This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions – Quiz 3 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 3 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. The integral $\int_0^{2\sqrt{3}}\frac{dx}{4+x^2}$ A) $\arctan\left(2\sqrt{3}\right)$. B) $\frac{\pi}{3}$. C) $\frac{\pi}{12}$. D) $\frac{\pi}{6}$. Show Answer Correct Answer: D) $\frac{\pi}{6}$. 2. 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]. 3. Fill in the blank for the Trigonometric Identity:$cot^2 A + 1 = csc^2 A$ A) $csc^2 A$. B) $sec^2 A$. C) $sin^2 A$. D) $tan^2 A$. Show Answer Correct Answer: A) $csc^2 A$. 4. The derivative of arctan(3x) is A) $\frac{1}{1+3x^2}$. B) $\frac{3}{1+9x^2}$. C) $\frac{9}{1+9x^2}$. D) $\frac{3}{1+3x^2}$. Show Answer Correct Answer: B) $\frac{3}{1+9x^2}$. 5. Refer to the graph labeled 'y = csc x'. Which trigonometric function does this graph represent? A) Cosecant. B) Sine. C) Cosine. D) Secant. Show Answer Correct Answer: A) Cosecant. 6. $\int\\frac{dx}{4x^2+9}$ A) $\frac{1}{3}\arctan\\frac{2x}{3}+C$. B) $-\frac{1}{3}\arctan\\frac{2x}{3}+C$. C) $\frac{1}{6}\arctan\\frac{2x}{3}+C$. D) $-\frac{1}{6}\arctan\\frac{2x}{3}+C$. Show Answer Correct Answer: C) $\frac{1}{6}\arctan\\frac{2x}{3}+C$. 7. What is d/dx (arccos x)? A) $\frac{1}{\sqrt{1-x^2}}$. B) $-\frac{1}{\sqrt{1-x^2}}$. C) $\frac{1}{1 + x^2}$. D) $-\frac{1}{(1+x^2)}$. Show Answer Correct Answer: B) $-\frac{1}{\sqrt{1-x^2}}$. 8. Tan(ArcSin(x/2)) A) DNE. B) $\frac{x}{\sqrt[]{4-x^2}}$. C) $\frac{x}{2-x}$. D) $\frac{2}{x}$. Show Answer Correct Answer: B) $\frac{x}{\sqrt[]{4-x^2}}$. 9. $\tan^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ A) $-\frac{\pi}{4}$. B) $-\frac{\pi}{2}$. C) $0$. D) $-\frac{\pi}{6}$. Show Answer Correct Answer: D) $-\frac{\pi}{6}$. 10. 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 = 3 sec t tan 3t. D) Dx/dt = sec 3t tan 3t. Show Answer Correct Answer: A) Dx/dt = 3 sec 3t tan 3t. 11. Fill in the blank for the Trigonometric Identity:$tan^2 A + 1 = sec^2 A$ A) $sec^2 A$. B) $cosec^2 A$. C) $sin^2 A$. D) $cot^2 A$. Show Answer Correct Answer: A) $sec^2 A$. 12. Refer to the figure shown (right triangle ABC). Fill in the blank:sin A = ..... A) Opposite side / hypotenuse. B) Adjacent side / hypotenuse. C) Opposite side / adjacent side. D) Adjacent side / opposite side. Show Answer Correct Answer: A) Opposite side / hypotenuse. 13. Find the second derivative of the given function:v = sin t + tan 2t. A) V" =-sin t + 4 $sec^2 2t tan 2t$. B) V" = $cos t + 2 sec^2 2t$. C) V" =-cos t + 4 $sec^2 2t tan 2t$. D) V" =-sin t + $2 sec^2 2t$. Show Answer Correct Answer: A) V" =-sin t + 4 $sec^2 2t tan 2t$. 14. What is the principal value of Arctan $\sqrt{3}$ A) $\pi$. B) $\frac{\pi}{2}$. C) $\frac{\pi}{3}$. D) $\frac{4\pi}{3}$. Show Answer Correct Answer: C) $\frac{\pi}{3}$. 15. $\int\\frac{x^2dx}{\sqrt{1-x^6}}$ A) $\frac{1}{3}\arccos x^3+C$. B) $-\frac{1}{3}\arccos x^3+C$. C) $\frac{1}{3}\arcsin x^3+C$. D) $-\frac{1}{3}\arcsin x^3+C$. Show Answer Correct Answer: C) $\frac{1}{3}\arcsin x^3+C$. 16. 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. 17. Use a calculator to approximate the value of expression, if possible:$\arctan\left(-3.5\right)$ A) -1.12925. B) 1.1659. C) Not possible. D) 3.1416. Show Answer Correct Answer: A) -1.12925. 18. $\tan^{-1}\left(-\sqrt[]{3}\right)$ A) $-\frac{\pi}{3}$. B) $-\frac{\pi}{6}$. C) $\frac{\pi}{3}$. D) $-\frac{\pi}{4}$. Show Answer Correct Answer: A) $-\frac{\pi}{3}$. 19. Find the y' of the given implicit function:$2. xy^2 = tan(x+1)^2 + 1$ A) Dy/dx = $[2 tan(x+1) sec^2(x+1)] / [2xy]$. B) Dy/dx = $[2 sec^2(x+1)] / [2y]$. C) Dy/dx = $[tan(x+1) sec^2(x+1)] / [xy^2]$. D) Dy/dx = [2 tan(x+1)] / [xy]. Show Answer Correct Answer: A) Dy/dx = $[2 tan(x+1) sec^2(x+1)] / [2xy]$. 20. 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). 21. 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. 22. When $\theta = 35^\circ$ $\frac{d\theta}{dt} = 0.33$ $\frac{dx}{dt}$ A) -0.502 km/sec. B) 0.502 km/sec. C) -1.002 km/sec. D) 0.102 km/sec. Show Answer Correct Answer: A) -0.502 km/sec. 23. Express cot(x) in terms of sin and cos. A) Cot(x) = sin(x) / cos(x). B) Cot(x) = cos(x) / sin(x). C) Cot(x) = 1 / tan(x). D) Cot(x) = sin(x) * cos(x). Show Answer Correct Answer: B) Cot(x) = cos(x) / sin(x). 24. $\sin^{-1}\left(-\frac{\sqrt[]{2}}{2}\right)$ A) $-\frac{\pi}{6}$. B) $\frac{\pi}{4}$. C) $-\frac{\pi}{4}$. D) $0$. Show Answer Correct Answer: C) $-\frac{\pi}{4}$. 25. 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. ← PreviousNext →Related QuizzesClass 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 1Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 2Class 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