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JEE Main Differential Equations — practice questions — page 4

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 91–102 of 102.

True or false: the Historical NoteRead 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 →True or false: what a solution isRead the answer and worked solution →General solution or particular solution?Read the answer and worked solution →Recognising the typeRead 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 →Complete the definition of a differential equationRead the answer and worked solution →Complete the definition of order and degreeRead the answer and worked solution →For the linear DE dy/dx + (1/x)y = x, the INTEGRATING FACTOR μ(x) is:Read the answer and worked solution →

Worked practice questions

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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Counting arbitrary constants

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Questions
  1. Question
    A first order equation's general solution carries
    Choices
    1. two
    2. none
    3. one arbitrary constant
    Correct choice
    one arbitrary constant
  2. Question
    A second order equation's general solution carries
    Choices
    1. two arbitrary constants
    2. one
    3. none
    Correct choice
    two arbitrary constants
  3. Question
    A particular solution carries
    Choices
    1. one
    2. no arbitrary constants
    3. as many as the order
    Correct choice
    no arbitrary constants
The order fixes how many constants a general solution carries. Source: syllabus Maths Part II, Ch 9 Differential Equations.

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Match each term to its meaning

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Matching pairs
  1. Left
    Dependent variable
    Right
    the one being differentiated
  2. Left
    Independent variable
    Right
    the one differentiated with respect to
  3. Left
    Order
    Right
    order of the highest derivative
The vocabulary the rest of the chapter assumes. Source: syllabus Maths Part II, Ch 9 Differential Equations.

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