Class CBSE Class 12 Mathematics Differential Equations Q #809
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
The sum of the order and the degree of the differential equation d/dx((dy/dx)³) is
(A) 2
(B) 3
(C) 5
(D) 0
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AI Tutor Explanation

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Step-by-Step Solution

  1. Given differential equation: d/dx((dy/dx)³)
  2. Simplify the equation: d/dx((dy/dx)³) = d/dx (y'³) = y'''' (using prime notation for derivatives)
  3. Rewrite the equation: d²y/dx² * 3(dy/dx)² = 0. This is equivalent to 3(dy/dx)²(d²y/dx²) = 0
  4. The order of a differential equation is the highest order derivative present in the equation. In this case, the highest order derivative is d²y/dx², so the order is 2.
  5. The degree of a differential equation is the power of the highest order derivative, when the differential equation is expressed in a form where all derivatives are free from radicals and fractions. In this case, the power of d²y/dx² is 1, so the degree is 1.
  6. The sum of the order and the degree is 2 + 1 = 3.

Correct Answer: 3

AI Suggestion: Option B

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the concepts of order and degree of a differential equation to solve the given problem. They must first simplify the equation and then identify the order and degree.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a procedure to first simplify the given differential equation and then identify its order and degree. This involves applying specific rules and steps.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding of the definitions and procedures related to order and degree of differential equations, which is a core concept covered in the textbook.

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