This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions – Quiz 7 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 7 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Given the function y = sin(u), the derivative of the function is:d/dx sin(u) = ..... A) Cos(u) du/dx. B) Sin(u) du/dx. C) -sin(u) du/dx. D) -cos(u) du/dx. Show Answer Correct Answer: A) Cos(u) du/dx. 2. Sec$^{-1}$ (-2) A) Pie/3. B) 2pie/3. C) -pie/3. D) None. Show Answer Correct Answer: B) 2pie/3. 3. Differentiate the function y = sin 4x cos x. A) Y' = 4 cos 4x cos x-sin 4x sin x. B) Y' = 4 sin 4x cos x + cos 4x sin x. C) Y' = cos 4x cos x + sin 4x sin x. D) Y' = 4 sin 4x sin x + cos 4x cos x. Show Answer Correct Answer: A) Y' = 4 cos 4x cos x-sin 4x sin x. 4. Fill in the blank:cos 2x = ..... A) $cos^2 x-sin^2 x$. B) $cos^2 x + sin^2 x$. C) 2cos x sin x. D) $1-2sin^2 x$. Show Answer Correct Answer: A) $cos^2 x-sin^2 x$. 5. $\csc\left(\frac{\pi}{3}\right)=?$ A) 2. B) -2. C) $\frac{2\sqrt{3}}{3}$. D) $-\frac{2\sqrt{3}}{3}$. Show Answer Correct Answer: C) $\frac{2\sqrt{3}}{3}$. 6. $\sin^{-1}\left(\sin\left(\frac{5\pi}{6}\right)\right)$ A) $\frac{1}{2}$. B) $\frac{-1}{2}$. C) $\frac{\pi}{6}$. D) $60^o$. Show Answer Correct Answer: C) $\frac{\pi}{6}$. 7. The integral $\int_{ }^{ }\frac{dx}{\sqrt{1-16x^2}}$ A) $\frac{1}{4}\arcsin\left(4x\right)+c$. B) $\frac{1}{4}\arccos\left(4x\right)+c$. C) $\arcsin\left(4x\right)+c$. D) $\arccos\left(4x\right)+c$. Show Answer Correct Answer: A) $\frac{1}{4}\arcsin\left(4x\right)+c$. 8. $\sin^{-1}\left(0\right)$ A) $0$. B) $\frac{\pi}{2}$. C) $-\frac{\pi}{2}$. D) $\pi$. Show Answer Correct Answer: A) $0$. 9. Explain a real-world application of inverse trigonometric functions in navigation. A) Inverse trigonometric functions are primarily used for mapping out land areas. B) Inverse trigonometric functions are used to calculate distances in navigation. C) Inverse trigonometric functions help calculate angles in navigation based on known distances. D) Inverse trigonometric functions help in determining speed during navigation. Show Answer Correct Answer: C) Inverse trigonometric functions help calculate angles in navigation based on known distances. 10. III. Find the y' of the given implicit function:3. tan$^{2}$(x + 2) = y$^{2}$ sin$^{2}$(x + 2)What is y'? A) Y' = $[tan(x + 2) sec(x + 2)] / [y sin^2(x + 2)]$. B) Y' = $[2 \tan(x + 2) \sec(x + 2)] / [2y \sin^2(x + 2)]$. C) Y' = $[tan(x + 2) sec(x + 2)] / [2y sin^2(x + 2)]$. D) Y' = $[2 \tan(x + 2) \sec(x + 2)] / [y \sin^2(x + 2)]$. Show Answer Correct Answer: C) Y' = $[tan(x + 2) sec(x + 2)] / [2y sin^2(x + 2)]$. 11. Evaluate $\tan^{-1}(1)$ A) $\frac{\pi}{6}$. B) $\frac{\pi}{4}$. C) $\frac{\pi}{3}$. D) $\frac{\pi}{2}$. Show Answer Correct Answer: B) $\frac{\pi}{4}$. 12. Find the first derivative of the given function:2. y = cos 4x A) Dy/dx =-4 sin 4x. B) Dy/dx = 4 cos 4x. C) Dy/dx = 4 sin 4x. D) Dy/dx =-4 cos 4x. Show Answer Correct Answer: A) Dy/dx =-4 sin 4x. 13. Write $Cos^{-1}\left(-\frac{\sqrt[]{3}}{2}\right)$ A) 150$^\circ$ or $\frac{5\pi}{6}$. B) 30$^\circ$ or $\frac{\pi}{6}$. C) 120$^\circ$ or $\frac{2\pi}{3}$. D) 90$^\circ$ or $\frac{\pi}{2}$. Show Answer Correct Answer: A) 150$^\circ$ or $\frac{5\pi}{6}$. 14. $\sin^{-1}\left(x\right)$ $\arcsin\left(x\right)$ A) Always. B) Never. C) Sometimes. D) None of the above. Show Answer Correct Answer: A) Always. 15. Select the correct derivative:d/dx (arctan x). A) $\frac{1}{1 + x^2}$. B) $\frac{x}{(1+x^2)}$. C) $\frac{1}{\sqrt{1-x^2}}$. D) $-\frac{1}{(1+x^2)}$. Show Answer Correct Answer: A) $\frac{1}{1 + x^2}$. 16. $\cos^{-1}\cos\left(\frac{7\pi}{6}\right)$ A) $\frac{7\pi}{6}$. B) $\frac{5\pi}{6}$. C) $-\frac{\pi}{6}$. D) Cannot be evaluated. Show Answer Correct Answer: B) $\frac{5\pi}{6}$. 17. If possible, find the exact value of the expression:$\cos^{-1}\left(-1\right)$ A) $\pi$. B) $\frac{\pi}{2}$. C) Not possible. D) 0. Show Answer Correct Answer: A) $\pi$. 18. Fill in the blank: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) $2 \sin^2 x$. 19. Evaluate $\tan^{-1}\left(-\frac{\sqrt{3}}{3}\right)$ A) $\frac{\pi}{6}$. B) $\frac{5\pi}{6}$. C) $-\frac{\pi}{6}$. D) $-\frac{5\pi}{3}$. Show Answer Correct Answer: C) $-\frac{\pi}{6}$. 20. Find $\arcsin\left(\cot\left(\frac{\pi}{4}\right)\right)$ A) $\frac{3\pi}{2}$. B) $0$. C) $\frac{7\pi}{6}$. D) $\frac{\pi}{2}$. Show Answer Correct Answer: D) $\frac{\pi}{2}$. 21. Complete the Product of Functions:cos x cos y = ..... A) 1/2 [cos(x + y) + cos(x-y)]. B) 1/2 [cos(x + y)-cos(x-y)]. C) Cos(x + y) + cos(x-y). D) Cos(x + y)-cos(x-y). Show Answer Correct Answer: A) 1/2 [cos(x + y) + cos(x-y)]. 22. I. The slope, tangent, and normal lines to a curve at a given point can be found using which mathematical concept? A) Differentiation. B) Integration. C) Matrix multiplication. D) Factorization. Show Answer Correct Answer: A) Differentiation. 23. What is the maximum possible area of the right triangle having a length of its hypotenuse 5 inches? A) 6 square inches. B) 8 square inches. C) 5 square inches. D) 10 square inches. Show Answer Correct Answer: A) 6 square inches. 24. Refer to the graph labeled 'y = sec x'. Which trigonometric function does this graph represent? A) Secant. B) Cosecant. C) Sine. D) Cosine. Show Answer Correct Answer: A) Secant. 25. $y=\left(\cot^{-1}x\right)^3$ A) $f'\left(x\right)=-\frac{3}{1+x^2}\left(\cot^{-1}x\right)^2$. B) $f'\left(x\right)=\frac{3}{1+x^2}\left(\cot^{-1}x\right)^2$. C) $f'\left(x\right)=-\frac{3}{1+x^2}$. D) None of them. Show Answer Correct Answer: A) $f'\left(x\right)=-\frac{3}{1+x^2}\left(\cot^{-1}x\right)^2$. ← 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 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