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 7 Integrals. It is a part of Assertion Reason Questions for CBSE Class 12 Maths Series.
| Chapter | 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 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): $\int \frac{1}{x^2+1} d x=\tan ^{-1} x+C$
Reason (R): The derivative of $\tan ^{-1} x$ is $\frac{1}{x^2+1}$.
Answer: (a) Both $A$ and $R$ are true, and $R$ is the correct explanation of $A$.
Difficulty Level: Moderate
Q2. Assertion (A): $\int \frac{d x}{\sqrt{1-x^2}}=\sin ^{-1} x+C$ is defined for all real $x$.
Reason (R): The domain of $\sin ^{-1} x$ is $[-1,1]$.
Answer: (c) A is false, but $R$ is true.
Difficulty Level: Moderate
Q3. Assertion (A): Integration is the reverse process of differentiation.
Reason (R): If $F^{\prime}(x)=f(x)$, then $\int f(x) d x=F(x)+C$.
Answer: (a) Both $A$ and $R$ are true, and $R$ is the correct explanation of $A$.
Difficulty Level: Moderate
Q4. Assertion (A): $\int x e^x d x=(x-1) e^x+C$
Reason (R): The integration of product of two functions can be done using integration by parts.
Answer: (b) Both $A$ and $R$ are true, but $R$ is not the correct explanation of $A$.
Difficulty Level: Tough
Q5. Assertion (A): If $\int_a^b f(x) d x=0$, then $f(x)=0$ for all $x \in[a, b]$.
Reason (R): The definite integral of a function over an interval being zero implies that the function is identically zero in that interval.
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
🚀 Boost Your Exam Prep: Get assertion reason questions for all subjects (Class 6-12) now!
Topics from which assertion reason questions may be asked
- Indefinite Integration
- Integration by Parts
- Substitution Method
- Definite Integration
Integration is the reverse of differentiation and helps in calculating areas and accumulation.
Assertion reason questions from the above given topic may be asked.
Download Customised White Label Study Materials in MS Word Format
We are providing teaching resources to teachers and coaching institute looking for customised study materials in MS word format. Our High-quality editable study material which is prepared by the expert faculties are Highly useful for Teachers, Mentors, Tutors, Faculties, Coaching Institutes, Coaching Experts, Tuition Centers.
Frequently Asked Questions (FAQs) on Integrals Assertion Reason Questions Class 12
Q1: What does the chapter ‘Integrals’ cover?
A1: It builds key concepts related to 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 Integrals?
A3: They strengthen core concepts and boost confidence in tackling tricky scenarios from 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.
