Class CBSE Class 12 Mathematics Differential Equations Q #1720
KNOWLEDGE BASED
APPLY
1 Marks 2026 AISSCE(Board Exam) MCQ SINGLE
The order and degree of the differential equation $1+(\frac{d^{3}y}{dx^{3}})^{3}=\lambda\frac{d^{2}y}{dx^{2}}$ is:
(A) Order = 3, Degree = 3
(B) Order = 2, Degree = 2
(C) Order = 3, Degree = 1
(D) Order = 2, Degree = 1
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Correct Answer: A

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Detailed Solution

Step 1: Identify the highest order derivative

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

Step 2: Determine the degree

The degree of a differential equation is defined as the highest power of the highest order derivative, provided the equation is a polynomial in terms of derivatives. Here, the highest order derivative is $\frac{d^{3}y}{dx^{3}}$, and its exponent is 3. Since the equation is already in polynomial form with respect to its derivatives, the degree is 3.

Final Answer: Order = 3, Degree = 3

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student must apply the definitions of order and degree to a specific mathematical expression.
Knowledge Dimension: PROCEDURAL
Justification: The student follows a specific algorithmic process to identify the highest order derivative and its corresponding power.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. This question tests the fundamental conceptual understanding of Chapter 9 (Differential Equations) as per the NCERT curriculum.

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