This quiz works best with JavaScript enabled. Home > Class 12 > 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 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. $Sin^{-1}\left\{Sin\left(\frac{2\pi}{3}\right)\right\}= ..... $ A) $\frac{-\pi}{3}$. B) $\frac{\pi}{3}$. C) $\frac{2\pi}{3}$. D) $\frac{-2\pi}{3}$. Show Answer Correct Answer: B) $\frac{\pi}{3}$. 2. A cylinder is to be inscribed in a given sphere. The shape of the cylinder for which its convex surface area is maximum is: A) A right circular cylinder whose height equals the diameter of its base. B) A right circular cylinder whose height equals the radius of its base. C) A right circular cylinder whose height is twice the radius of its base. D) A right circular cylinder whose height is half the diameter of its base. Show Answer Correct Answer: A) A right circular cylinder whose height equals the diameter of its base. 3. $\int\\frac{dx}{x\sqrt{4x^2-9}}$ A) $\frac{1}{3}\arctan\\frac{2x}{3}+C$. B) $-\frac{1}{3}\arctan\\frac{2x}{3}+C$. C) $-\frac{1}{3}\operatorname{arcsec}\\frac{2x}{3}+C$. D) $\frac{1}{3}\operatorname{arcsec}\\frac{2x}{3}+C$. Show Answer Correct Answer: D) $\frac{1}{3}\operatorname{arcsec}\\frac{2x}{3}+C$. 4. II. Find the second derivative of the given function:$2. y = csc((1/3)x^2)$ A) Y" = $csc((1/3)x^2) cot((1/3)x^2) (4/9)x^2-csc((1/3)x^2) (4/9)x^2$. B) $y" =-csc((1/3)x^2) cot((1/3)x^2) (4/9)x^2 + csc((1/3)x^2) (4/9)x^2$. C) $y" =-csc((1/3)x^2) cot((1/3)x^2) (4/9)x^2-csc((1/3)x^2) (4/9)x^2$. D) $y" =-csc((1/3)x^2) cot((1/3)x^2) (2/9)x^2-csc((1/3)x^2) (4/9)x^2$. Show Answer Correct Answer: C) $y" =-csc((1/3)x^2) cot((1/3)x^2) (4/9)x^2-csc((1/3)x^2) (4/9)x^2$. 5. Fill in the blank:The derivative of sin(u) with respect to u is ..... A) Cos(u). B) Sin(u). C) -sin(u). D) -cos(u). Show Answer Correct Answer: A) Cos(u). 6. $\cos^{-1}\left(\sin\left(\frac{5\pi}{3}\right)\right)=$ A) $\frac{5\pi}{6}$. B) $-\frac{\pi}{6}$. C) $-\frac{\pi}{4}$. D) $\frac{\pi}{3}$. Show Answer Correct Answer: A) $\frac{5\pi}{6}$. 7. Use a calculator to approximate the value of expression, if possible:$\cos^{-1}\left(-0.349\right)$ A) -1.9273. B) 1.9273. C) Not possible. D) 12.3565. Show Answer Correct Answer: B) 1.9273. 8. Complete the Double Angle Formula:cos 2x = ..... A) $cos^2 x-sin^2 x$. B) $cos^2 x + sin^2 x$. C) $2cos^2 x-1$. D) 1-2 $sin^2 x$. Show Answer Correct Answer: A) $cos^2 x-sin^2 x$. 9. If $\tan^{-1}\left(\frac{4}{3}\right)=x\\then\\\\cos x= ..... $ A) $\frac{3}{5}$. B) $\frac{5}{3}$. C) $\frac{3}{4}$. D) $\frac{4}{3}$. Show Answer Correct Answer: A) $\frac{3}{5}$. 10. From the figure shown, fill in the blank:sec A = ..... / ..... A) Hypotenuse / adjacent side. B) Adjacent side / hypotenuse. C) Opposite side / hypotenuse. D) Opposite side / adjacent side. Show Answer Correct Answer: A) Hypotenuse / adjacent side. 11. Evaluate. cos [ arccos(-2) ] A) -2. B) No solution. C) 2. D) $\frac{1}{2}$. Show Answer Correct Answer: B) No solution. 12. Refer to the figure shown (right triangle ABC). Fill in the blank:csc A = ..... A) Hypotenuse / opposite side. B) Opposite side / hypotenuse. C) Adjacent side / hypotenuse. D) Opposite side / adjacent side. Show Answer Correct Answer: A) Hypotenuse / opposite side. 13. $y=3^{\sin^4x}$ A) $y'=4\ln2\sin^3x\left(3^{\sin^4x}\right)$. B) $y'=4\ln3\left(\sin^3x\cos x\right)3^{\sin^4x}$. C) $y'=-4\ln3\left(\sin^3x\cos x\right)3^{\sin^4x}$. D) None of them. Show Answer Correct Answer: B) $y'=4\ln3\left(\sin^3x\cos x\right)3^{\sin^4x}$. 14. From the trigonometric identity, A) 1. B) 0. C) 2. D) Sin(u). Show Answer Correct Answer: A) 1. 15. Complete the Sum Formula:sin(x + y) = ..... A) Sin x cos y + cos x sin y. B) Sin x sin y + cos x cos y. C) Sin x cos y-cos x sin y. D) Sin x sin y-cos x cos y. Show Answer Correct Answer: A) Sin x cos y + cos x sin y. 16. $\cos^{-1}0$ A) $\frac{\pi}{2}$. B) $0$. C) $\frac{\pi}{4}$. D) $2\pi$. Show Answer Correct Answer: A) $\frac{\pi}{2}$. 17. For a function to have an inverse it must be ..... A) One-to-one. B) Rational. C) A polynomial. D) A trigonometric function. Show Answer Correct Answer: A) One-to-one. 18. Which of the following is equal to $\cos2\theta$ A) $2\sin\theta\cos\theta$. B) $2\sin^2\theta-1$. C) $2\cos^2\theta+1$. D) None of the choices. Show Answer Correct Answer: D) None of the choices. 19. Sin $^{-1}$ [sin x]=x, for every x in A) [-1, 1]. B) [0. pie]. C) [-pie/2, pie/2]. D) None. Show Answer Correct Answer: C) [-pie/2, pie/2]. 20. I. What is the slope of the tangent line to a curve at a given point? A) The derivative of the curve at that point. B) The value of the curve at that point. C) The area under the curve at that point. D) The intercept of the curve at that point. Show Answer Correct Answer: A) The derivative of the curve at that point. 21. What is the first step in finding the slope, the tangent, and normal lines to a given curve at a specific point? A) Find the derivative of the curve at the given point. B) Draw the curve without calculation. C) Estimate the slope visually. D) Use the midpoint formula. Show Answer Correct Answer: A) Find the derivative of the curve at the given point. 22. Evaluate $\cos^{-1}(0)$ A) $\frac{\pi}{4}$. B) $\frac{\pi}{2}$. C) $\pi$. D) $\frac{3\pi}{2}$. Show Answer Correct Answer: B) $\frac{\pi}{2}$. 23. $Tan\left(ArcTan\left(3\right)\right)$ A) DNE. B) 3. C) 1/2. D) 1. Show Answer Correct Answer: B) 3. 24. Find the exact value of $\sin\left(\tan^{-1}\left(\sqrt{3}\right)\right)$ A) $\frac{\sqrt{3}}{2}$. B) $\frac{\sqrt{2}}{2}$. C) $-\frac{\sqrt{3}}{2}$. D) $-\frac{\sqrt{2}}{2}$. Show Answer Correct Answer: A) $\frac{\sqrt{3}}{2}$. 25. What is the domain of $\sin^{-1}\left(x\right)$ A) $\left(-\infty, -1\right)$. B) $\left[1, \infty\right)$. C) $\left(-\infty, -1\right]$. D) $\left(1, \infty\right)$. E) $\left[-1, 1\right]$. Show Answer Correct Answer: E) $\left[-1, 1\right]$. ← 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 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