Hello students, we are providing assertion reason questions for class 12. Assertion Reason questions are the new question format that is introduced in CBSE board. The resources for assertion reason questions are very less. So, to help students we have created chapterwise assertion reason questions for class 12 maths. In this article, you will find assertion reason questions for CBSE Class 12 Maths Chapter 5 Continuity and Differentiability. It is a part of Assertion Reason Questions for CBSE Class 12 Maths Series.
| Chapter | Continuity and Differentiability |
| Type of Questions | Assertion Reason Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 12 |
| Subject | Maths |
| Useful for | Class 12 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 12 Maths Chapterwise Assertion Reason |
Assertion Reason Questions on Continuity and Differentiability
Assertion Reason Questions
Directions: Each of the following questions consists of two statements: an Assertion (A) and a Reason (R). Answer them by selecting the correct option:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.
Q1. Assertion (A): The function $f(x)=|x|$ is continuous at $x=0$.
Reason (R): $f(x)=|x|$ is differentiable at $x=0$.
Answer: (c) $A$ is true, but $R$ is false.
Difficulty Level: Moderate
Q2. Assertion (A): If a function is differentiable at a point, then it is also continuous at that point.
Reason (R): Differentiability implies continuity.
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Difficulty Level: Moderate
Q3. Assertion (A): The function $f(x)=\left\{\begin{array}{ll}x^2 \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}\right.$ is differentiable at $x=0$.
Reason (R): $f(x)$ is continuous at $x=0$.
Answer: (b) Both $A$ and $R$ are true, but $R$ is not the correct explanation of $A$.
Difficulty Level: Tough
Q4. Assertion (A): The function $f(x)=x^3$ is continuous and differentiable at all real values of $x$.
Reason (R): Polynomial functions are always continuous and differentiable on $\mathbb{R}$.
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Difficulty Level: Moderate
Q5. Assertion (A): The function $f(x)=\tan ^{-1}(x)$ is not differentiable at $x=0$.
Reason (R): Inverse trigonometric functions are discontinuous at $x=0$.
Answer: (d) A is false, but $R$ is true.
Difficulty Level: Tough
Also check
- Probability Class 12 Assertion Reason Questions Maths Chapter 13
- Linear Programming Class 12 Assertion Reason Questions Maths Chapter 12
- Three Dimensional Geometry Class 12 Assertion Reason Questions Maths Chapter 11
- Vectors Class 12 Assertion Reason Questions Maths Chapter 10
- Differential Equations Class 12 Assertion Reason Questions Maths Chapter 9
- Applications of the Integrals Class 12 Assertion Reason Questions Maths Chapter 8
- Integrals Class 12 Assertion Reason Questions Maths Chapter 7
- Applications of Derivatives Class 12 Assertion Reason Questions Maths Chapter 6
- Continuity and Differentiability Class 12 Assertion Reason Questions Maths Chapter 5
- Determinants Class 12 Assertion Reason Questions Maths Chapter 4
- Matrices Class 12 Assertion Reason Questions Maths Chapter 3
- Inverse Trigonometric Functions Class 12 Assertion Reason Questions Maths Chapter 2
- Relations and Functions Class 12 Assertion Reason Questions Maths Chapter 1
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Topics from which assertion reason questions may be asked
- Continuity of Functions
- Differentiability
- Chain Rule
- Derivatives of Inverse Trig Functions
These concepts help us understand the smoothness and changes of functions.
Assertion reason questions from the above given topic may be asked.
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Frequently Asked Questions (FAQs) on Continuity and Differentiability Assertion Reason Questions Class 12
Q1: What does the chapter ‘Continuity and Differentiability’ cover?
A1: It builds key concepts related to continuity and differentiability and prepares you for logical reasoning-based questions.
Q2: What are assertion reason questions?
A2: These consist of two statements: an assertion and a reason. Students need to determine their correctness and relationship.
Q3: Why practice assertion reason questions in Continuity and Differentiability?
A3: They strengthen core concepts and boost confidence in tackling tricky scenarios from continuity and differentiability.
Q4: Are assertion reason questions part of CBSE board exams?
A4: Yes, they are included under competency-based formats to test depth of understanding.
