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 6 Applications of Derivatives. It is a part of Assertion Reason Questions for CBSE Class 12 Maths Series.
| Chapter | Applications of Derivatives |
| 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 Applications of Derivatives
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 slope of the tangent to the curve $y=f(x)$ at any point is given by $f^{\prime}(x)$.
Reason (R): Derivative represents the rate of change of a function.
Answer: (a) Both $A$ and $R$ are true, and $R$ is the correct explanation of $A$.
Difficulty Level: Moderate
Q2. Assertion (A): If a function has a maximum or minimum at a point, then the derivative at that point is always non-zero.
Reason (R): A function has an extremum at points where its derivative vanishes.
Answer: (d) A is false, but R is true.
Difficulty Level: Tough
Q3. Assertion (A): If $f^{\prime \prime}(x)>0$ for all $x \in(a, b)$, then $f(x)$ is concave downward on $(a, b)$.
Reason (R): Positive second derivative implies convexity.
Answer: (c) $A$ is false, but $R$ is true.
Difficulty Level: Tough
Q4. Assertion (A): A function is increasing in an interval if its derivative is positive throughout the interval.
Reason (R): If $f^{\prime}(x)>0$ for all $x \in(a, b)$, then $f(x)$ increases on that interval.
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Difficulty Level: Moderate
Q5. Assertion (A): The function $f(x)=x^3-3 x$ has a local maximum at $x=1$.
Reason $(\mathrm{R})$ : The value of the first derivative changes sign at $x=1$, and $f^{\prime \prime}(1)<0$.
Answer: (b) Both $A$ and $R$ are true, but $R$ is not the correct explanation of $A$.
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
- Rate of Change
- Increasing and Decreasing Functions
- Maxima and Minima
- Tangents and Normals
Derivatives help in solving problems of maxima, minima, and rate of change.
Assertion reason questions from the above given topic may be asked.
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Frequently Asked Questions (FAQs) on Applications of Derivatives Assertion Reason Questions Class 12
Q1: What does the chapter ‘Applications of Derivatives’ cover?
A1: It builds key concepts related to applications of derivatives 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 Applications of Derivatives?
A3: They strengthen core concepts and boost confidence in tackling tricky scenarios from applications of derivatives.
Q4: Are assertion reason questions part of CBSE board exams?
A4: Yes, they are included under competency-based formats to test depth of understanding.
