Continuity and Differentiability Class 12 MCQ is one of the best strategies to prepare for the CBSE Class 12 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more MCQ on Continuity and Differentiability Class 12, which will help them all through their board test.

## Continuity and Differentiability Class 12 MCQ Questions with Answer

Class 12 Maths MCQ with answers are given here to Chapter 5 Continuity and Differentiability. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 12 Mathematics syllabus. By Solving these Class 12 MCQs, you will be able to analyze all of the concepts quickly in the chapter and get ready for the Class 12 Annual exam.

Learn Continuity and Differentiability Class 12 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 12 Mathematics Continuity and Differentiability MCQ with answers given below.

**Question 1. The number of points at which the function f (x) = 1/x-[x] is not continuous is**

(a) 1

(b) 2

(c) 3

(d) none of these

## Answer

D

**Question 2. 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

## Answer

A

**Question 3. 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

## Answer

A

**Question 4. The function f (x) = 4-x2 /4x-x3 is**

(a) discontinuous at only one point

(b) discontinuous at exactly two points

(c) discontinuous at exactly three points

(d) none of these

## Answer

C

**Question 5. The function f(x) = |x| + |x – 1| is**

(a) continuous at x = 0 as well as at x = 1.

(b) continuous at x = 1 but not at x = 0.

(c) discontinuous at x = 0 as well as at x = 1.

(d) continuous at x = 0 but not at x = 1.

## Answer

A

**Question 6. The value of c in Rolle’s Theorem for the function f(x) = ex sin x, in [0, π] is**

(a) π/6

(b) π/4

(c) π/2

(d) 3π/4

## Answer

D

**Question 7. Let f (x) = sinx . Then**

(a) f is everywhere differentiable

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

(c) f is everywhere continuous but not differentiable at x (2n + 1)π/2 , n ∈ Z

(d) none of these

## Answer

B

**Question 8. If f (x) x sin 1/x, where x ! 0 , then the value of the function f at x = 0, so that the function is continuous at x = 0, is**

(a) 0

(b) –1

(c) 1

(d) None of these

## Answer

A

**Question 9. The function f(x) = [x], where [x] denotes the greatest integer function, is continuous at**

(a) 4

(b) –2

(c) 1

(d) 1.5

## Answer

D

**Question 10. The function f : R → R given by f(x) = – |x – 1| is [CBSE 2020 (65/2/1)]**

(a) continuous as well as differentiable at x = 1

(b) not continuous but differentiable at x = 1

(c) continuous but not differentiable at x = 1

(d) neither continuous nor differentiable at x = 1

## Answer

C

**Question 11. The value of c in Mean Value Theorem for the function f(x) = x(x – 2), x ∈ [1, 2] is**

(a) 3/2

(b) 2/3

(c) 1/2

(d) 7/4

## Answer

A

**Question 12. If u sin-1 (2x/1+x2) and v tan-1 (2x/1-x2) , then d u/dv is**

(a) 1/2

(b) x

(c) 1-x2/1+x2[4, -4]Φ

(d) 1

## Answer

D

**Question 13. If y = log tanx , then the value of dy/dx at x = π/4 is**

(a) 0

(b) 1

(c) 1/2

(d) ∞

## Answer

B

**Question 14. Differential coefficient of sec (tan–1x) w.r.t. x is**

(a) x/√(1+x2)

(b) x/(1+x2)

(c) x/(1+x2)

(d) 1/√(1+x2)

## Answer

A

**Question 15. The function (x) =x-1/x(x2-1) is discontinuous at**

(a) exactly one point

(b) exactly two points

(c) exactly three points

(d) no point

## Answer

C

**Question 16. If y = A e5x + B e–5x, then d2y/dx2 is equal to**

(a) 25 y

(b) 5 y

(c) –25 y

(d) 15 y

## Answer

A

**Question 17. For the curve √x + √y =1 ,dy/dx , at(1/4 ,1/4) is**

(a) 1/2

(b) 1

(c) –1

(d) 2

## Answer

C

**Question 18. The set of points where the functions f given by f (x) = |x – 3| cos x is differentiable is**

(a) R

(b) R – {3}

(c) (0, ∞)

(d) none of these

## Answer

B

**Question 19. If f ′(1) = 2 and y = f (log ex), then dy/dx at x = e is**

(a) 0

(b) 1

(c) e

(d) 2/e

## Answer

D

**Question 20. If f(x) = 2x and g(x) = x2/2 + 1 , then which of the following can be a discontinuous function?**(a) f(x) + g(x)

(b) f(x) – g(x)

(c) f(x) . g(x)

(d) g(x)/ f(x )

## Answer

D

Whoever needs to take the CBSE Class 12 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 12 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Continuity and Differentiability Class 12 MCQ are ready by the subject specialists themselves.

**Fill in the blanks**

**Question 1. d/dx sec(tan-1)= _____________ .**

## Answer

**x/√1 + x2**

**Questions 2. If f (x) = cos x , then f (π/4) = _____________ .**

## Answer

**-1/√2**

**Questions** 3. If f(x) = (x + 1), then (d/dx) fof (x) = _____________ .

## Answer

1

**Question 4. The function f (x) = 2 -X ^{2} /9X – X^{3 }is discontinuous exactly at _____________ points. **

## Answer

three

**Question 5. If cos (xy) = k, where k is a constant and xy ≠ np, n ∈ Z, then dy/dx is equal to _____________ . **

## Answer

**-y/x**

**Question 6. The number of points of discontinuity of f defined by f(x) = |x| – |x + 1| is _____________. **

## Answer

0

**Questions **7. The number of points at which the function f(x)=1/log|x| is discontinuous is _________ .

## Answer

**three**

**Question 8. If y = tan–1 x + cot–1 x, x ∈ R, then dy/dx is equal to _____________ . **

## Answer

0

You can easily get good marks If you study with the help of Class 12 Continuity and Differentiability MCQ. We trust that information provided is useful for you. NCERT MCQ Questions for Class 12 Continuity and Differentiability PDF Free Download would without a doubt create positive results.

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### Frequently Asked Question (FAQs)

## How many MCQ questions are there in Class 12 Chapter 5 Mathematics?

In Class 12 Chapter 5 Mathematics, we have provided 28 Important MCQ Questions, But in the future, we will add more MCQs so that you can get good marks in the Class 12 exam.

## Can we score good marks in Class 12 Mathematics with the help of Continuity and Differentiability MCQ Questions?

Yes, MCQ Question is one of the best strategies to make your preparation better for the CBSE Board Exam. It also helps to know the student’s basic understanding of each chapter. So, You can score good marks in the Class 12 Mathematics exam.