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JEE Main Differential Equations — practice questions — page 2

Explore 102 free Differential Equations questions in JEE Main 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 102.

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 →The process of finding anti derivatives is called:Read the answer and worked solution →An equation involving derivatives of a dependent variable is a:Read the answer and worked solution →An equation with derivatives in one independent variable only is:Read the answer and worked solution →An equation with derivatives in several independent variables is:Read the answer and worked solution →The order of a differential equation is the order of its:Read the answer and worked solution →An equation whose highest derivative is the second has order:Read the answer and worked solution →Degree can be defined only if the equation is a polynomial in:Read the answer and worked solution →The degree is the highest power of the derivative that is:Read the answer and worked solution →For an equation with a sine of a derivative, the degree is:Read the answer and worked solution →A solution containing arbitrary constants is called the:Read the answer and worked solution →A solution free from arbitrary constants is called:Read the answer and worked solution →A particular solution comes from the general one by fixing the:Read the answer and worked solution →The general solution of a differential equation is also called its:Read the answer and worked solution →For a family of curves, the order equals the number of:Read the answer and worked solution →A family of curves with two arbitrary constants gives an order of:Read the answer and worked solution →A first order and first degree equation involves derivatives of order:Read the answer and worked solution →Equations solvable by moving x and y to opposite sides use:Read the answer and worked solution →Equations built from functions of the same degree throughout are:Read the answer and worked solution →A differential equation states a relation between a function and its:Read the answer and worked solution →The study at this stage is confined to equations that are:Read the answer and worked solution →An equation whose highest derivative is the third has order:Read the answer and worked solution →The power counted for the degree must be a whole number that is:Read 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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