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WBJEE Order and Degree — practice questions

Explore 28 free Order and Degree questions in WBJEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Order and Degree questions and exercises with answers

Showing questions 1–28 of 28.

The **order** of a differential equation is:Read the answer and worked solution →The order and degree of $x^2 \dfrac{d^2y}{dx^2} + 3x \dfrac{dy}{dx} + 4y = 0$ are respectively:Read the answer and worked solution →The order and degree of $\sqrt{1 + (dy/dx)^2} = d^2y/dx^2$ are:Read the answer and worked solution →Complete the definition of order and degreeRead the answer and worked solution →True or false: order and degreeRead the answer and worked solution →General solution or particular solution?Read the answer and worked solution →Match each method to the form it solvesRead the answer and worked solution →Recognising the typeRead the answer and worked solution →Complete the definition of a differential equationRead the answer and worked solution →Order the steps: solve by separating variablesRead the answer and worked solution →Tap every statement true of a general solutionRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →True or false: methods of solutionRead the answer and worked solution →Order, degree, or neither?Read the answer and worked solution →Counting arbitrary constantsRead the answer and worked solution →Match each term to its meaningRead the answer and worked solution →Flip and pair: form with nameRead the answer and worked solution →Order the reasoning: from equation to particular solutionRead the answer and worked solution →True or false: the Historical NoteRead the answer and worked solution →Tap every equation type the chapter coversRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: forms and methodsRead the answer and worked solution →Reading definitions backRead the answer and worked solution →Which belongs to which idea?Read the answer and worked solution →True or false: what a solution isRead the answer and worked solution →

Worked practice questions

The **order** of a differential equation is:

  1. The highest power of the dependent variable
  2. The highest-order derivative present in the equation
  3. The number of arbitrary constants in the solution
  4. Always equal to its degree
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Correct answer: B. The highest-order derivative present in the equation

Order = highest order of derivative appearing. e.g. $d^2y/dx^2 + 3(dy/dx) + y = 0$ has order 2 (because of $d^2y/dx^2$). The order is always a positive integer.

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The order and degree of $x^2 \dfrac{d^2y}{dx^2} + 3x \dfrac{dy}{dx} + 4y = 0$ are respectively:

  1. 1, 1
  2. 2, 1
  3. 2, 2
  4. 1, 2
Show answer and solution

Correct answer: B. 2, 1

Highest-order derivative is $d^2y/dx^2$ → order 2. Its power is 1 → degree 1.

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The order and degree of $\sqrt{1 + (dy/dx)^2} = d^2y/dx^2$ are:

  1. 2, 1
  2. 2, 2
  3. 1, 2
  4. 1, 1
Show answer and solution

Correct answer: B. 2, 2

**Square both sides:** $1 + (dy/dx)^2 = (d^2y/dx^2)^2$. Highest derivative $d^2y/dx^2$ → order 2; its power → degree 2.

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