Class CBSE Class 12 Mathematics Differential Equations Q #1714
COMPETENCY BASED
APPLY
1 Marks 2026 AISSCE(Board Exam) MCQ SINGLE
Product of the order and degree of differential equation $1+(\frac{dy}{dx})^{3}=\lambda(\frac{d^{3}y}{dx^{3}})^{2}$ is:
(A) 5
(B) 6
(C) 2
(D) 3
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Correct Answer: B

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Detailed Solution

Step 1: Identify the Order

The order of a differential equation is the order of the highest derivative present in the equation. In the given equation $1+(\frac{dy}{dx})^{3}=\lambda(\frac{d^{3}y}{dx^{3}})^{2}$, the highest derivative is $\frac{d^{3}y}{dx^{3}}$. Therefore, the order is 3.

Step 2: Identify the Degree

The degree of a differential equation is the power of the highest order derivative, provided the equation is a polynomial in derivatives. Here, the highest order derivative is $\frac{d^{3}y}{dx^{3}}$ and its exponent is 2. Thus, the degree is 2.

Step 3: Calculate the Product

The question asks for the product of the order and the degree. $$Product = Order \times Degree$$ $$Product = 3 \times 2 = 6$$

Final Answer: 6

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student must identify the definitions of order and degree from the standard curriculum and apply them to a specific algebraic expression.
Knowledge Dimension: PROCEDURAL
Justification: The student follows a specific sequence of steps (identifying highest derivative, then its power) to arrive at the solution.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. This question tests the foundational understanding of Differential Equations (Chapter 9), which is a core competency requirement for board examinations.

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