Start learning →

Maharashtra HSC Class 12 (Commerce) Algebra — practice questions

Explore 25 free Algebra questions in Maharashtra HSC Class 12 (Commerce) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Algebra with Quill →

Algebra questions and exercises with answers

Showing questions 1–25 of 25.

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 →Assertion and reasonRead 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 →Tap every statement true of the identity matrixRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →True or false: inversesRead the answer and worked solution →Complete the scalar multiplication rulesRead the answer and worked solution →Which operation needs matching orders?Read the answer and worked solution →Spot the odd one outRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →Assertion and reason: structureRead the answer and worked solution →Order the steps: test whether A is symmetricRead the answer and worked solution →True or false: orders and shapesRead the answer and worked solution →

Worked practice questions

Match each kind of matrix to its condition

Read exercise and reference answers
Matching pairs
  1. Left
    Row matrix
    Right
    exactly one row
  2. Left
    Column matrix
    Right
    exactly one column
  3. Left
    Square matrix
    Right
    as many rows as columns
  4. Left
    Diagonal matrix
    Right
    every off-diagonal entry is 0
  5. Left
    Identity matrix
    Right
    1s on the diagonal, 0s elsewhere
  6. Left
    Zero matrix
    Right
    every entry is 0
The chapter's taxonomy, straight from the summary. Source: syllabus Maths Part I, Ch 3 Matrices.

Open this exercise →

Sort each matrix by its shape

Read exercise and reference answers
Items
  1. Item
    Order 1 × 4
    Category
    Row matrix
  2. Item
    Order 1 × n
    Category
    Row matrix
  3. Item
    Order 3 × 1
    Category
    Column matrix
  4. Item
    Order m × 1
    Category
    Column matrix
  5. Item
    Order 3 × 3
    Category
    Square matrix
  6. Item
    Order n × n
    Category
    Square matrix
Categories
  1. Item
    Row matrix
  2. Item
    Column matrix
  3. Item
    Square matrix
Order m × n decides the name: one row, one column, or equal counts. Source: syllabus Maths Part I, Ch 3 Matrices.

Open this exercise →

Tap every matrix that must be square

Read exercise and reference answers
Questions
  1. Items
    1. Text
      Diagonal matrix
      Matches the category
      Yes
    2. Text
      Scalar matrix
      Matches the category
      Yes
    3. Text
      Identity matrix
      Matches the category
      Yes
    4. Text
      Row matrix
      Matches the category
      No
    5. Text
      Zero matrix
      Matches the category
      No
    Category
    Must be a square matrix
  2. Items
    1. Text
      A′ = −A
      Matches the category
      Yes
    2. Text
      It is a square matrix
      Matches the category
      Yes
    3. Text
      A′ = A
      Matches the category
      No
    4. Text
      Every entry is zero
      Matches the category
      No
    Category
    True of a SKEW symmetric matrix
Diagonal, scalar and identity matrices are all special square matrices a zero matrix need not be. Source: syllabus Maths Part I, Ch 3 Matrices.

Open this exercise →

How to practise

  1. Choose a Algebra question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

More Mathematics topics

Limits and ContinuityApplication of DerivativesDifferential EquationsLinear ProgrammingMathematicsMatricesMatrices and DeterminantsOptimization