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MP Board Class 12 (MPBSE) Linear Programming — practice questions — page 2

Explore 51 free Linear Programming questions in MP Board Class 12 (MPBSE) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Linear Programming questions and exercises with answers

Showing questions 31–51 of 51.

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

When is a product defined?

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Questions
  1. Question
    For AB to be defined, the columns of A must match
    Choices
    1. the columns of B
    2. the rows of B
    3. nothing in particular
    Correct choice
    the rows of B
  2. Question
    If A is m × n and B is n × p, then AB has order
    Choices
    1. n × n
    2. p × m
    3. m × p
    Correct choice
    m × p
  3. Question
    Is AB = BA in general?
    Choices
    1. No
    2. Yes, always
    3. Only for row matrices
    Correct choice
    No
  4. Question
    (AB)′ equals
    Choices
    1. A′B′
    2. B′A′
    3. AB
    Correct choice
    B′A′
AB exists only when the number of columns of A matches the number of rows of B, and the answer takes the outer dimensions. Source: syllabus Maths Part I, Ch 3 Matrices.

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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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