This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions – Quiz 5 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 5 (31 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. From the trigonometric identity, fill in the blank:$sin^2(u) + cos^2(u)$ A) 0. B) Sin(u) + cos(u). C) 2. D) 1. Show Answer Correct Answer: D) 1. 2. I. Find the slope, the tangent and normal lines to the given curves at the points indicated. What is the slope of the tangent line to the curve at the indicated point? A) The slope is equal to the y-coordinate of the point. B) The slope is equal to the derivative of the curve at the point. C) The slope is always zero at any point. D) The slope is equal to the x-coordinate of the point. Show Answer Correct Answer: B) The slope is equal to the derivative of the curve at the point. 3. If possible, find the exact value of the expression:$\tan^{-1}\left(1\right)$ A) 0. B) Not possible. C) $\frac{\pi}{2}$. D) $\frac{\pi}{4}$. Show Answer Correct Answer: D) $\frac{\pi}{4}$. 4. Which of the following is equal to $\sin\left(\alpha-\beta\right)$ A) $\sin\alpha\cos\beta-\sin\beta\cos\alpha$. B) $\cos\alpha\cos\beta+\sin\alpha\sin\beta$. C) $\cos\alpha\cos\beta-\sin\alpha\sin\beta$. D) $\sin\alpha\cos\beta+\sin\beta\cos\alpha$. Show Answer Correct Answer: A) $\sin\alpha\cos\beta-\sin\beta\cos\alpha$. 5. If possible, find the exact value of the expression:$\arcsin\left(-\frac{1}{2}\right)$ A) $-\frac{\pi}{6}$. B) $-\frac{\pi}{4}$. C) $\frac{\pi}{4}$. D) $\frac{\pi}{6}$. Show Answer Correct Answer: A) $-\frac{\pi}{6}$. 6. Complete the Power of Function:$sin^2 x$ A) $cos^2 x$. B) Sin 2x. C) 1/2 (1 + cos 2x). D) 1/2 (1-cos 2x). Show Answer Correct Answer: D) 1/2 (1-cos 2x). 7. $y=e^{\cos\left(3x\right)}$ A) $y'=-\sin\left(3x\right)e^{3x}$. B) $y'=3\sin\left(3x\right)e^{3x}$. C) $y'=-3\sin\left(3x\right)e^{3x}$. D) None of them. Show Answer Correct Answer: C) $y'=-3\sin\left(3x\right)e^{3x}$. 8. Fill in the blank:By the derivative of a quotient, if y = tan(u) = sin(u)/cos(u), then dy/du = ..... A) $-\sin(u)/\cos^2(u)$. B) $\frac{1}{\cos^2(u)}$. C) $cos^2(u) + \frac{sin^2(u)}{cos^2(u)}$. D) $sin^2(u) / cos^2(u)$. Show Answer Correct Answer: B) $\frac{1}{\cos^2(u)}$. 9. $\sin^{-1}\left(-0.2\right)$ A) $-78.1$. B) $-11.5$. C) $0$. D) $11.5$. Show Answer Correct Answer: B) $-11.5$. 10. Complete the Product of Functions:sin x cos y = ..... A) Sin(x) + cos(y). B) Sin(xy). C) 1/2 [sin(x + y)-sin(x-y)]. D) 1/2 [sin(x + y) + sin(x-y)]. Show Answer Correct Answer: D) 1/2 [sin(x + y) + sin(x-y)]. 11. Complete the Power of Function:$tan^2 x$ A) (1-cos 2x) / (1 + cos 2x). B) (1 + sin 2x) / (1-sin 2x). C) (1-sin 2x) / (1 + sin 2x). D) (1 + cos 2x) / (1-cos 2x). Show Answer Correct Answer: A) (1-cos 2x) / (1 + cos 2x). 12. The inverse of the function f(x) is written as ..... A) F $^{+}$(x). B) F $^{-1}$(x). C) F $^{2}$(x). D) F '(x). Show Answer Correct Answer: B) F $^{-1}$(x). 13. What is the inverse of tan(x)? A) Cot(x). B) Sin(x). C) Sec(x). D) Arctan(x). Show Answer Correct Answer: D) Arctan(x). 14. If sin(x) = 0.6, what is x in radians? A) 3.1416. B) 1.0472. C) 0.9273. D) 0.6435, 2.4981. Show Answer Correct Answer: D) 0.6435, 2.4981. 15. From the trigonometric identity, $sec^2 y = 1 + tan^2 y$ A) $sec^2 y = u^2-1$. B) $sec^2 y = 1-u^2$. C) $sec^2 y = 1/u^2$. D) $sec^2 y = 1 + u^2$. Show Answer Correct Answer: D) $sec^2 y = 1 + u^2$. 16. III. Find the y' of the given implicit function:$2xy^2 = \tan(x + 1)^2 + 1$ A) Y' = $[2sec^2(x+1)tan(x+1)-y^2]/[4xy]$. B) Y' = $[sec^2(x+1)tan(x+1)-y^2]/[4xy]$. C) $y' = \frac{sec^2(x+1)(tan(x+1)+1)-y^2}{4xy}$. D) Y' = $[2sec^2(x+1)(tan(x+1)+1)-y^2]/[4xy]$. Show Answer Correct Answer: D) Y' = $[2sec^2(x+1)(tan(x+1)+1)-y^2]/[4xy]$. 17. What does the negative sign indicate in the value of $\frac{dx}{dt}$ A) The negative sign indicates that the airplane is accelerating. B) The negative sign indicates that the airplane is moving away. C) The negative sign indicates that the airplane is approaching. D) The negative sign indicates that the airplane is stationary. Show Answer Correct Answer: C) The negative sign indicates that the airplane is approaching. 18. From the figure shown, fill in the blank:cot A = ..... / ..... A) Opposite side / adjacent side. B) Opposite side / hypotenuse. C) Adjacent side / opposite side. D) Hypotenuse / opposite side. Show Answer Correct Answer: C) Adjacent side / opposite side. 19. What happens to the domain and range when finding the inverse of a function? A) The domain becomes the range. B) They remain unchanged. C) The range becomes the domain. D) Both domain and range become infinite. Show Answer Correct Answer: C) The range becomes the domain. 20. The integration of f(x)= tan(x) dx is: A) Sec$^{2}$ (x) + C. B) Ln Isin(x)I +C. C) -ln Isin(x)I +C. D) -ln Icos(x)I + C. Show Answer Correct Answer: D) -ln Icos(x)I + C. 21. The derivative of arccos(4x) is A) $\frac{1}{\sqrt{1-4x^2}}$. B) $\frac{1}{\sqrt{1-16x^2}}$. C) $\frac{-4}{\sqrt{1-16x^2}}$. D) $\frac{-1}{\sqrt{1-16x^2}}$. Show Answer Correct Answer: C) $\frac{-4}{\sqrt{1-16x^2}}$. 22. Refer to the graph labeled 'y = tan x'. Which trigonometric function does this graph represent? A) Cotangent. B) Sine. C) Tangent. D) Cosine. Show Answer Correct Answer: C) Tangent. 23. Refer to the figure shown (right triangle ABC). cot A = ..... A) Hypotenuse / opposite side. B) Opposite side / hypotenuse. C) Opposite side / adjacent side. D) Adjacent side / opposite side. Show Answer Correct Answer: D) Adjacent side / opposite side. 24. The graph of the inverse sine function can be obtained by: A) Reflecting the graph of sine across the x-axis. B) Interchanging the x and y axes. C) Rotating the graph of sine. D) Reflecting the graph of sine across the y-axis. Show Answer Correct Answer: B) Interchanging the x and y axes. 25. Given the function $y = \tan^{-1}u$ A) $d/dx (tan^{-1}u) = du/dx / (1 + u^2)$. B) $d/dx (tan^{-1}u) = du/dx / (1-u^2)$. C) $d/dx (tan^{-1}u) = du/dx / (1 + 2u)$. D) $d/dx (tan^{-1}u) = du/dx * (1 + u^2)$. Show Answer Correct Answer: A) $d/dx (tan^{-1}u) = du/dx / (1 + u^2)$. 26. Fill in the blank:The final simplified derivative for cot(u) is dy/dx = ..... A) -$sec^2(u) du/dx$. B) $sec^2(u) du/dx$. C) -$-csc^2(u) du/dx$. D) $csc^2(u) du/dx$. Show Answer Correct Answer: C) -$-csc^2(u) du/dx$. 27. The integral $\int_{ }^{ }\frac{4x-5}{\sqrt{4x-x^2}}dx$ A) $-2\sqrt{4x-x^2}+3\arcsin\frac{\left(x-2\right)}{2}+c$. B) $-\sqrt{4x-x^2}+3\arcsin\frac{\left(x-2\right)}{2}+c$. C) $-4\sqrt{4x-x^2}+3\arcsin\frac{\left(x-2\right)}{2}+c$. D) $-\sqrt{4x-x^2}+\frac{3}{2}\arcsin\frac{\left(x-2\right)}{2}+c$. Show Answer Correct Answer: C) $-4\sqrt{4x-x^2}+3\arcsin\frac{\left(x-2\right)}{2}+c$. 28. $\int\\frac{dx}{9+x^2}$ A) $3\arctan\\frac{x}{3}+C$. B) $-3\arctan\\frac{x}{3}+C$. C) $\frac{1}{3}\arctan\\frac{x}{3}+C$. D) $-\frac{1}{3}\arctan\\frac{x}{3}+C$. Show Answer Correct Answer: C) $\frac{1}{3}\arctan\\frac{x}{3}+C$. 29. Refer to the graph labeled 'y = cos x'. Which trigonometric function does this graph represent? A) Sine. B) Cosecant. C) Cosine. D) Secant. Show Answer Correct Answer: C) Cosine. 30. Determine d/dx (arccot u) with u = u(x). A) $\frac{1}{\sqrt{1-u^2}}$. B) $\frac{-u'}{\sqrt{1-u^2}}$. C) $\frac{-u'}{(1+u^2)}$. D) $\frac{1}{1 + u^2}$. Show Answer Correct Answer: C) $\frac{-u'}{(1+u^2)}$. 31. Evaluate. $\tan^{-1}\left(\sin\left(\frac{3\pi}{2}\right)\right)$ A) $\frac{\pi}{4}$. B) $-\frac{\pi}{2}$. C) $-\frac{\pi}{4}$. D) UNDEFINED. E) $\frac{\pi}{2}$. Show Answer Correct Answer: C) $-\frac{\pi}{4}$. ← PreviousRelated QuizzesScience QuizzesClass 12 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 3Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 4Class 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