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JEE Main Differential Equations — practice questions — page 3

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 61–90 of 102.

Solutions of a differential equation form a set that is a:Read the answer and worked solution →True or false on differential equationsRead the answer and worked solution →Quick picks on differential equationsRead the answer and worked solution →Match each term to its meaningRead the answer and worked solution →General or particularRead the answer and worked solution →Ordinary or partialRead the answer and worked solution →Find the order and degreeRead the answer and worked solution →Fill the gaps on differential equationsRead the answer and worked solution →Spot the one that does not fitRead the answer and worked solution →The process of finding anti derivatives is called:Read 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 →

Worked practice questions

Solutions of a differential equation form a set that is a:

  1. Single one
  2. Empty set
  3. Fixed point
  4. Whole family
Show answer and solution

Correct answer: D. Whole family

1. The general solution carries arbitrary constants. 2. Each choice of those constants gives one solution. 3. So the solutions form a whole family. _Source: syllabus Mathematics Part II, Chapter 9, Differential Equations._

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True or false on differential equations

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Questions
  1. Statement is true
    Yes
    Statement
    Order is set by the highest derivative.
  2. Statement is true
    No
    Statement
    Degree is defined for every equation.
  3. Statement is true
    Yes
    Statement
    The general solution holds arbitrary constants.
  4. Statement is true
    No
    Statement
    A particular solution holds arbitrary constants.
  5. Statement is true
    Yes
    Statement
    One independent variable gives an ordinary one.
  6. Statement is true
    No
    Statement
    Partial equations are taken up at this stage.
Instructions
Decide whether each statement is true or false.
_Source: syllabus Mathematics Part II, Chapter 9, Differential Equations._

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Quick picks on differential equations

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Questions
  1. Question
    Order is read from the derivative that is:
    Choices
    1. Highest
    2. Lowest
    3. Middle
    Correct choice
    Highest
  2. Question
    A solution with arbitrary constants is:
    Choices
    1. Particular
    2. General
    3. Trivial
    Correct choice
    General
  3. Question
    One independent variable gives an equation that is:
    Choices
    1. Partial
    2. Vectorial
    3. Ordinary
    Correct choice
    Ordinary
  4. Question
    Degree needs the equation to be a polynomial in:
    Choices
    1. Derivatives
    2. Constants
    3. Logarithms
    Correct choice
    Derivatives
  5. Question
    Two arbitrary constants give an order of:
    Choices
    1. One
    2. Two
    3. Four
    Correct choice
    Two
Instructions
Tap the correct answer before the round moves on.
_Source: syllabus Mathematics Part II, Chapter 9, Differential Equations._

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