**Find here the NCERT chapter-wise Multiple Choice Questions from Class 12 Mathematics book Chapter 5 Continuity and Differentiability with Answers Pdf free download. This may assist you to understand and check your knowledge about the chapters. Students also can take a free test of the Multiple Choice Questions of Continuity and Differentiability. Each question has four options followed by the right answer. These MCQ Questions are selected supported by the newest exam pattern as announced by CBSE.**

## MCQ Questions for Class 12 Mathematics with Answers

## Q1. If x² + y² = 1, then

(a) yy” – (2y’)² + 1 = 0

(b) yy” + (y’)² + 1 = 0

(c) yy” – (y’)² – 1 = 0

(d) yy” + (2y’)² + 1 = 0

(b) yy” + (y’)² + 1 = 0

## Q2. The function f(x) = e^{|x|} is

(a) continuous everywhere but not differentiable at x = 0

(b) continuous and differentiable everywhere

(c) not continuous at x = 0

(d) None of these

(a) continuous everywhere but not differentiable at x = 0

## Q3. The function f(x) = [x], where [x] denotes the greatest integer function, is continuous at:

(a) 4

(b)-2

(c) 1

(d) 1.5.

(d) 1.5.

## Q4. The value of c in mean value theorem for the function f(x) = (x – 3)(x – 6)(x – 9) in [3, 5] is

(a) 6 ± √(13/3)

(b) 6 + √(13/3)

(c) 6 – √(13/3)

(d) None of these

(c) 6 – √(13/3)

## Q5. Let f(x) = |sin x| Then

(a) f is everywhere differentiable

(b) f is everywhere continuous but not differentiable at x = nπ, n ∈ Z

(c) f is everywhere continuous but no differentiable at x = (2n + 1) π/2 n ∈ Z

(d) None of these

(b) f is everywhere continuous but not differentiable at x = nπ, n ∈ Z

## Q6. The value of ‘c’ in Rolle’s Theorem for the function f(x) = x³ – 3x in the interval [0, √3] is

(a) 1

(b) -1

(c) 3/2

(d) 1/3

(a) 1

## Q7. The number of discontinuous functions y(x) on [-2, 2] satisfying x² + y² = 4 is

(a) 0

(b) 1

(c) 2

(d) >2

(a) 0

## Q8. If y = ae^{x}+ be^{-x }+ c Where a, b, c are parameters, they y’ is equal to

(a) ae^{x} – be^{-x}

(b) ae^{x }+ be^{-x}

(c) -(ae^{x} + be^{-x})

(d) ae^{x} – be^{x}

(a)

## Q9. Let f : (- 1, 1) → R be a differentiable function with f(0) = – 1 and f'(0) = 1.

Let g(x) = [f (2f(x) + 2)]². Then g'(0) =

(a) 4

(b) -4

(c) log 2

(d) -log 2.

(b) -4

## Q10. The derivative of y = (1 – x)(2 – x) ….. (n – x) at x = 1 is equal to

(a) 0

(b) (-1)(n – 1)!

(c) n! – 1

(d) (-1)n-1(n – 1)!

(b) (-1)(n – 1)!

## Q11. For x ∈ R, f(x) = |log 2 – sin x| and g(x) =f(f(x)), then

(a) g is not differentiable at x = 0

(b) g'(0) = cos (log 2)

(c) g'(0) = -cos (log 2)

(d) g is differentiable at x = 0 and g'(0) = – sin (log 2).

(b) g'(0) = cos (log 2)

## Q12. What are the kinds of discontinuity?

(a) Minor and major kinds

(b) Increment and decrement kinds

(c) First and second kinds

(d) Zero and one kinds

(c) First and second kinds

## Q13. What is/are conditions for a function to be continuous on (a,b)?

(a) The function is continuous at each point of (a,b)

(b) The function is right continuous

(c) The function is left continuous

(d) Right continuous, left continuous, continuous at each point of (a,b)

(d) Right continuous, left continuous, continuous at each point of (a,b)

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## MCQ Questions for Class 12 Mathematics Chapter wise with Answers

**Lesson 1. Relations and Functions MCQs****Lesson 2. Inverse Trigonometric Functions MCQs****Lesson 3. Matrices MCQs****Lesson 4. Determinants MCQs****Lesson 5. Continuity and Differentiability MCQs****Lesson 6. Application of Derivatives MCQs****Lesson 7. Integrals MCQs****Lesson 8. Application of Integrals MCQs****Lesson 9. Differential Equations MCQs****Lesson 10. Vector Algebra MCQs****Lesson 11. Three Dimensional Geometry MCQs****Lesson 12. Linear Programming MCQs****Lesson 13. Probability MCQs**