This quiz works best with JavaScript enabled. Home > Cbse > Class 11 > Science > Mathematics > Class 11 Mathematics Chapter 13 Limits And Derivatives – Quiz 1 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 13 Limits And Derivatives Quiz 1 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Find the average rate of change of f(x)=2x$^{2}$+3x-1 from 1 to 2. A) 9. B) 18. C) 3. D) -9. Show Answer Correct Answer: A) 9. 2. $\lim_{t\rightarrow0}\\frac{\frac{1}{x+t}-\frac{1}{x}}{t}= ..... $ A) $-x$. B) $-x^{-2}$. C) $\frac{1}{2}x^{-1}$. D) $0$. E) $x^{-2}$. Show Answer Correct Answer: B) $-x^{-2}$. 3. What is the derivative of f(x) =-2/x A) F'(x) = 2/x$^{ 2}$. B) F'(x) = 0. C) F'(x) =-2. D) F'(x) =-2/x$^{ }$ $^{ 2}$. Show Answer Correct Answer: A) F'(x) = 2/x$^{ 2}$. 4. Find the derivative f(x) = tanxcosx A) F'(x) = sec$^{2}$xcosx-tanxcosx. B) F'(x) = sec$^{2}$xcosx-tanxsinx. C) F'(x) = sec$^{2}$xsinx. D) F'(x) = sec$^{2}$xcosx + tanxsinx. Show Answer Correct Answer: B) F'(x) = sec$^{2}$xcosx-tanxsinx. 5. Evaluate $\lim_{x\rightarrow0}-3$ A) 5. B) 0. C) 3. D) -3. Show Answer Correct Answer: D) -3. 6. What is the derivative of tan(x)? A) Csc$^{2}$(x). B) -sec$^{2}$(x). C) Sec$^{2}$(x). D) -csc$^{2}$(x). Show Answer Correct Answer: C) Sec$^{2}$(x). 7. If y = (sin x + cos x)/(sin x-cos x), dy/dx at x = 0 is A) Does not exist. B) 0. C) -2. D) 1/2. Show Answer Correct Answer: C) -2. 8. Evaluate $\lim_{x\rightarrow6}\\frac{x^2-6x}{x^2-7x+6}$ A) $\frac{6}{7}$. B) $\frac{6}{5}$. C) The limit does not exist. D) 1. Show Answer Correct Answer: B) $\frac{6}{5}$. 9. $\frac{d}{dx}\left(\sqrt[]{x}\right)$ A) $\frac{1}{2}x$. B) $x^{-\frac{1}{2}}$. C) $x^{\frac{1}{2}}$. D) $\frac{1}{2}x^{-\frac{1}{2}}$. Show Answer Correct Answer: D) $\frac{1}{2}x^{-\frac{1}{2}}$. 10. $Evaluate\\lim_{x\rightarrow0}\left[\operatorname{cosec}x-\cot x\right]$ A) -1. B) 1. C) 2. D) 0. Show Answer Correct Answer: D) 0. 11. Find the derivative of the given equationf(s) = 12-8s A) -8x. B) -8. C) 12-8. D) -8s. Show Answer Correct Answer: B) -8. 12. FInd the derivative:f(x) = (-2/3)x$^{3}$-(1/2)x$^{2}$ + 9x A) -2x$^{2}$-x + 9. B) 2x$^{2}$-x-9. C) -2x$^{2}$ + x + 9. D) 2x$^{2}$-x + 9. Show Answer Correct Answer: A) -2x$^{2}$-x + 9. 13. The first principles definition of the derivative of f(x) is $f'\left(x\right)=\lim_{h\longrightarrow0}\\frac{4\left(x+h\right)^3-4x^3}{h}$ A) $x^3$. B) $-4x^3$. C) $4x^3$. D) $4\left(x+h\right)^3$. Show Answer Correct Answer: C) $4x^3$. 14. Find dy/dx by Implicit Differentiation2xy$^{3 }$-x$^{2}$y = 2 A) 2y(x-y$^{2}$)/x(6y$^{2}$-x). B) 2xy-2y$^{3}$. C) -2y/x. D) 2. Show Answer Correct Answer: A) 2y(x-y$^{2}$)/x(6y$^{2}$-x). 15. Find the derivative of f(x) = (x$^{6}$ + 4)$^{5}$ A) F '(x) = 6x$^{5}$(x$^{6}$ + 4)$^{4}$. B) F '(x) = 5x$^{5}$(x$^{4}$ + 4)$^{4}$. C) F '(x) = 30x$^{6}$(x$^{6}$ + 4)$^{4}$. D) F '(x) = 30x$^{5}$(x$^{6}$ + 4)$^{4}$. Show Answer Correct Answer: D) F '(x) = 30x$^{5}$(x$^{6}$ + 4)$^{4}$. 16. Find an equation of the tangent line to the graph of f(x) at the point (1, 100)f(x) = (5x$^{5}$ + 5)$^{2}$ A) Y =-500 x-400. B) Y = 500x-400. C) Y = 100x + 400. D) Y = 500x + 400. Show Answer Correct Answer: B) Y = 500x-400. 17. What is the equation of the line tangent to f(x)=x$^{4}$-2x at the point x=-1? A) Y=-6x-3. B) Y=2x+3. C) Y=2x+5. D) Y=-6x+3. Show Answer Correct Answer: A) Y=-6x-3. 18. What is the meaning of a discontinuity at point A in a function? A) The graph can be drawn without lifting the pencil. B) The function is defined at A. C) The limit exists at A. D) The graph has a break at A. Show Answer Correct Answer: D) The graph has a break at A. 19. Differentiate f(x) = 5x$^{7}$. A) 5x$^{6}$. B) 35x$^{6}$. C) 210x$^{5}$. D) 1050x$^{4}$. Show Answer Correct Answer: B) 35x$^{6}$. 20. What does continuity in a function imply? A) The function has a limit at every point. B) The function has no asymptotes. C) The function can be drawn without lifting the pencil. D) The function is always increasing. Show Answer Correct Answer: C) The function can be drawn without lifting the pencil. 21. Use a graph to estimate $\lim_{x\rightarrow-2}\left(4x^2+3x-1\right)$ A) 21. B) -15. C) -23. D) 9. Show Answer Correct Answer: D) 9. 22. Differentiate y= x$^{3}$ + 2x A) 3x+2. B) 3x$^{3}$+2x. C) 3x$^{2}$+2. D) 3x. Show Answer Correct Answer: C) 3x$^{2}$+2. 23. $f\left(x\right)=x^{-6}$ $f'\left(x\right)$ A) $\frac{-6}{x^7}$. B) $-6x^{-7}$. C) $\frac{-6}{x^{-7}}$. D) $-6x^{-5}$. Show Answer Correct Answer: A) $\frac{-6}{x^7}$. 24. $\lim_{x\rightarrow0}\\frac{\sin3x}{5x}$ A) 2. B) 3/5. C) 2/3. D) 2+3/5. Show Answer Correct Answer: B) 3/5. 25. Find the derivative of the given equationf(x) = x$^{4}$ + 4x$^{3 }$-2x$^{2}$ A) 4x$^{3}$ + 12x$^{2 }$+ 4x. B) 4x + 12x-4x. C) X$^{3}$ + x$^{2 }$-x. D) 4x$^{3}$ + 12x$^{2 }$-4x. Show Answer Correct Answer: D) 4x$^{3}$ + 12x$^{2 }$-4x. 26. Differentiate y = (x$^{3 }$-1)$^{100}$ A) 100(x$^{3 }$-1)$^{99}$. B) 99(x$^{3 }$-1)$^{98}$. C) 300x$^{2}$(x$^{3 }$-1)$^{99}$. D) 100(3x$^{2}$)$^{99}$. Show Answer Correct Answer: C) 300x$^{2}$(x$^{3 }$-1)$^{99}$. 27. Find the derivative of:$f\left(x\right)=4\sqrt{x}$ A) $f'\left(x\right)=2x^{-\frac{1}{2}}$. B) $f'\left(x\right)=4x^{\frac{1}{2}}$. C) $f'\left(x\right)=2\sqrt{x}$. D) $f'\left(x\right)=\frac{2}{\sqrt{x}}$. Show Answer Correct Answer: A) $f'\left(x\right)=2x^{-\frac{1}{2}}$. 28. Find the derivative. f(x) =-8x$^{-3}$ + 5x A) F'(x) =-24x$^{-4}$ + 5. B) F'(x) = 24x$^{-4}$ + 5. C) F'(x) = 24x$^{-2}$ + 5. D) F'(x) = 24x$^{-4}$-5. Show Answer Correct Answer: B) F'(x) = 24x$^{-4}$ + 5. 29. Evaluate $\lim_{x\rightarrow-1}\frac{x^4-1}{x+1}$ A) 1. B) Undefined. C) 0. D) -4. Show Answer Correct Answer: D) -4. 30. Evaluate $\lim_{x\rightarrow-4}\\frac{3x^2+11x-4}{x^2+3x-4}$ A) $\frac{13}{5}$. B) $-33$. C) The limit does not exist. D) $\frac{0}{0}$. Show Answer Correct Answer: A) $\frac{13}{5}$. 31. Find the slope at x = 3 of the equation f(x) = 3x$^{2}$ A) 18. B) 6x. C) 27. D) 3x. Show Answer Correct Answer: A) 18. 32. Find the vertical asymptote(s) (if any) of the graph of the function. 3x / (x$^{2}$ + 9) A) X=3. B) X=0. C) None. D) X=3, x=-3. Show Answer Correct Answer: C) None. 33. Find $\lim_{x\rightarrow\infty}\\frac{2x^2}{x+1}$ A) 1. B) 2. C) $\infty$. D) 0. Show Answer Correct Answer: C) $\infty$. 34. $f\left(x\right)=10x^{-4}-5x^{-2}+x+1$ A) $-40x^{-5}-10x^{-3}+1$. B) $-40x^{-5}+10x^{-3}+1$. C) $40x^{-5}+10x^{-1}+1$. D) $-40x^{-3}+10x^{-1}+1$. Show Answer Correct Answer: B) $-40x^{-5}+10x^{-3}+1$. 35. Approximate the instantaneous rate of change of the function at x =-1. $f\left(x\right)=3x^2+2x-1$ A) 3. B) -4. C) -1/4. D) -2. Show Answer Correct Answer: B) -4. 36. $Evaluate\\lim_{x\rightarrow1}\\frac{x^{15}-1}{x^{10}-1}$ A) -3/2. B) 2/3. C) -2/3. D) 3/2. Show Answer Correct Answer: D) 3/2. 37. If $\lim_{x\rightarrow c}f\left(x\right)=-\infty$ $\lim_{x\rightarrow c}g\left(x\right)=+\infty$ $\lim_{x\rightarrow c}\left[f\left(x\right)+g\left(x\right)\right]=0$ A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 38. Determine the derivative of f(x) = 6x A) 2x$^{2}$. B) 6. C) X. D) 6x. Show Answer Correct Answer: B) 6. 39. Write the slope of the line tangent to the graph of y=x$^{2}$-2 at the point x =-8. A) -8. B) -16. C) 2. D) -4. Show Answer Correct Answer: B) -16. 40. If $f\left(x\right)$ $\lim_{x\rightarrow c}f\left(x\right)$ A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 41. The equation of motion of a particle is s = 2t$^{3 }$-5t$^{2 }$+ 3t + 4, which is the function of its acceleration? A) A(t) = 12. B) A(t) = 6t$^{2 }$-10t$^{ }$+ 3. C) A(t) = 2t$^{3 }$-5t$^{2 }$+ 3t + 4. D) A(t) = 12t-10. Show Answer Correct Answer: D) A(t) = 12t-10. 42. Evaluate $\lim_{x\rightarrow+\infty}\\frac{-4}{3-x^2}$ A) $-\frac{4}{3}$. B) $\frac{4}{3}$. C) 0. D) The limit does not exist. Show Answer Correct Answer: C) 0. 43. Find the derivative of the given equationf(x) = $\frac{1}{x^2}$ A) F'(x) = 1/2x. B) F'(x) =-2x. C) F'(x) =-2x$^{-3}$. D) F'(x) = 2x. Show Answer Correct Answer: C) F'(x) =-2x$^{-3}$. 44. Differentiate h(x) = 3x$^{5/3}$-6x$^{1/6}$ + 3x A) H'(x) = 3x$^{4/3}$-x$^{-5/6}$ + 3. B) H'(x) = 5x$^{2/3}$-x$^{-5/6}$ + 3. C) H'(x) = 3x$^{2/3}$-6x + 3. D) H'(x) = 5x$^{4/3}$-6x + 3. Show Answer Correct Answer: B) H'(x) = 5x$^{2/3}$-x$^{-5/6}$ + 3. 45. Evaluate $\lim_{x\rightarrow0}\frac{x^2+x}{x^2-3x}$ A) 0. B) $\frac{\text{-1}}{\text{3}}$. C) $\frac{\text{1}}{\text{3}}$. D) Undefined. Show Answer Correct Answer: B) $\frac{\text{-1}}{\text{3}}$. 46. What is the value of the limit $\lim_{x \to 2} (3x + 1)$ A) 5. B) 6. C) 7. D) 8. Show Answer Correct Answer: C) 7. 47. Given that $y=\frac{x+2}{x-3}$ A) $y'=\frac{2x-5}{\left(x-3\right)^2}$. B) $y'=-\frac{1}{\left(x-3\right)^2}$. C) $y'=-\frac{5}{\left(x-3\right)^2}$. D) $y'=\frac{2x-1}{\left(x-3\right)^2}$. Show Answer Correct Answer: C) $y'=-\frac{5}{\left(x-3\right)^2}$. 48. $\lim_{x\rightarrow1}\\frac{x^3-3x^2+2x}{x^3-4x^2+3x}= ..... $ A) $1$. B) $\frac{1}{2}$. C) $2$. D) $\frac{1}{4}$. E) $\frac{3}{4}$. Show Answer Correct Answer: B) $\frac{1}{2}$. 49. Evaluate $\lim_{x\rightarrow0}\left(2x+3\right)$ A) 0. B) 3. C) 5. D) 7. Show Answer Correct Answer: B) 3. 50. Find and simplify y' if $y=\frac{4x^2-5}{x+3}$ A) $y'=\frac{8x^2+8x+5}{\left(x+3\right)^2}$. B) $y'=\frac{4x^2+24x+5}{\left(x+3\right)^2}$. C) $y'=\frac{4x^2+24x-5}{\left(x+3\right)^2}$. D) $y'=\frac{8x^2+24x+5}{\left(4x^2-5\right)^2}$. Show Answer Correct Answer: B) $y'=\frac{4x^2+24x+5}{\left(x+3\right)^2}$. 51. $Evaluate\\lim_{h\rightarrow0}\\frac{h^3+2h^2-4h}{h}$ A) Does not exist. B) -4. C) 0. D) 5. Show Answer Correct Answer: B) -4. 52. What is the limit of f(x) as x approaches a, if f(x) = a? A) A. B) F(a). C) 0. D) 1. Show Answer Correct Answer: B) F(a). 53. What is f'(x) if f(x) = cos(5x$^{4}$)? A) F'(x) =-20x$^{3}$ sin(5x$^{4}$). B) F'(x) = 20x$^{3}$ sin(5x$^{4}$). C) F'(x) = sin(20x$^{3}$). D) F'(x) =-sin(20x$^{3}$). Show Answer Correct Answer: A) F'(x) =-20x$^{3}$ sin(5x$^{4}$). 54. Find the antiderivative of the function f(x) = 2x$^{5}$. A) F(x) = x$^{6}$. B) F(x) = 1/3x3 + C. C) F(x) = 1/3x$^{6}$ + C. D) F(x) = 1/3x$^{6}$. Show Answer Correct Answer: C) F(x) = 1/3x$^{6}$ + C. 55. The derivative of a function is its A) Instantaneous rate of change. B) Maximum/Minimum. C) Common Denominator. D) Slope. Show Answer Correct Answer: A) Instantaneous rate of change. 56. What is the limit of f(x) as x approaches a, if f(a) = u and g(a) = v? A) U + v. B) U * v. C) U-v. D) U / v. Show Answer Correct Answer: D) U / v. 57. Find the derivative of the given equationf(x) = x$^{3}$ + x$^{2}$ + 3 A) 3x$^{2}$ + 2x. B) 3x + 2x + 3. C) X$^{3}$ + x$^{2}$. D) 3x + 2x. Show Answer Correct Answer: A) 3x$^{2}$ + 2x. 58. Find $\lim_{x\rightarrow\infty}\frac{2+5n^2}{n^2}$ A) 7. B) Does not exist. C) 0. D) 5. Show Answer Correct Answer: D) 5. 59. What is the derivative of sin(x)? A) -cos(x). B) Cos(x). C) -sin(x). D) Sin(x). Show Answer Correct Answer: B) Cos(x). 60. Find the second derivative of the function:f (x) = 2x-5x$^{6}$ A) F ''(x) = 2-30x$^{5}$. B) F ''(x)= 2-30x$^{}$. C) F ''(x) =-150x$^{4}$. D) F ''(x) =-30x$^{5}$. Show Answer Correct Answer: C) F ''(x) =-150x$^{4}$. 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