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JEE Advanced Differential Equations — practice questions

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 1–30 of 70.

A matrix with all elements zero is called:Read the answer and worked solution →Number of rows in matrix A times number of columns in A x B should equal:Read the answer and worked solution →Mode of {1, 2, 2, 3, 4, 4, 4, 5}:Read the answer and worked solution →Value of arctan(1):Read the answer and worked solution →Simplify arctan(sin x / (1+cos x)) for x ∈ (-π, π):Read the answer and worked solution →arccos(x) + arccos(-x) =Read 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 →The general solution of a 3rd-order DE contains how many arbitrary constants?Read the answer and worked solution →The DE dy/dx = y/x is best solved by:Read 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 →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 →A mass on a spring obeys d²x/dt² + ω²x = 0 (SHM). The period of oscillation is: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 →

Worked practice questions

A matrix with all elements zero is called:

  1. Identity matrix
  2. Zero (null) matrix
  3. Diagonal matrix
  4. Square matrix
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Correct answer: B. Zero (null) matrix

Null/zero matrix has all entries equal to 0. Identity matrix has 1s on the diagonal and 0s elsewhere.

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Number of rows in matrix A times number of columns in A x B should equal:

  1. Rows of B
  2. Columns of B
  3. Number of cols of A = rows of B
  4. Always equal
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Correct answer: C. Number of cols of A = rows of B

For matrix product A x B to be defined, columns of A must equal rows of B. Result has rows of A and cols of B.

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Mode of {1, 2, 2, 3, 4, 4, 4, 5}:

  1. 2
  2. 3
  3. 4
  4. 5
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Correct answer: C. 4

Mode is the most frequent value. 4 appears 3 times, more than any other. Mode = 4.

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More Mathematics topics

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