This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions – Quiz 11 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 11 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. 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. What is the height of the wall? A) 6 meters. B) 7 meters. C) 8 meters. D) 5 meters. Show Answer Correct Answer: A) 6 meters. 2. What kind of number do you plug into a trigonometric function? A) Scalar. B) Vector. C) Angle. D) Area. Show Answer Correct Answer: C) Angle. 3. If $\cos\left(\tan^{-1}x\right)=\sin\left(\cot^{-1}\left(\frac{3}{4}\right)\right)$ A) X=3/4. B) X=-3/4. C) X=3/4, -3/4. D) None of the above. Show Answer Correct Answer: C) X=3/4, -3/4. 4. For the minimum length of the ladder, L = x + y = 4/sin(46.27$^\circ$) + 3.5/cos(46.27$^\circ$). What is the minimum length of the ladder? A) 10.6 meters. B) 8.2 meters. C) 12.4 meters. D) 9.7 meters. Show Answer Correct Answer: A) 10.6 meters. 5. III. Find the y' of the given implicit function:$4. x^2 y\cos y = \sin x + \tan y$ A) Y' = $[cos x + sec^2 y] / [x^2 cos y-x^2 y sin y-x^2 sin y]$. B) Y' = $[cos x + sec^2 y] / [x^2 cos y-x^2 y sin y]$. C) Y' = $[cos x + sec^2 y] / [x^2 cos y + x^2 y sin y]$. D) Y' = $[cos x-sec^2 y] / [x^2 cos y-x^2 y sin y]$. Show Answer Correct Answer: A) Y' = $[cos x + sec^2 y] / [x^2 cos y-x^2 y sin y-x^2 sin y]$. 6. From the trigonometric identity, fill in the blank:$sin^2(u) + cos^2(u)$ A) 1. B) 0. C) 2. D) Sin(u) + cos(u). Show Answer Correct Answer: A) 1. 7. 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 derivative of the curve at the point. B) The slope is always zero at any point. C) The slope is equal to the y-coordinate of the point. D) The slope is equal to the x-coordinate of the point. Show Answer Correct Answer: A) The slope is equal to the derivative of the curve at the point. 8. What is the value of $\frac{dx}{dt}$ $\theta = 35^\circ$ $\frac{d\theta}{dt} = 0.33$ A) -0.502 km/sec. B) 0.502 km/sec. C) -0.330 km/sec. D) 0.330 km/sec. Show Answer Correct Answer: A) -0.502 km/sec. 9. If possible, find the exact value of the expression:$\tan^{-1}\left(1\right)$ A) $\frac{\pi}{4}$. B) 0. C) $\frac{\pi}{2}$. D) Not possible. Show Answer Correct Answer: A) $\frac{\pi}{4}$. 10. Which of the following is equal to $\sin\left(\alpha-\beta\right)$ A) $\cos\alpha\cos\beta+\sin\alpha\sin\beta$. B) $\cos\alpha\cos\beta-\sin\alpha\sin\beta$. C) $\sin\alpha\cos\beta+\sin\beta\cos\alpha$. D) $\sin\alpha\cos\beta-\sin\beta\cos\alpha$. Show Answer Correct Answer: D) $\sin\alpha\cos\beta-\sin\beta\cos\alpha$. 11. 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: D) $-\frac{\pi}{6}$. 12. Complete the Power of Function:$sin^2 x$ A) 1/2 (1-cos 2x). B) 1/2 (1 + cos 2x). C) $cos^2 x$. D) Sin 2x. Show Answer Correct Answer: A) 1/2 (1-cos 2x). 13. $y=e^{\cos\left(3x\right)}$ 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) $y'=-3\sin\left(3x\right)e^{3x}$. 14. Fill in the blank:By the derivative of a quotient, if y = tan(u) = sin(u)/cos(u), then dy/du = ..... A) $cos^2(u) + \frac{sin^2(u)}{cos^2(u)}$. B) $sin^2(u) / cos^2(u)$. C) $-\sin(u)/\cos^2(u)$. D) $\frac{1}{\cos^2(u)}$. Show Answer Correct Answer: D) $\frac{1}{\cos^2(u)}$. 15. $\sin^{-1}\left(-0.2\right)$ A) $-78.1$. B) $11.5$. C) $-11.5$. D) $0$. Show Answer Correct Answer: C) $-11.5$. 16. Complete the Product of Functions:sin x cos y = ..... A) 1/2 [sin(x + y) + sin(x-y)]. B) 1/2 [sin(x + y)-sin(x-y)]. C) Sin(x) + cos(y). D) Sin(xy). Show Answer Correct Answer: A) 1/2 [sin(x + y) + sin(x-y)]. 17. Complete the Power of Function:$tan^2 x$ A) (1-cos 2x) / (1 + cos 2x). B) (1 + cos 2x) / (1-cos 2x). C) (1-sin 2x) / (1 + sin 2x). D) (1 + sin 2x) / (1-sin 2x). Show Answer Correct Answer: A) (1-cos 2x) / (1 + cos 2x). 18. The inverse of the function f(x) is written as ..... A) F $^{-1}$(x). B) F $^{2}$(x). C) F '(x). D) F $^{+}$(x). Show Answer Correct Answer: A) F $^{-1}$(x). 19. What is the inverse of tan(x)? A) Arctan(x). B) Cot(x). C) Sec(x). D) Sin(x). Show Answer Correct Answer: A) Arctan(x). 20. If sin(x) = 0.6, what is x in radians? A) 0.9273. B) 0.6435, 2.4981. C) 3.1416. D) 1.0472. Show Answer Correct Answer: B) 0.6435, 2.4981. 21. From the trigonometric identity, $sec^2 y = 1 + tan^2 y$ A) $sec^2 y = 1 + u^2$. B) $sec^2 y = 1-u^2$. C) $sec^2 y = u^2-1$. D) $sec^2 y = 1/u^2$. Show Answer Correct Answer: A) $sec^2 y = 1 + u^2$. 22. III. Find the y' of the given implicit function:$2xy^2 = \tan(x + 1)^2 + 1$ A) Y' = $[sec^2(x+1)tan(x+1)-y^2]/[4xy]$. B) Y' = $[2sec^2(x+1)tan(x+1)-y^2]/[4xy]$. C) Y' = $[2sec^2(x+1)(tan(x+1)+1)-y^2]/[4xy]$. D) $y' = \frac{sec^2(x+1)(tan(x+1)+1)-y^2}{4xy}$. Show Answer Correct Answer: C) Y' = $[2sec^2(x+1)(tan(x+1)+1)-y^2]/[4xy]$. 23. What does the negative sign indicate in the value of $\frac{dx}{dt}$ 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 away. D) The negative sign indicates that the airplane is stationary. Show Answer Correct Answer: A) The negative sign indicates that the airplane is approaching. 24. Complete the Double Angle Formula:cos 2x = 1 ..... A) $2 \sin^2 x$. B) $sin^2 x$. C) $2\cos^2 x$. D) $cos^2 x$. Show Answer Correct Answer: A) $2 \sin^2 x$. 25. From the figure shown, fill in the blank:cot A = ..... / ..... A) Adjacent side / opposite side. B) Opposite side / adjacent side. C) Hypotenuse / opposite side. D) Opposite side / hypotenuse. Show Answer Correct Answer: A) Adjacent side / opposite side. ← 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 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 10 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books