This quiz works best with JavaScript enabled. Home > Class 12 > 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 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Complete the Trigonometric Identity: A) $csc^2 A$. B) $sec^2 A$. C) $sin^2 A$. D) $tan^2 A$. Show Answer Correct Answer: A) $csc^2 A$. 2. By the derivative of a quotient, if y = tan(u) = sin(u)/cos(u), what is dy/du? A) Dy/du = $cos^2(u) + \frac{sin^2(u)}{cos^2(u)}$. B) Dy/du = $1 / cos^2(u)$. C) $dy/du = sin^2(u) / cos^2(u)$. D) Dy/du = cos(u) / sin(u). Show Answer Correct Answer: A) Dy/du = $cos^2(u) + \frac{sin^2(u)}{cos^2(u)}$. 3. 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. 4. $\sin^{-1}\left(\cos\left(\frac{\pi}{4}\right)\right)$ A) $\frac{\sqrt{2}}{2}$. B) $\frac{\pi}{6}$. C) $\frac{\pi}{4}$. D) $\frac{\pi}{3}$. Show Answer Correct Answer: C) $\frac{\pi}{4}$. 5. Fill in the blank for the Double Angle Formula:tan 2x = (2 tan x) / ( ..... ) A) $1-\tan^2 x$. B) $1 + \tan^2 x$. C) $tan^2 x-1$. D) $2 \tan^2 x$. Show Answer Correct Answer: A) $1-\tan^2 x$. 6. 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) Cos(u) du/dx. D) Tan(u) du/dx. Show Answer Correct Answer: A) $sec^2(u) du/dx$. 7. Given the function y = sin(u), what is the derivative of the function with respect to u? A) Cos(u). B) Sin(u). C) -sin(u). D) -cos(u). Show Answer Correct Answer: A) Cos(u). 8. 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. 9. What is the range for $\cos^{-1}\left(x\right)$ A) $\left(0, \\pi\right)$. B) $\left[0, \pi\right]$. C) $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$. D) $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$. Show Answer Correct Answer: B) $\left[0, \pi\right]$. 10. An airplane is flying at an altitude of 0.5 km above 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) 0.24 km/sec. B) 0.16 km/sec. C) 0.33 km/sec. D) 0.5 km/sec. Show Answer Correct Answer: A) 0.24 km/sec. 11. Evaluate. $\sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ A) $-\frac{\pi}{6}$. B) $-\frac{\pi}{4}$. C) $-\frac{\pi}{3}$. D) $\frac{5\pi}{3}$. E) $\frac{4\pi}{3}$. Show Answer Correct Answer: C) $-\frac{\pi}{3}$. 12. 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. 13. Evaluate $\cos^{-1}\left(-\frac{\sqrt{2}}{2}\right)$ A) $\frac{3\pi}{4}$. B) $\frac{5\pi}{6}$. C) $\frac{2\pi}{3}$. D) $\pi$. Show Answer Correct Answer: A) $\frac{3\pi}{4}$. 14. 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). 15. $\sin^{-1}\left(\frac{\sqrt[]{3}}{2}\right)$ A) $0$. B) $\frac{\pi}{2}$. C) $\frac{\pi}{3}$. D) $\frac{\pi}{6}$. Show Answer Correct Answer: C) $\frac{\pi}{3}$. 16. Complete the Product of Functions:sin x sin y = ..... A) 1/2 [cos(x-y)-cos(x + y)]. B) 1/2 [cos(x + y) + cos(x-y)]. C) Sin(x + y) + sin(x-y). D) Cos(x) cos(y). Show Answer Correct Answer: A) 1/2 [cos(x-y)-cos(x + y)]. 17. What does the negative sign in dx/dt indicate about the airplane's motion? A) The negative sign indicates that the airplane is approaching. 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 moving away. Show Answer Correct Answer: A) The negative sign indicates that the airplane is approaching. 18. What is the speed of the airplane according to the calculation shown? A) 0.502 km/sec. B) 0.250 km/sec. C) 1.000 km/sec. D) 0.750 km/sec. Show Answer Correct Answer: A) 0.502 km/sec. 19. 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. 20. $\operatorname{cosec}^{-1}\left(2\right)$ A) $\frac{\pi}{3}$. B) $\frac{\pi}{4}$. C) $\frac{\pi}{3}$. D) 1. Show Answer Correct Answer: A) $\frac{\pi}{3}$. 21. Evaluate $\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)$ A) $\frac{\pi}{6}$. B) $\frac{\pi}{4}$. C) $\frac{\pi}{3}$. D) $\frac{\pi}{2}$. Show Answer Correct Answer: A) $\frac{\pi}{6}$. 22. Find the first derivative of the given function:y = sin 5x A) Dy/dx = 5 cos 5x. B) Dy/dx = cos 5x. C) Dy/dx = 5 sin 5x. D) Dy/dx = 5 cos x. Show Answer Correct Answer: A) Dy/dx = 5 cos 5x. 23. Use a calculator to approximate the value of expression, if possible:$\arcsin\-1.1$ A) -3.258. B) 14.75. C) Not possible. D) -12.35. Show Answer Correct Answer: C) Not possible. 24. 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) 6.02 meters. B) 5.00 meters. C) 7.50 meters. D) 4.50 meters. Show Answer Correct Answer: A) 6.02 meters. 25. Evaluate. $\tan\left(\cos^{-1}\left(-\frac{3}{5}\right)\right)$ A) $-\frac{3}{5}$. B) $\frac{3}{5}$. C) $-\frac{4}{3}$. D) $\frac{4}{3}$. E) UNDEFINED. Show Answer Correct Answer: C) $-\frac{4}{3}$. ← PreviousNext →Related 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 2 Inverse Trigonometric Functions Quiz 6Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 7Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 8Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 9Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 10Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books