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JEE Advanced Differential Equations — practice questions — page 2

Explore 70 free Differential Equations questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Differential Equations questions and exercises with answers

Showing questions 31–60 of 70.

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 →Two are true, one is notRead the answer and worked solution →Assertion and reason: forms and methodsRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Tap every equation type the chapter coversRead the answer and worked solution →Match each method to the form it solvesRead the answer and worked solution →A mass on a spring obeys d²x/dt² + ω²x = 0 (SHM). The period of oscillation is:Read the answer and worked solution →The general solution of a 3rd-order DE contains how many arbitrary constants?Read the answer and worked solution →Spot the odd one outRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Reading definitions backRead the answer and worked solution →Tap every statement true of a general solutionRead the answer and worked solution →Which belongs to which idea?Read the answer and worked solution →If a population grows exponentially as dN/dt = 0.1 N (with t in years), the DOUBLING TIME is:Read the answer and worked solution →By Newton's law of cooling, a hot tea cup at 90°C in a room at 25°C cools so that:Read the answer and worked solution →True or false: order and degreeRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →The DE dy/dx = y/x is best solved by:Read the answer and worked solution →Order the steps: solve by separating variablesRead the answer and worked solution →The ORDER and DEGREE of the DE (d²y/dx²)³ + (dy/dx)⁵ + y = 0 are:Read 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 →Counting arbitrary constantsRead the answer and worked solution →

Worked practice questions

Order the reasoning: from equation to particular solution

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Steps
  1. Read off the order of the equation
  2. Recognise which method its form admits
  3. Integrate to reach the general solution
  4. Apply the given initial condition
  5. Solve for the constants to get the particular solution
The full arc of a typical question. Source: syllabus Maths Part II, Ch 9 Differential Equations.

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True or false: the Historical Note

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Questions
  1. Statement is true
    Yes
    Statement
    Leibnitz is credited with the birth of differential equations.
  2. Statement is true
    Yes
    Statement
    Leibnitz introduced the integral sign and the dy notation.
  3. Statement is true
    Yes
    Statement
    Leibnitz discovered the method of separation of variables.
  4. Statement is true
    No
    Statement
    Differential equations began in the twentieth century.
  5. Statement is true
    Yes
    Statement
    Leibnitz was working on a problem about tangents to a curve.
From the note that closes the chapter. Source: syllabus Maths Part II, Ch 9 Differential Equations.

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Tap every equation type the chapter covers

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Questions
  1. Items
    1. Text
      Variable separable
      Matches the category
      Yes
    2. Text
      Homogeneous equations
      Matches the category
      Yes
    3. Text
      First order linear equations
      Matches the category
      Yes
    4. Text
      Laplace transforms
      Matches the category
      No
    5. Text
      Fourier series
      Matches the category
      No
    Category
    A method this chapter covers
Keeping the topic honest about its own scope. Source: syllabus Maths Part II, Ch 9 Differential Equations.

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