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 9 Differential Equations. It is a part of Assertion Reason Questions for CBSE Class 12 Maths Series.
| Chapter | Differential Equations |
| 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 Differential Equations
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 order of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^3+y=0$ is 2 .
Reason (R): The order of a differential equation is the highest order derivative present in the equation.
Answer: (a) Both $A$ and $R$ are true, and $R$ is the correct explanation of $A$.
Difficulty Level: Moderate
Q2. Assertion (A): The solution of $\frac{d y}{d x}=2 x$ is $y=x^2+C$, where $C$ is a constant.
Reason (R): Integrating both sides gives $y=x^2+C$.
Answer: (a) Both $A$ and $R$ are true, and $R$ is the correct explanation of $A$.
Difficulty Level: Moderate
Q3. Assertion (A): The differential equation $\frac{d y}{d x}+y=e^x$ is a linear differential equation.
Reason (R): Linear differential equations are of the form $\frac{d y}{d x}+P(x) y=Q(x)$.
Answer: (a) Both A and R are true, and R is the correct explanation of A .
Difficulty Level: Moderate
Q4. Assertion (A): The solution of the differential equation $\frac{d y}{d x}=\frac{1}{x}$ is $y=\ln x+C$, valid for all real numbers $x \neq 0$.
Reason (R): The logarithmic function $\ln x$ is defined for all real $x$.
Answer: (c) A is true, but $R$ is false.
Difficulty Level: Tough
Q5. Assertion (A): The general solution of a first-order differential equation involves one arbitrary constant.
Reason (R): Higher-order differential equations involve fewer constants.
Answer: (b) Both A and R are true, but R is not the correct explanation of A.
Difficulty Level: Moderate
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
- Order and Degree
- Formation of DEs
- General and Particular Solutions
- Solving First Order Linear DE
They model real-world systems like population growth and radioactive decay.
Assertion reason questions from the above given topic may be asked.
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Frequently Asked Questions (FAQs) on Differential Equations Assertion Reason Questions Class 12
Q1: What does the chapter ‘Differential Equations’ cover?
A1: It builds key concepts related to differential equations 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 Differential Equations?
A3: They strengthen core concepts and boost confidence in tackling tricky scenarios from differential equations.
Q4: Are assertion reason questions part of CBSE board exams?
A4: Yes, they are included under competency-based formats to test depth of understanding.
