Mathematics Test

Result

Mathematics Test - 35

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Weekly Quiz Competition

Question 1
5 / -1

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

A
Reflexive relation

B
Symmetric relation

C
Equivalence relation

D
Transitive relation

Solution

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
5 / -1

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

A
1547

B
1458

C
1448

D
1541

Solution

It is given that a * b=3a^b + 5.

Then, 8 * 3 = 3(8³) + 5 = 3(512) + 5 = 1536 + 5 = 1541.
Question 3
5 / -1

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

A
Transitive

B
Commutative

C
Associative

D
Distributive

Solution

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
5 / -1

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

A
R = {(7, 8), (8, 7), (8, 9)}

B
R = {(7, 7), (8, 8), (9, 9)}

C
R = {0}

D
R = {(7, 8), (8, 8), (8, 9)}

Solution

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
5 / -1

Which of the following condition is incorrect for matrix multiplication?

A
A(BC) = (AB)C

B
A(B + C) = AB + AC

C
AB = 0 if either A or B is 0

D
AB = BA

Solution

Matrix multiplication is never commutative i.e. AB ≠ BA. Therefore, the condition AB = BA is incorrect.
Question 6
5 / -1

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

A
(A’)’ = A

B
(A + B)’ = A’ + B’

C
(AB) ’= (BA)’

D
(kA)’ = KA’

Solution

(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
5 / -1

A

B

C

D

Solution

To find the transpose of the matrix of the given matrix, interchange the rows with columns and columns with rows.
Question 8
5 / -1

Which of the following is the reversal law of transposes?

A
(A-B)’ = B’ - A’

B
(AB)’ = B’A’

C
(AB)’ = (BA)’

D
(A+B)’ = B’ + A’

Solution

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
5 / -1

A
symmetric matrix

B
skew-symmetric matrix

C
null matrix

D
diagonal matrix

Solution
Question 10
5 / -1

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

A
A = -A’

B
A = |A|

C
A = A’

D
A = IA

Solution

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