Maths 12th Continuity and Differentiability MCQs: The Central Board of Secondary Education (CBSE) holds the term-end board exams for class 12, which is considered among the top and hardest exams in the country. It’s the most important test in a school student’s life in India and helps influence his or her future.
The board exam comprises a large syllabus, and the question paper consists of various types of questions like long-answer, short answer and objective multiple-choice. The MCQs are often tricky and time-consuming so every student must practice them thoroughly before exams.
MCQs for the mathematics exam of CBSE Class 12 are particularly challenging since they require fast calculation and quick thinking from students. MCQs from Continuity and Differentiability and other calculus chapters trouble students the most. But if you practice the following CBSE Class 12 Chapter 5 Continuity and Differentiability MCQs, you’ll definitely see an improvement in your mathematical skills and confidence.
We have covered MCQ of different concepts and varying difficulty order. The answers are provided with each question. Be sure to go practice the questions till you can solve them without any mistakes. You can check out the MCQs for CBSE Class 12 Maths Chapter 5 Continuity and Differentiability below.
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Related: CBSE Class 12 Maths Important MCQs for Board Exams 2026: Updated
MCQs for CBSE Class 12 Maths Chapter 5 Continuity and Differentiability with Solutions
1: The function f(x) = [ln(1+ax)-ln(1-bx)]/x, not defined at x=0. The value should be assigned to f at x=0, so that it is continuous at x =0, is
(a) a+b
(b) a-b
(c) b-a
(d) ln a+ ln b
2: If x sin(a+y) = sin y, then dy/dx is equal to
(a) [sin2(a+y)]/sin a
(b) sin a /[sin2(a+y)]
(c) [sin(a+y)]/sin a
(d) sin a /[sin(a+y)]
Also Check: CBSE Class 12 Mathematics Syllabus 2025-26: Download PDF
3: The function f(x) = [x], where [x] denotes the greatest integer function is continuous at:
(a) 4
(b) -2
(c) 1
(d) 1.5
4: Consider the following in respect of the function f(x) = 10x:
- Its domain is (∞, ∞)
- It is a continuous function
- It is differentiable at x = 0
Which of the above statements are correct?
(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3
Related: NCERT Solutions for Class 12 Maths PDF: Updated for 2025-26
5: 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 not differentiable at x = (2n + 1) , n ∈ Z.
(d) none of these
6: If the function f(x) = (2x-sin-1x)/(2x+tan-1x) is continuous at each point of its domain, then the value of f(0) is
(a) 1/3
(b) -1/3
(c) 2/3
(d) 2
7: 
Also Read: CBSE Class 12 Maths Sample Paper 2025-26, Download Model Paper PDF FREE
8: 
9: The value of c in Rolle’s theorem for the function, f(x) = sin 2x in [0, π/2] is
(a) π/4
(b) π/6
(c) π/2
(d) π/3
10: 
11. 
12. The function f (x) = e |x|is
A) continuous everywhere but not differentiable at x = 0
B) not continuous at x = 0
C) continuous and differentiable everywhere
D) none of these
13. 
14.
15. The set of points where the function f (x) = |3x - 2| is differentiable, is
Answers
| Question Number | Answers |
| 1 | (a) a+b |
| 2 | (a) [sin2(a+y)]/sin a |
| 3 | (d) 1.5 |
| 4 | (d) 1, 2 and 3 |
| 5 | (b) f is everywhere continuous but not differentiable at x = nπ, n ∈ Z. |
| 6 | (a) 1/3 |
| 7 | (b) |
| 8 | (b) |
| 9 | Option (a) π/4 |
| 10 | (b) |
| 11 | (b) 2 |
| 12 | (a)continuous everywhere but not differentiable at x = 0 |
| 13 | (b) |
| 14 | (d) 0 |
| 15 | (c) |
MCQs for CBSE Class 12 Maths Chapter 5 Continuity and Differentiability with Solutions: Download PDF
Given here is the PDF of MCQs for CBSE Class 12 Maths Chapter 5 Continuity and Differentiability with Solutions. You can find all the questions shared here extracted in the PDF. Use this prepare for the exam and get fluent in Mathematics equations from each chapters.
| MCQs for CBSE Class 12 Maths Chapter 5 Continuity and Differentiability with Solutions: PDF |
Students can use these MCQs to strengthen their maths formula based questions and short questions. These can be used as practice questions for the upcoming board exams to help elevate the understanding of each chapter through multiple choice questions.
Recommended:
NCERT Book for Class 12 Maths 2025-26 All Chapters, PDF Download
CBSE Class 12 Maths Deleted Syllabus 2025-26: Check Topics Not To Prepare for Board Exam
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