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WBJEE Limits and Continuity — practice questions — page 4

Explore 131 free Limits and Continuity questions in WBJEE 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 91–120 of 131.

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 →Complete the arc length relationRead the answer and worked solution →Match each identity to its nameRead the answer and worked solution →The Pythagorean identitiesRead the answer and worked solution →Odd function or even function?Read the answer and worked solution →Complete the degree and radian conversionRead the answer and worked solution →True or false: identities and parityRead the answer and worked solution →Match each sum or difference formula to its resultRead the answer and worked solution →Signs in the expansionRead the answer and worked solution →Which formula does this belong to?Read the answer and worked solution →True or false: periodicityRead the answer and worked solution →Complete the complementary angle rulesRead the answer and worked solution →

Worked practice questions

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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Complete the equality condition

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Missing parts
  1. Answer
    same order
    Choices
    1. same order
    2. same determinant
    3. same first row
  2. Answer
    aᵢⱼ = bᵢⱼ
    Choices
    1. aᵢⱼ = bᵢⱼ
    2. aᵢⱼ = bⱼᵢ
    3. aᵢⱼ = 0
Complete the statement
Two matrices A and B are equal when they have the {0} and every corresponding entry satisfies {1}.
Two matrices are equal only when both conditions hold. Source: syllabus Maths Part I, Ch 3 Matrices.

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