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Mathematics Test - 35
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Mathematics Test - 35
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  • Question 1/10
    5 / -1

    (a,a) ∈ R, for every a ∈ A. This condition is for which of the following relations?

    Solutions

    The above is the condition for a reflexive relation. A relation is said to be reflexive if every element in the set is related to itself.

  • Question 2/10
    5 / -1

    Let ‘*’ be a binary operation defined by a * b = 3ab + 5. Find 8 * 3.

    Solutions

    It is given that a * b=3ab + 5.

    Then, 8 * 3 = 3(83) + 5 = 3(512) + 5 = 1536 + 5 = 1541.

  • Question 3/10
    5 / -1

    Which of the following is not a type of binary operation?

    Solutions

    Transitive is not a type of binary operation. It is a type of relation. Distributive, associative, commutative are different types of binary operations.

  • Question 4/10
    5 / -1

    Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?

    Solutions

    The relation R= {(7, 7), (8, 8), (9, 9)} is reflexive as every element is related to itself i.e. (a,a) ∈ R, for every a∈A. and it is not transitive as it does not satisfy the condition that for a relation R in a set A if (a1, a2)∈R and (a2, a3)∈R implies that (a1, a3) ∈ R for every a1, a2, a3 ∈ R.

  • Question 5/10
    5 / -1

    Which of the following condition is incorrect for matrix multiplication?

    Solutions

    Matrix multiplication is never commutative i.e. AB ≠ BA. Therefore, the condition AB = BA is incorrect.

  • Question 6/10
    5 / -1

    Which of the following is not the property of transpose of a matrix?

    Solutions

    (AB)’ = (BA)’is incorrect. We know that matrix multiplication is not commutative i.e. AB ≠ BA. Hence, its transpose will also not be commutative.
    (AB)’=B’A’

  • Question 7/10
    5 / -1

    Solutions

    To find the transpose of the matrix of the given matrix, interchange the rows with columns and columns with rows.

  • Question 8/10
    5 / -1

    Which of the following is the reversal law of transposes?

    Solutions

    According to the reverse law of transposes the transpose of the product is the product of the transposes taken in the reverse order i.e. (AB)’ = B’ A’.

  • Question 9/10
    5 / -1

    Solutions

  • Question 10/10
    5 / -1

    Which of the following conditions holds true for a skew-symmetric matrix?

    Solutions

    A matrix is said to be skew-symmetric if it is equal to the negative of its transpose i.e. A = -A’.

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