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Maharashtra HSC Class 12 (Commerce) Limits and Continuity — practice questions — page 2

Explore 50 free Limits and Continuity questions in Maharashtra HSC Class 12 (Commerce) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Limits and Continuity questions and exercises with answers

Showing questions 31–50 of 50.

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

True or false: transposes

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Questions
  1. Statement is true
    Yes
    Statement
    (A′)′ = A.
  2. Statement is true
    Yes
    Statement
    (A + B)′ = A′ + B′.
  3. Statement is true
    No
    Statement
    (AB)′ = A′B′.
  4. Statement is true
    Yes
    Statement
    (AB)′ = B′A′.
  5. Statement is true
    Yes
    Statement
    (kA)′ = kA′.
The transpose rules, with the product rule as the one that bites. Source: syllabus Maths Part I, Ch 3 Matrices.

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Symmetric or skew symmetric?

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Items
  1. Item
    A′ = A
    Category
    Symmetric
  2. Item
    Entry (i,j) equals entry (j,i)
    Category
    Symmetric
  3. Item
    A′ = −A
    Category
    Skew symmetric
  4. Item
    Entry (i,j) is the negative of entry (j,i)
    Category
    Skew symmetric
Categories
  1. Item
    Symmetric
  2. Item
    Skew symmetric
One condition is A′ = A, the other A′ = −A, and the chapter notes every square matrix splits into a sum of the two. Source: syllabus Maths Part I, Ch 3 Matrices.

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True or false: matrix algebra

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Questions
  1. Statement is true
    Yes
    Statement
    A + B = B + A.
  2. Statement is true
    Yes
    Statement
    (A + B) + C = A + (B + C) when all have the same order.
  3. Statement is true
    No
    Statement
    AB = BA for all matrices.
  4. Statement is true
    Yes
    Statement
    A(BC) = (AB)C.
  5. Statement is true
    Yes
    Statement
    A(B + C) = AB + AC.
  6. Statement is true
    No
    Statement
    Two matrices of different orders can be added.
Addition behaves like ordinary arithmetic multiplication does not. Source: syllabus Maths Part I, Ch 3 Matrices.

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More Mathematics topics

AlgebraApplication of DerivativesDifferential EquationsLinear ProgrammingMathematicsMatricesMatrices and DeterminantsOptimization