This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions – Quiz 1 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 1 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Find the principal value of $\sec^{-1}\left(-\sqrt{2}\right)$ A) $-\frac{3\pi}{4}$. B) $-\frac{\pi}{4}$. C) $\frac{\pi}{4}$. D) $\frac{3\pi}{4}$. Show Answer Correct Answer: D) $\frac{3\pi}{4}$. 2. Find the exact value of $\cos\left(\tan^{-1}\left(\frac{4}{3}\right)\right)$ A) $\frac{5}{3}$. B) $\frac{5}{4}$. C) $\frac{3}{5}$. D) $\frac{4}{5}$. Show Answer Correct Answer: C) $\frac{3}{5}$. 3. Refer to the graph labeled 'y = cot x'. Which trigonometric function does this graph represent? A) Tangent. B) Sine. C) Cotangent. D) Secant. Show Answer Correct Answer: C) Cotangent. 4. Convert 1/sin(x) to its corresponding function. A) Tan(x). B) Sec(x). C) Cot(x). D) Csc(x). Show Answer Correct Answer: D) Csc(x). 5. A wall is 3 meters away from a building. The shortest ladder that can reach the building with one end resting on the ground outside the wall is 10 meters. How high is the wall? A) 8 meters. B) 7 meters. C) 6 meters. D) 9 meters. Show Answer Correct Answer: A) 8 meters. 6. A ladder leans against a wall forming a 30$^\circ$ angle with the ground. What is the height of the wall if the ladder is 10 feet long? A) 8 feet. B) 5 feet. C) 3 feet. D) 7 feet. Show Answer Correct Answer: B) 5 feet. 7. $\sin^{-1}\left(\frac{2x}{1+x^2}\right)=2\tan^{-1}x\\\\if\\\ ..... $ A) $x<1$. B) $x\le1$. C) $\left|x\right|\le1$. D) $\left|x\right|<1$. Show Answer Correct Answer: C) $\left|x\right|\le1$. 8. Fill in the blank: A) 0. B) 2. C) 1. D) Sin A. Show Answer Correct Answer: C) 1. 9. Which of the following pairs of functions are both odd? A) $y=\sin^{-1}x$ $y=\cos^{-1}x$. B) $y=\sin^{-1}x$ $y=\tan^{-1}x$. C) $y=\cos^{-1}x$ $y=\tan^{-1}x$. D) None of the choices. Show Answer Correct Answer: B) $y=\sin^{-1}x$ $y=\tan^{-1}x$. 10. $\sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)-2\sec^{-1}\left(2\tan\left(\frac{\pi}{6}\right)\right)$ A) $\frac{2\pi}{3}$. B) $-\frac{2\pi}{3}$. C) $\frac{\pi}{3}$. D) $-\frac{\pi}{3}$. Show Answer Correct Answer: B) $-\frac{2\pi}{3}$. 11. What is the value of $\arcsin(-\frac{\sqrt{3}}{2})-\arcsin(\frac{\sqrt{3}}{2})$ A) $-\frac{\pi}{3}$. B) $-\frac{2\pi}{3}$. C) 0. D) $-\frac{\pi}{4}$. Show Answer Correct Answer: B) $-\frac{2\pi}{3}$. 12. I. Find the first derivative of the given function:1. y = sin 5x A) Dy/dx = cos 5x. B) Dy/dx = 5 cos 5x. C) Dy/dx = 5 cos x. D) Dy/dx = 5 sin 5x. Show Answer Correct Answer: B) Dy/dx = 5 cos 5x. 13. What does the negative sign indicate in the calculated speed of the airplane? A) The airplane is moving away. B) The airplane is stationary. C) The airplane is approaching. D) The airplane is accelerating. Show Answer Correct Answer: C) The airplane is approaching. 14. $\cot^{-1}\left(-1\right)= ..... $ A) $\frac{\pi}{4}$. B) $\frac{-3\pi}{4}$. C) $\frac{-\pi}{4}$. D) $\frac{3\pi}{4}$. Show Answer Correct Answer: D) $\frac{3\pi}{4}$. 15. Find $\arcsin\left(-\frac{\sqrt{3}}{2}\right)$ A) Does not exist. B) $-30^{\circ}$. C) $-60^{\circ}$. D) $120^{\circ}$. Show Answer Correct Answer: C) $-60^{\circ}$. 16. Given the function y = sec u, what is the derivative of the function with respect to x? A) Sec u cot u (du/dx). B) Sin u cos u (du/dx). C) Sec u tan u (du/dx). D) Csc u cot u (du/dx). Show Answer Correct Answer: C) Sec u tan u (du/dx). 17. Apply the chain rule:d/dx (arcsin u) where u = u(x). A) $\frac{-u'}{\sqrt{1-u^2}}$. B) $\frac{1}{1 + u^2}$. C) $\frac{u'}{\sqrt{1-u^2}}$. D) $\frac{|u|}{\sqrt[]{u^2-1}}$. Show Answer Correct Answer: C) $\frac{u'}{\sqrt{1-u^2}}$. 18. An airplane is flying at an altitude of 0.5 km above an observer. At a given instant, an observer notes that the angle of elevation of the airplane is 35 degrees and is increasing at a rate of 0.33 radian/sec. What is the speed of the airplane? A) 0.16 km/sec. B) 0.29 km/sec. C) 0.41 km/sec. D) 0.23 km/sec. Show Answer Correct Answer: D) 0.23 km/sec. 19. What is the value of arcsin(-1) + arcsin(0), in radians? A) $\frac{-\pi}{2}$. B) -1. C) 0. D) $\frac{\pi}{2}$. Show Answer Correct Answer: A) $\frac{-\pi}{2}$. 20. Which of the following functions is decreasing? A) $y=\sin^{-1}x$. B) $y=\cos^{-1}x$. C) $y=\tan^{-1}x$. D) None of the choices. Show Answer Correct Answer: B) $y=\cos^{-1}x$. 21. I. Find the first derivative of the given function:4. x = $\sqrt{\sin t + t^2}$ A) $\frac{(sin t + 2t)}{(2\sqrt{(sin t + t^2)})}$. B) $\frac{cos t + t^2}{2\sqrt{sin t + t^2}}$. C) $\frac{(cos t + 2t)}{\sqrt{(sin t + t^2)}}$. D) $(cos t + 2t)/(2\sqrt{(sin t + t^2)}$. Show Answer Correct Answer: D) $(cos t + 2t)/(2\sqrt{(sin t + t^2)}$. 22. What does $\cos\left(\arccos\left(88\right)\right)$ A) $\cos\left(88^{\circ}\right)$. B) 88. C) 0. D) $\cos^{-1}\left(88\right)$. Show Answer Correct Answer: B) 88. 23. The integral $\int_{ }^{ }\frac{x^2}{4+x^2}dx$ A) $x-\frac{1}{2}\arctan\left(\frac{x}{2}\right)+C$. B) $x-4\arctan\left(\frac{x}{2}\right)+C$. C) $x+2\arctan\left(\frac{x}{2}\right)+C$. D) $x-2\arctan\left(\frac{x}{2}\right)+C$. Show Answer Correct Answer: D) $x-2\arctan\left(\frac{x}{2}\right)+C$. 24. Find d/dx (arccsc u) when u = u(x). A) $\frac{1}{|u|\\sqrt[]{u^2-1}}$. B) $\frac{-u'}{\sqrt{1-u^2}}$. C) $\frac{1}{1 + u^2}$. D) $\frac{-u'}{|u|\\sqrt[]{u^2-1}}$. Show Answer Correct Answer: D) $\frac{-u'}{|u|\\sqrt[]{u^2-1}}$. 25. Complete the Trigonometric Identity: A) $sec^2 A$. B) $sin^2 A$. C) $tan^2 A$. D) $csc^2 A$. Show Answer Correct Answer: D) $csc^2 A$. 26. By the derivative of a quotient, if y = tan(u) = sin(u)/cos(u), what is dy/du? A) $dy/du = sin^2(u) / cos^2(u)$. B) Dy/du = $cos^2(u) + \frac{sin^2(u)}{cos^2(u)}$. C) Dy/du = $1 / cos^2(u)$. D) Dy/du = cos(u) / sin(u). Show Answer Correct Answer: B) Dy/du = $cos^2(u) + \frac{sin^2(u)}{cos^2(u)}$. 27. Which of the following tasks involves finding the critical points, determining maxima and minima, and finding inflection points of a curve? A) Analyzing the curve for its turning and inflection points. B) Calculating the area under the curve. C) Finding the equation of the tangent line. D) Determining the symmetry of the curve. Show Answer Correct Answer: A) Analyzing the curve for its turning and inflection points. 28. $\sin^{-1}\left(\cos\left(\frac{\pi}{4}\right)\right)$ A) $\frac{\sqrt{2}}{2}$. B) $\frac{\pi}{3}$. C) $\frac{\pi}{6}$. D) $\frac{\pi}{4}$. Show Answer Correct Answer: D) $\frac{\pi}{4}$. 29. Fill in the blank for the Double Angle Formula:tan 2x = (2 tan x) / ( ..... ) A) $2 \tan^2 x$. B) $1 + \tan^2 x$. C) $1-\tan^2 x$. D) $tan^2 x-1$. Show Answer Correct Answer: C) $1-\tan^2 x$. 30. Given the function y = tan(u), fill in the blank:The derivative of the function is d/dx tan(u) = ..... A) $sec^2(u) du/dx$. B) Sin(u) du/dx. C) Tan(u) du/dx. D) Cos(u) du/dx. Show Answer Correct Answer: A) $sec^2(u) du/dx$. 31. Given the function y = sin(u), what is the derivative of the function with respect to u? A) -cos(u). B) Sin(u). C) Cos(u). D) -sin(u). Show Answer Correct Answer: C) Cos(u). 32. In the unit circle, which quadrants are used for the principal values of the inverse sine function? A) Quadrants II and III. B) Quadrants I and IV. C) Quadrants III and IV. D) Quadrants I and II. Show Answer Correct Answer: B) Quadrants I and IV. 33. What is the range for $\cos^{-1}\left(x\right)$ A) $\left[0, \pi\right]$. B) $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$. C) $\left(0, \\pi\right)$. D) $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$. Show Answer Correct Answer: A) $\left[0, \pi\right]$. 34. Evaluate. $\sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ A) $-\frac{\pi}{4}$. B) $-\frac{\pi}{3}$. C) $\frac{4\pi}{3}$. D) $\frac{5\pi}{3}$. E) $-\frac{\pi}{6}$. Show Answer Correct Answer: B) $-\frac{\pi}{3}$. 35. Discuss the significance of inverse trigonometric functions in physics. A) They are used to calculate the speed of light in a vacuum. B) They help in solving quadratic equations in physics. C) Inverse trigonometric functions are significant in physics for determining angles from side ratios in various applications, including mechanics and wave motion. D) Inverse trigonometric functions are only relevant in pure mathematics. Show Answer Correct Answer: C) Inverse trigonometric functions are significant in physics for determining angles from side ratios in various applications, including mechanics and wave motion. 36. Evaluate $\cos^{-1}\left(-\frac{\sqrt{2}}{2}\right)$ A) $\frac{2\pi}{3}$. B) $\frac{5\pi}{6}$. C) $\frac{3\pi}{4}$. D) $\pi$. Show Answer Correct Answer: C) $\frac{3\pi}{4}$. 37. Convert 1/tan(x) to its corresponding function. A) Cot(x). B) Sec(x). C) Tan(x). D) Csc(x). Show Answer Correct Answer: A) Cot(x). 38. $\sin^{-1}\left(\frac{\sqrt[]{3}}{2}\right)$ A) $\frac{\pi}{6}$. B) $0$. C) $\frac{\pi}{3}$. D) $\frac{\pi}{2}$. Show Answer Correct Answer: C) $\frac{\pi}{3}$. 39. Complete the Product of Functions:sin x sin y = ..... A) 1/2 [cos(x + y) + cos(x-y)]. B) Sin(x + y) + sin(x-y). C) 1/2 [cos(x-y)-cos(x + y)]. D) Cos(x) cos(y). Show Answer Correct Answer: C) 1/2 [cos(x-y)-cos(x + y)]. 40. What does the negative sign in dx/dt indicate about the airplane's motion? A) The negative sign indicates that the airplane is moving away. B) The negative sign indicates that the airplane is accelerating. C) The negative sign indicates that the airplane is moving upward. D) The negative sign indicates that the airplane is approaching. Show Answer Correct Answer: D) The negative sign indicates that the airplane is approaching. 41. What is the speed of the airplane according to the calculation shown? A) 1.000 km/sec. B) 0.502 km/sec. C) 0.750 km/sec. D) 0.250 km/sec. Show Answer Correct Answer: B) 0.502 km/sec. 42. Does sin(sin$^{-1}$2)=2? A) Yes. B) No. C) All the above. D) None of the above. Show Answer Correct Answer: B) No. 43. $\operatorname{cosec}^{-1}\left(2\right)$ A) $\frac{\pi}{3}$. B) $\frac{\pi}{3}$. C) 1. D) $\frac{\pi}{4}$. Show Answer Correct Answer: A) $\frac{\pi}{3}$. 44. Evaluate $\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)$ A) $\frac{\pi}{3}$. B) $\frac{\pi}{4}$. C) $\frac{\pi}{2}$. D) $\frac{\pi}{6}$. Show Answer Correct Answer: D) $\frac{\pi}{6}$. 45. Use a calculator to approximate the value of expression, if possible:$\arcsin\-1.1$ A) -12.35. B) 14.75. C) Not possible. D) -3.258. Show Answer Correct Answer: C) Not possible. 46. A wall 4 meters high is 3.5 meters away from a building. What is the minimum length of a ladder that can reach the building with one end resting on the ground outside the wall? A) 4.50 meters. B) 5.00 meters. C) 6.02 meters. D) 7.50 meters. Show Answer Correct Answer: C) 6.02 meters. 47. Evaluate. $\tan\left(\cos^{-1}\left(-\frac{3}{5}\right)\right)$ A) $-\frac{3}{5}$. B) $-\frac{4}{3}$. C) $\frac{4}{3}$. D) $\frac{3}{5}$. E) UNDEFINED. Show Answer Correct Answer: B) $-\frac{4}{3}$. 48. The integral $\int_0^{2\sqrt{3}}\frac{dx}{4+x^2}$ A) $\arctan\left(2\sqrt{3}\right)$. B) $\frac{\pi}{6}$. C) $\frac{\pi}{3}$. D) $\frac{\pi}{12}$. Show Answer Correct Answer: B) $\frac{\pi}{6}$. 49. Which of the following statements is true regarding the sine function? A) It does not have an inverse. B) It is defined for all real numbers. C) It has a range of [-1, 1]. D) It is one-one and onto over its natural domain. Show Answer Correct Answer: C) It has a range of [-1, 1]. 50. Fill in the blank for the Trigonometric Identity:$cot^2 A + 1 = csc^2 A$ A) $sin^2 A$. B) $tan^2 A$. C) $sec^2 A$. D) $csc^2 A$. Show Answer Correct Answer: D) $csc^2 A$. 51. The derivative of arctan(3x) is A) $\frac{1}{1+3x^2}$. B) $\frac{9}{1+9x^2}$. C) $\frac{3}{1+9x^2}$. D) $\frac{3}{1+3x^2}$. Show Answer Correct Answer: C) $\frac{3}{1+9x^2}$. 52. Refer to the graph labeled 'y = csc x'. Which trigonometric function does this graph represent? A) Sine. B) Cosine. C) Cosecant. D) Secant. Show Answer Correct Answer: C) Cosecant. 53. $\int\\frac{dx}{4x^2+9}$ A) $-\frac{1}{6}\arctan\\frac{2x}{3}+C$. B) $-\frac{1}{3}\arctan\\frac{2x}{3}+C$. C) $\frac{1}{3}\arctan\\frac{2x}{3}+C$. D) $\frac{1}{6}\arctan\\frac{2x}{3}+C$. Show Answer Correct Answer: D) $\frac{1}{6}\arctan\\frac{2x}{3}+C$. 54. What is d/dx (arccos x)? A) $-\frac{1}{(1+x^2)}$. B) $-\frac{1}{\sqrt{1-x^2}}$. C) $\frac{1}{\sqrt{1-x^2}}$. D) $\frac{1}{1 + x^2}$. Show Answer Correct Answer: B) $-\frac{1}{\sqrt{1-x^2}}$. 55. Tan(ArcSin(x/2)) A) $\frac{x}{\sqrt[]{4-x^2}}$. B) DNE. C) $\frac{x}{2-x}$. D) $\frac{2}{x}$. Show Answer Correct Answer: A) $\frac{x}{\sqrt[]{4-x^2}}$. 56. $\tan^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ A) $-\frac{\pi}{4}$. B) $-\frac{\pi}{6}$. C) $-\frac{\pi}{2}$. D) $0$. Show Answer Correct Answer: B) $-\frac{\pi}{6}$. 57. I. Find the first derivative of the given function:3. x = sec 3t. Find dx/dt. A) Dx/dt = 3 sec 3t tan 3t. B) Dx/dt = sec 3t tan t. C) Dx/dt = sec 3t tan 3t. D) Dx/dt = 3 sec t tan 3t. Show Answer Correct Answer: A) Dx/dt = 3 sec 3t tan 3t. 58. Fill in the blank for the Trigonometric Identity:$tan^2 A + 1 = sec^2 A$ A) $sin^2 A$. B) $sec^2 A$. C) $cosec^2 A$. D) $cot^2 A$. Show Answer Correct Answer: B) $sec^2 A$. 59. Refer to the figure shown (right triangle ABC). Fill in the blank:sin A = ..... A) Opposite side / adjacent side. B) Adjacent side / hypotenuse. C) Adjacent side / opposite side. D) Opposite side / hypotenuse. Show Answer Correct Answer: D) Opposite side / hypotenuse. 60. Find the second derivative of the given function:v = sin t + tan 2t. A) V" =-cos t + 4 $sec^2 2t tan 2t$. B) V" =-sin t + 4 $sec^2 2t tan 2t$. C) V" = $cos t + 2 sec^2 2t$. D) V" =-sin t + $2 sec^2 2t$. Show Answer Correct Answer: B) V" =-sin t + 4 $sec^2 2t tan 2t$. Next →Related QuizzesScience QuizzesClass 12 QuizzesClass 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 2Class 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