This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 5 Continuity And Differentiability – Quiz 2 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 5 Continuity And Differentiability Quiz 2 (26 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. The function f(x) = sin ( $\pi$ $\pi$ A) Continuous as well as differentiable for all x $\in$. B) Continuous for all x but not differentiable at some x. C) Differentiable for all x but not continuous at some x. D) None. Show Answer Correct Answer: A) Continuous as well as differentiable for all x $\in$. 2. The number of points at which the function f (x) = $\frac{1}{x-\left[x\right]}$ A) Non of these. B) 3. C) 2. D) 1. Show Answer Correct Answer: A) Non of these. 3. Cos |x| is differentiable everywhere. A) False. B) True. C) All the above. D) None of the above. Show Answer Correct Answer: B) True. 4. If a function is differentiable at x=c, can it be discontinuous at x=c? A) Yes. B) No. C) It all depends on the function in question. D) None of the above. Show Answer Correct Answer: B) No. 5. If f(2)=3 and f'(2)=-1, then the equation of the tangent line to f(x) at x = 2 is A) Y-2 = 3(x + 1). B) Y-3 =-1(x-2). C) Y-1 = 2(x-3). D) Y + 1 = 2(x-3). Show Answer Correct Answer: B) Y-3 =-1(x-2). 6. F(x) = 5x-4 ; 0 < x <= 1& f(x) = 4x$^{2}$ + 3ax ; 1 < x < 2 is continuous for all x $\in$ A) 1/3. B) 1. C) -1. D) 0. Show Answer Correct Answer: C) -1. 7. Determine any point(s) of discontinuity for the following function. $f\left(x\right)=\frac{3x-6}{x^2-9x+14}$ A) X = 2. B) X = 7. C) X = 2 and x = 7. D) X = 0. E) None. Show Answer Correct Answer: A) X = 2. 8. What is the limit of the function f(x) = 1/x as x approaches 0? A) Infinity. B) -Infinity. C) Undefined. D) 0. Show Answer Correct Answer: C) Undefined. 9. The number of points of discontinuinity of the function f(x) = $\frac{x^2-3x+2}{4x-x^3}$ A) 1. B) 2. C) 3. D) None. Show Answer Correct Answer: B) 2. 10. If f . g is continuous at x = a, then f and g are separately continuous at x = a. A) False. B) True. C) All the above. D) None of the above. Show Answer Correct Answer: A) False. 11. If f is continuous on its domain D, then | f | is also continuous on D. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 12. The derivative of log ( cosec x-cot x) with respect to x is A) Cosec x cot x. B) Cot x. C) Cosec x. D) Cosec x + cot x. Show Answer Correct Answer: C) Cosec x. 13. Differentiation of $a^x$ A) 0. B) $xa^{x-1}$. C) $a^x\log a$. D) None of the above. Show Answer Correct Answer: C) $a^x\log a$. 14. Explain the concept of differentiability. A) Differentiability guarantees that a function is always increasing. B) Differentiability is the same as continuity in mathematics. C) Differentiability only applies to linear functions. D) Differentiability refers to the existence of the derivative of a function at every point within a given interval. Show Answer Correct Answer: D) Differentiability refers to the existence of the derivative of a function at every point within a given interval. 15. A polynomial function is continuous to all real numbers. A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: A) TRUE. 16. Derivative of cos(sinx) A) -sin(cosx). B) -sin(sinx). C) -cosx.sin(sinx). D) Cosx. sin(sinx). Show Answer Correct Answer: C) -cosx.sin(sinx). 17. Identify the point(s) of discontinuity. $f\left(x\right)=\frac{4}{x-6}$ A) X = 0. B) X =-6. C) X = 6. D) X = 4. Show Answer Correct Answer: C) X = 6. 18. The function f(x) = $\frac{\left(4-x^2\right)}{4x-x^3}$ A) Discontinuous at only one point. B) Discontinuous at exactly two points. C) Discontinuous at exactly three points. D) None of these. Show Answer Correct Answer: C) Discontinuous at exactly three points. 19. Which of the following statements is true regarding the function f(x) = |x|? A) It has a point of discontinuity at x = 0. B) It is differentiable everywhere. C) It is not continuous at x = 0. D) It is continuous everywhere. Show Answer Correct Answer: D) It is continuous everywhere. 20. One of the conditions a function must satisfy to be continuous at x=c is "f(c) must exist" A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: A) TRUE. 21. Which of the following statements is true regarding limits of functions? A) Limits can exist at points of discontinuity. B) If a limit exists, the function must be continuous at that point. C) Limits can only be evaluated from the left or right, not both. D) None of the above. Show Answer Correct Answer: A) Limits can exist at points of discontinuity. 22. A continuous function can have some points where limit does not exist. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 23. The function f (x) = [x], where [x] denotes the greatest integer function, is continuous at: A) 1. B) 1.5. C) 4. D) -2. Show Answer Correct Answer: B) 1.5. 24. For what x value, if any, is the function below neither continuous nor differentiable? $f\left(x\right)=\frac{2-x}{\left|2-x\right|}$ A) 2. B) -2. C) 0. D) None of these. Show Answer Correct Answer: A) 2. 25. How can you determine if a function is differentiable at a point? A) Count the number of discontinuities at the point. B) Calculate the derivative of the function and check if it exists at the given point. C) Check if the function is continuous at the point. D) Verify if the function is integrable at the point. Show Answer Correct Answer: B) Calculate the derivative of the function and check if it exists at the given point. 26. Statement 1:The function f(x) = $\left|x\right|$ $\left|x+1\right|$ A) Statement 1 is false, and Statement 2 is true. B) Statement 1 is false, and Statement 2 is true. C) Statement 1 is true, and Statement 2 is true, Statement 2 is the correct explanation for Statement 1. D) Statement 1 is true, and Statement 2 is true, Statement 2 is the not correct explanation for Statement 1. Show Answer Correct Answer: D) Statement 1 is true, and Statement 2 is true, Statement 2 is the not correct explanation for Statement 1. ← PreviousRelated QuizzesScience QuizzesClass 12 QuizzesClass 12 Mathematics Chapter 5 Continuity And Differentiability Quiz 1Class 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 QuizClass 12 Mathematics Chapter 13 Probability QuizClass 12 Mathematics Chapter 2 Inverse Trigonometric Functions QuizClass 12 Mathematics Chapter 3 Matrices Quiz 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books