pi$. 34. Differentiate the function y = $x^2 cot x$ A) $y' = 2x\cot x-x^2 \sec^2 x$. B) $y' = 2x\cot x-x^2\csc^2 x$. C) $y' = 2x\cot x + x^2\csc^2 x$. D) $y' = 2x \tan x-x^2 \sec^2 x$. Show Answer Correct Answer: B) $y' = 2x\cot x-x^2\csc^2 x$. 35. What kind of number do you get as a result of an inverse trigonometric function? A) Area. B) Angle. C) Vector. D) Scalar. Show Answer Correct Answer: B) Angle. 36. Describe the domain of the arccosine function. A) [-1, 0]. B) [0, 1]. C) [-1, 1]. D) [-2, 2]. Show Answer Correct Answer: C) [-1, 1]. 37. $Sin^{-1}\left\{Sin\left(\frac{2\pi}{3}\right)\right\}= ..... $ A) $\frac{-2\pi}{3}$. B) $\frac{\pi}{3}$. C) $\frac{-\pi}{3}$. D) $\frac{2\pi}{3}$. Show Answer Correct Answer: B) $\frac{\pi}{3}$. 38. A cylinder is to be inscribed in a given sphere. The shape of the cylinder for which its convex surface area is maximum is: A) A right circular cylinder whose height is half the diameter of its base. B) A right circular cylinder whose height is twice the radius of its base. C) A right circular cylinder whose height equals the diameter of its base. D) A right circular cylinder whose height equals the radius of its base. Show Answer Correct Answer: C) A right circular cylinder whose height equals the diameter of its base. 39. $\int\\frac{dx}{x\sqrt{4x^2-9}}$ A) $-\frac{1}{3}\operatorname{arcsec}\\frac{2x}{3}+C$. B) $\frac{1}{3}\operatorname{arcsec}\\frac{2x}{3}+C$. C) $-\frac{1}{3}\arctan\\frac{2x}{3}+C$. D) $\frac{1}{3}\arctan\\frac{2x}{3}+C$. Show Answer Correct Answer: B) $\frac{1}{3}\operatorname{arcsec}\\frac{2x}{3}+C$. 40. II. Find the second derivative of the given function:$2. y = csc((1/3)x^2)$ A) $y" =-csc((1/3)x^2) cot((1/3)x^2) (2/9)x^2-csc((1/3)x^2) (4/9)x^2$. B) Y" = $csc((1/3)x^2) cot((1/3)x^2) (4/9)x^2-csc((1/3)x^2) (4/9)x^2$. C) $y" =-csc((1/3)x^2) cot((1/3)x^2) (4/9)x^2-csc((1/3)x^2) (4/9)x^2$. D) $y" =-csc((1/3)x^2) cot((1/3)x^2) (4/9)x^2 + csc((1/3)x^2) (4/9)x^2$. Show Answer Correct Answer: C) $y" =-csc((1/3)x^2) cot((1/3)x^2) (4/9)x^2-csc((1/3)x^2) (4/9)x^2$. 41. Fill in the blank:The derivative of sin(u) with respect to u is ..... A) -sin(u). B) -cos(u). C) Sin(u). D) Cos(u). Show Answer Correct Answer: D) Cos(u). 42. $\cos^{-1}\left(\sin\left(\frac{5\pi}{3}\right)\right)=$ A) $-\frac{\pi}{6}$. B) $\frac{\pi}{3}$. C) $-\frac{\pi}{4}$. D) $\frac{5\pi}{6}$. Show Answer Correct Answer: D) $\frac{5\pi}{6}$. 43. Use a calculator to approximate the value of expression, if possible:$\cos^{-1}\left(-0.349\right)$ A) 12.3565. B) -1.9273. C) Not possible. D) 1.9273. Show Answer Correct Answer: D) 1.9273. 44. Complete the Double Angle Formula:cos 2x = ..... A) $cos^2 x + sin^2 x$. B) 1-2 $sin^2 x$. C) $2cos^2 x-1$. D) $cos^2 x-sin^2 x$. Show Answer Correct Answer: D) $cos^2 x-sin^2 x$. 45. If $\tan^{-1}\left(\frac{4}{3}\right)=x\\then\\\\cos x= ..... $ A) $\frac{3}{4}$. B) $\frac{4}{3}$. C) $\frac{3}{5}$. D) $\frac{5}{3}$. Show Answer Correct Answer: C) $\frac{3}{5}$. 46. From the figure shown, fill in the blank:sec A = ..... / ..... A) Opposite side / hypotenuse. B) Adjacent side / hypotenuse. C) Hypotenuse / adjacent side. D) Opposite side / adjacent side. Show Answer Correct Answer: C) Hypotenuse / adjacent side. 47. Evaluate. cos [ arccos(-2) ] A) $\frac{1}{2}$. B) 2. C) No solution. D) -2. Show Answer Correct Answer: C) No solution. 48. Refer to the figure shown (right triangle ABC). Fill in the blank:csc A = ..... A) Opposite side / hypotenuse. B) Adjacent side / hypotenuse. C) Opposite side / adjacent side. D) Hypotenuse / opposite side. Show Answer Correct Answer: D) Hypotenuse / opposite side. 49. From the trigonometric identity, A) 1. B) 0. C) Sin(u). D) 2. Show Answer Correct Answer: A) 1. 50. Complete the Sum Formula:sin(x + y) = ..... A) Sin x cos y-cos x sin y. B) Sin x cos y + cos x sin y. C) Sin x sin y + cos x cos y. D) Sin x sin y-cos x cos y. Show Answer Correct Answer: B) Sin x cos y + cos x sin y. 51. Which of the following is equal to $\cos2\theta$ A) $2\sin\theta\cos\theta$. B) $2\sin^2\theta-1$. C) $2\cos^2\theta+1$. D) None of the choices. Show Answer Correct Answer: D) None of the choices. 52. Sin $^{-1}$ [sin x]=x, for every x in A) [-1, 1]. B) [0. pie]. C) [-pie/2, pie/2]. D) None. Show Answer Correct Answer: C) [-pie/2, pie/2]. 53. I. What is the slope of the tangent line to a curve at a given point? A) The area under the curve at that point. B) The derivative of the curve at that point. C) The value of the curve at that point. D) The intercept of the curve at that point. Show Answer Correct Answer: B) The derivative of the curve at that point. 54. What is the first step in finding the slope, the tangent, and normal lines to a given curve at a specific point? A) Find the derivative of the curve at the given point. B) Draw the curve without calculation. C) Estimate the slope visually. D) Use the midpoint formula. Show Answer Correct Answer: A) Find the derivative of the curve at the given point. 55. Evaluate $\cos^{-1}(0)$ A) $\frac{3\pi}{2}$. B) $\pi$. C) $\frac{\pi}{4}$. D) $\frac{\pi}{2}$. Show Answer Correct Answer: D) $\frac{\pi}{2}$. 56. $Tan\left(ArcTan\left(3\right)\right)$ A) DNE. B) 1. C) 1/2. D) 3. Show Answer Correct Answer: D) 3. 57. Find the exact value of $\sin\left(\tan^{-1}\left(\sqrt{3}\right)\right)$ A) $-\frac{\sqrt{2}}{2}$. B) $\frac{\sqrt{2}}{2}$. C) $-\frac{\sqrt{3}}{2}$. D) $\frac{\sqrt{3}}{2}$. Show Answer Correct Answer: D) $\frac{\sqrt{3}}{2}$. 58. What is the domain of $\sin^{-1}\left(x\right)$ A) $\left(-\infty, -1\right)$. B) $\left(1, \infty\right)$. C) $\left[1, \infty\right)$. D) $\left(-\infty, -1\right]$. E) $\left[-1, 1\right]$. Show Answer Correct Answer: E) $\left[-1, 1\right]$. 59. Find the second derivative of the given function:v = $sin t + tan 2t$ $\frac{d^2v}{dt^2}$ A) $\frac{d^2v}{dt^2} =\cos t + 2 \sec^2 2t$. B) $d^2v/dt^2 =-sin t + 4 sec^2 2t tan 2t$. C) $\frac{d^2v}{dt^2} =-\cos t + 4 \tan^2 2t$. D) $\frac{d^2v}{dt^2} = \sin t + 8 \sec^2 2t \tan 2t$. Show Answer Correct Answer: B) $d^2v/dt^2 =-sin t + 4 sec^2 2t tan 2t$. 60. Evaluate $\sin^{-1}\left(-1\right)$ A) $-\frac{\pi}{4}$. B) $\frac{\pi}{2}$. C) $0$. D) $-\frac{\pi}{2}$. Show Answer Correct Answer: D) $-\frac{\pi}{2}$. ← PreviousNext →Related QuizzesScience QuizzesClass 12 QuizzesClass 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 1Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 3Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 4Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 5Class 12 Mathematics Chapter 1 Relations And Functions QuizClass 12 Mathematics Chapter 10 Vector Algebra QuizClass 12 Mathematics Chapter 11 Three Dimensional Geometry QuizClass 12 Mathematics Chapter 12 Linear Programming Quiz 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books