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JEE Advanced Determinants — practice questions — page 2

Explore 73 free Determinants questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Determinants questions and exercises with answers

Showing questions 31–60 of 73.

True or false: adjoint and inverseRead the answer and worked solution →Assertion and reason: invertibilityRead the answer and worked solution →Tap every statement that is true of a non-singular matrixRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Flip and pair: symbol with meaningRead the answer and worked solution →Complete the area formulaRead the answer and worked solution →Adjoint and identityRead the answer and worked solution →Order the steps for the area of a triangleRead the answer and worked solution →Which side of the inverse test?Read the answer and worked solution →True or false: expanding a determinantRead the answer and worked solution →Match each condition to what it tells youRead the answer and worked solution →Assertion and reason: cofactorsRead the answer and worked solution →Spot the odd oneRead the answer and worked solution →Tap everything the chapter actually definesRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →Two true, one false: scope of the chapterRead the answer and worked solution →Match each kind of matrix to its conditionRead the answer and worked solution →Sort each matrix by its shapeRead the answer and worked solution →Tap every matrix that must be squareRead the answer and worked solution →Complete the definition of a matrixRead the answer and worked solution →When is a product defined?Read the answer and worked solution →True or false: transposesRead the answer and worked solution →Symmetric or skew symmetric?Read the answer and worked solution →True or false: matrix algebraRead the answer and worked solution →Complete the equality conditionRead the answer and worked solution →Order the steps: is AB defined, and what order is it?Read the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Special square matricesRead the answer and worked solution →

Worked practice questions

True or false: adjoint and inverse

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Questions
  1. Statement is true
    Yes
    Statement
    A (adj A) = (adj A) A = |A| I.
  2. Statement is true
    Yes
    Statement
    adj A is the transpose of the matrix of cofactors.
  3. Statement is true
    No
    Statement
    Every square matrix has an inverse.
  4. Statement is true
    Yes
    Statement
    If AB = BA = I then B is the inverse of A.
  5. Statement is true
    Yes
    Statement
    (A⁻¹)⁻¹ = A.
  6. Statement is true
    No
    Statement
    A singular matrix still has an inverse.
Each line is a summary bullet, stated straight or bent. Source: syllabus Maths Part I, Ch 4 Determinants.

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Assertion and reason: invertibility

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Questions
  1. Reason
    A⁻¹ is adj A divided by |A|, and dividing by zero is undefined.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    A matrix with |A| = 0 has no inverse.
  2. Reason
    The determinant used for the area of a triangle vanishes for them.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    Three collinear points enclose no area.
  3. Reason
    The cofactor carries an extra factor of (−1)^(i+j).
    Verdict
    The assertion is false and the reason is true.
    Assertion
    A minor always equals its cofactor.
Tests whether the reason genuinely explains the assertion, not just whether both happen to be true. Source: syllabus Maths Part I, Ch 4 Determinants.

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Tap every statement that is true of a non-singular matrix

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Questions
  1. Items
    1. Text
      |A| ≠ 0
      Matches the category
      Yes
    2. Text
      A⁻¹ exists
      Matches the category
      Yes
    3. Text
      A (adj A) = |A| I
      Matches the category
      Yes
    4. Text
      |A| = 0
      Matches the category
      No
    5. Text
      A has no inverse
      Matches the category
      No
    Category
    True of a NON-singular matrix
  2. Items
    1. Text
      It carries a factor of ½
      Matches the category
      Yes
    2. Text
      It is zero when the points are collinear
      Matches the category
      Yes
    3. Text
      Its third column is all 1s
      Matches the category
      Yes
    4. Text
      It is always positive before taking modulus
      Matches the category
      No
    5. Text
      It needs four points
      Matches the category
      No
    Category
    True of the AREA determinant of a triangle
Non-singular, invertible and |A| ≠ 0 are three names for one condition. Source: syllabus Maths Part I, Ch 4 Determinants.

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