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 8 Applications of the Integrals. It is a part of Assertion Reason Questions for CBSE Class 12 Maths Series.
| Chapter | Applications of the Integrals |
| 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 the Integrals
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 area enclosed between two curves $y=f(x)$ and $y=g(x)$ from $x=a$ to $x=b$ is given by $\int_a^b|f(x)-g(x)| d x$.
Reason (R): Area is always a non-negative quantity.
Answer: (a) Both $A$ and $R$ are true, and $R$ is the correct explanation of $A$.
Difficulty Level: Moderate
Q2. Assertion (A): The area bounded between $y=x^2$ and $y=x+2$ is given by $\int_{-1}^2\left[(x+2)-x^2\right] d x$.
Reason $(\mathrm{R})$ : The curve $y=x+2$ lies above $y=x^2$ in the interval $[-1,2]$.
Answer: (a) Both $A$ and $R$ are true, and $R$ is the correct explanation of $A$.
Difficulty Level: Moderate
Q3. Assertion (A): The area under the curve $y=\sin x$ from $x=0$ to $x=\pi$ is zero.
Reason (R): $\sin x$ is positive in the interval $(0, \pi)$.
Answer: (c) $A$ is false, but $R$ is true.
Difficulty Level: Tough
Q4. Assertion (A): Definite integration is used in finding the volume of solids as well as area under curves.
Reason (R): Area bounded by curves is computed using the definite integral formula.
Answer: (b) Both A and R are true, but R is not the correct explanation of A.
Difficulty Level: Moderate
Q5. Assertion (A): If two curves intersect at points $x=a$ and $x=b$, the area enclosed is always calculated as $\int_a^b[f(x)-g(x)] d x$ without checking which curve lies above.
Reason (R): The definite integral of a function gives area regardless of the function’s sign.
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
- Area under Curve
- Area between Curves
Integral applications include computing areas under curves and between functions.
Assertion reason questions from the above given topic may be asked.
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Frequently Asked Questions (FAQs) on Applications of the Integrals Assertion Reason Questions Class 12
Q1: What does the chapter ‘Applications of the Integrals’ cover?
A1: It builds key concepts related to applications of the integrals 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 the Integrals?
A3: They strengthen core concepts and boost confidence in tackling tricky scenarios from applications of the integrals.
Q4: Are assertion reason questions part of CBSE board exams?
A4: Yes, they are included under competency-based formats to test depth of understanding.
