Below you will find **MCQ Questions of Chapter 5 Continuity and Differentiability Class 12 Maths Free PDF Download** that will help you in gaining good marks in the examinations and also cracking competitive exams. These Class 12 MCQ Questions with answers will widen your skills and understand concepts in a better manner.

# MCQ Questions for Class 12 Maths Chapter 5 Continuity and Differentiability with answers

1. If the function is continuous for every x ∈ R then

(a) k ∈ [-2, 0)

(b) k ∈ (0,∞)

(c) k ∈ (-∞, 0)

(d) k ∈ R

► (a) k ∈ [-2, 0)

2. Find dy/dx if x= a cos θ, y = b sin θ

(a) -b/a cotθ

(b) -ab sinθ cosθ

(c) -b/a tanθ

(d) -b/a

► (a) -b/a cotθ

3. The set of all points where the function is differentiable is

(a) (0, ∞)

(b) (-∞, ∞)

(c) (-∞, ∞) - {0}

(d) (-∞, ∞) - {0, 1, 2}

► (c) (-∞, ∞) - {0}

4. is equal to

(a) 0

(b) 1

(c) does not exist

(d) none of these

► (b) 1

5. If f (x + y) = 2f (x) f (y) for all x, y ∈ R where f ' (0) = 3 and f (4) = 2, then f ' (4) is equal to

(a) 6

(b) 12

(c) 4

(d) 3

► (b) 12

6. The function is continuous at

(a) x < 0

(b) x > 1

(c) 0 < x < 1

(d) x > 0

► (d) x > 0

7. If f (x) =x^{2}g(x) and g (x) is twice differentiable then f’’’ (x) is equal to

(a) x^{2}g′′(x)+4xg′(x)+2g(x)

(b) x^{2}g′′(x)+2xg′(x)+2g(x)

(c) 2 g ’’ (x)

(d) none of these

► (a) x^{2}g′′(x)+4xg′(x)+2g(x)

8. Find dy/dx if x = cos^{3}θ, y = sin3 θ

(a) -cotθ

(b) cotθ

(c) -tanθ

(d) tanθ

► (c) -tanθ

9. f (x) = max {x, x^{3}},then the number of points where f (x) is not differentiable, are

(a) 1

(b) 2

(c) 3

(d) 4

► (c) 3

10. is equal to:

(a) 1/2

(b) 1/3

(c) 3/2

(d) none of these

► (c) 3/2

11. If f : R → R be a differentiable function, such that f (x + 2y) = f (x) + f (2y) + 4xy for all x, y ∈ R then

(a) f ' (1) = f ' (0)+ 1

(b) f ' (1) = f ' (0)- 1

(c) f ' (0) = f ' (1)+ 2

(d) f ' (0) = f ' (1)- 2

► (d) f ' (0) = f ' (1)- 2

12. is equal to:

(a) e^{2}

(b) e^{1/2}

(c) e

(d) none of these

► (c) e

13.

(a) differentiable at x = 1

(b) differentiable at x = 2

(c) differentiable at x = 1 and x = 2

(d) not differentiable at x = 0

► (b) differentiable at x = 2

14. The function f (x) = [x] is

(a) derivable for all x

(b) discontinuous only for integral x

(c) continuous for all x

(d) a constant function

► (b) discontinuous only for integral x

15.

(a) is positive

(b) is negative

(c) vanishes

(d) does not exist.

► (b) is negative

16. is equal to:

(a) 1

(b) – 1

(c) 0

(d) none of these

► (c) 0

Hope the given MCQ Questions will help you in cracking exams with good marks. These **Continuity and Differentiability MCQ Questions** will help you in practising more and more questions in less time.