This quiz works best with JavaScript enabled. Home > Class 12 > 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 (25 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) $\frac{\pi}{4}$. B) $\frac{3\pi}{4}$. C) $-\frac{\pi}{4}$. D) $-\frac{3\pi}{4}$. Show Answer Correct Answer: B) $\frac{3\pi}{4}$. 2. Find the exact value of $\cos\left(\tan^{-1}\left(\frac{4}{3}\right)\right)$ A) $\frac{3}{5}$. B) $\frac{5}{3}$. C) $\frac{4}{5}$. D) $\frac{5}{4}$. Show Answer Correct Answer: A) $\frac{3}{5}$. 3. Find dy/dx. A) Dy/dx = $[2 \tan(x+1) \sec^2(x+1)] / [2xy]$. B) Dy/dx = $[tan(x+1) sec^2(x+1)] / [xy]$. C) Dy/dx = $[2 tan(x+1) sec^2(x+1)] / [xy]$. D) Dy/dx = $[tan(x+1) sec^2(x+1)] / [2xy]$. Show Answer Correct Answer: A) Dy/dx = $[2 \tan(x+1) \sec^2(x+1)] / [2xy]$. 4. Refer to the graph labeled 'y = cot x'. Which trigonometric function does this graph represent? A) Cotangent. B) Tangent. C) Secant. D) Sine. Show Answer Correct Answer: A) Cotangent. 5. Convert 1/sin(x) to its corresponding function. A) Tan(x). B) Cot(x). C) Sec(x). D) Csc(x). Show Answer Correct Answer: D) Csc(x). 6. 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) 6 meters. B) 7 meters. C) 8 meters. D) 9 meters. Show Answer Correct Answer: C) 8 meters. 7. 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) 3 feet. B) 5 feet. C) 8 feet. D) 7 feet. Show Answer Correct Answer: B) 5 feet. 8. $\sin^{-1}\left(\frac{2x}{1+x^2}\right)=2\tan^{-1}x\\\\if\\\ ..... $ A) $x<1$. B) $x\le1$. C) $\left|x\right|<1$. D) $\left|x\right|\le1$. Show Answer Correct Answer: D) $\left|x\right|\le1$. 9. Fill in the blank: A) 1. B) 0. C) 2. D) Sin A. Show Answer Correct Answer: A) 1. 10. 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) $y=\sin^{-1}x$ $y=\tan^{-1}x$. 11. $\sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)-2\sec^{-1}\left(2\tan\left(\frac{\pi}{6}\right)\right)$ A) $-\frac{\pi}{3}$. B) $-\frac{2\pi}{3}$. C) $\frac{\pi}{3}$. D) $\frac{2\pi}{3}$. Show Answer Correct Answer: B) $-\frac{2\pi}{3}$. 12. What is the value of $\arcsin(-\frac{\sqrt{3}}{2})-\arcsin(\frac{\sqrt{3}}{2})$ A) $-\frac{2\pi}{3}$. B) $-\frac{\pi}{4}$. C) $-\frac{\pi}{3}$. D) 0. Show Answer Correct Answer: A) $-\frac{2\pi}{3}$. 13. I. Find the first derivative of the given function:1. 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. 14. What does the negative sign indicate in the calculated speed of the airplane? A) The airplane is moving away. B) The airplane is approaching. C) The airplane is stationary. D) The airplane is accelerating. Show Answer Correct Answer: B) The airplane is approaching. 15. $\cot^{-1}\left(-1\right)= ..... $ A) $\frac{\pi}{4}$. B) $\frac{-\pi}{4}$. C) $\frac{3\pi}{4}$. D) $\frac{-3\pi}{4}$. Show Answer Correct Answer: C) $\frac{3\pi}{4}$. 16. Find $\arcsin\left(-\frac{\sqrt{3}}{2}\right)$ A) $-30^{\circ}$. B) $-60^{\circ}$. C) $120^{\circ}$. D) Does not exist. Show Answer Correct Answer: B) $-60^{\circ}$. 17. Given the function y = sec u, what is the derivative of the function with respect to x? A) Sec u tan u (du/dx). B) Sec u cot u (du/dx). C) Csc u cot u (du/dx). D) Sin u cos u (du/dx). Show Answer Correct Answer: A) Sec u tan u (du/dx). 18. 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: A) $\frac{u'}{\sqrt{1-u^2}}$. 19. 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) 0.23 km/sec. B) 0.16 km/sec. C) 0.29 km/sec. D) 0.41 km/sec. Show Answer Correct Answer: A) 0.23 km/sec. 20. What is the value of arcsin(-1) + arcsin(0), in radians? A) $\frac{-\pi}{2}$. B) $\frac{\pi}{2}$. C) -1. D) 0. Show Answer Correct Answer: A) $\frac{-\pi}{2}$. 21. 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) $y=\cos^{-1}x$. 22. I. Find the first derivative of the given function:4. x = $\sqrt{\sin t + t^2}$ A) $(cos t + 2t)/(2\sqrt{(sin t + t^2)}$. B) $\frac{(sin t + 2t)}{(2\sqrt{(sin t + t^2)})}$. C) $\frac{cos t + t^2}{2\sqrt{sin t + t^2}}$. D) $\frac{(cos t + 2t)}{\sqrt{(sin t + t^2)}}$. Show Answer Correct Answer: A) $(cos t + 2t)/(2\sqrt{(sin t + t^2)}$. 23. What does $\cos\left(\arccos\left(88\right)\right)$ A) 88. B) 0. C) $\cos\left(88^{\circ}\right)$. D) $\cos^{-1}\left(88\right)$. Show Answer Correct Answer: A) 88. 24. The integral $\int_{ }^{ }\frac{x^2}{4+x^2}dx$ A) $x+2\arctan\left(\frac{x}{2}\right)+C$. B) $x-4\arctan\left(\frac{x}{2}\right)+C$. C) $x-2\arctan\left(\frac{x}{2}\right)+C$. D) $x-\frac{1}{2}\arctan\left(\frac{x}{2}\right)+C$. Show Answer Correct Answer: C) $x-2\arctan\left(\frac{x}{2}\right)+C$. 25. Find d/dx (arccsc u) when u = u(x). A) $\frac{-u'}{|u|\\sqrt[]{u^2-1}}$. B) $\frac{1}{|u|\\sqrt[]{u^2-1}}$. C) $\frac{1}{1 + u^2}$. D) $\frac{-u'}{\sqrt{1-u^2}}$. Show Answer Correct Answer: A) $\frac{-u'}{|u|\\sqrt[]{u^2-1}}$. Next →Related 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 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