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Rajasthan Board Class 12 (RBSE) Determinants — practice questions

Explore 25 free Determinants questions in Rajasthan Board Class 12 (RBSE) 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 1–25 of 25.

Singular or non-singular?Read the answer and worked solution →Match each term to its definitionRead the answer and worked solution →Minors and cofactorsRead the answer and worked solution →True or false: cofactor expansionRead the answer and worked solution →Order the steps for finding A⁻¹Read the answer and worked solution →Determinant of a 2 × 2 matrixRead the answer and worked solution →Complete the inverse ruleRead the answer and worked solution →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 →

Worked practice questions

Singular or non-singular?

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Items
  1. Item
    |A| = 0
    Category
    Singular
  2. Item
    |A| = −7
    Category
    Non-singular
  3. Item
    A has no inverse
    Category
    Singular
  4. Item
    A⁻¹ exists
    Category
    Non-singular
  5. Item
    |A| = 1
    Category
    Non-singular
  6. Item
    A(adj A) = O
    Category
    Singular
Categories
  1. Item
    Singular
  2. Item
    Non-singular
Your syllabus defines a square matrix as singular when |A| = 0 and non-singular when |A| ≠ 0. The whole inverse story hangs on which side a matrix falls. Source: syllabus Maths Part I, Ch 4 Determinants.

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Match each term to its definition

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Matching pairs
  1. Left
    Minor Mᵢⱼ
    Right
    delete the iᵗʰ row and jᵗʰ column, take the determinant
  2. Left
    Cofactor Aᵢⱼ
    Right
    (−1)^(i+j) × Mᵢⱼ
  3. Left
    adj A
    Right
    transpose of the matrix of cofactors
  4. Left
    Singular matrix
    Right
    a square matrix with |A| = 0
These four definitions carry most of the chapter. Source: syllabus Maths Part I, Ch 4 Determinants.

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Minors and cofactors

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Questions
  1. Question
    How is the minor M₂₃ formed?
    Choices
    1. Delete row 3 and column 2
    2. Delete column 2 only
    3. Delete row 2 and column 3
    Correct choice
    Delete row 2 and column 3
  2. Question
    Cofactor A₂₃ equals
    Choices
    1. −M₂₃
    2. M₂₃
    3. 2M₃
    Correct choice
    −M₂₃
  3. Question
    Cofactor A₂₂ equals
    Choices
    1. −M₂₂
    2. M₂₂
    3. 0
    Correct choice
    M₂₂
  4. Question
    The sign attached to a cofactor is
    Choices
    1. (−1)^(i×j)
    2. always negative
    3. (−1)^(i+j)
    Correct choice
    (−1)^(i+j)
The sign factor (−1)^(i+j) is the only difference between a minor and its cofactor, and it is where most marks are lost. Source: syllabus Maths Part I, Ch 4 Determinants.

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