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All questions of Binary Operations for JAMB Exam
If the binary operation ∗ is defined as a ∗ b = a^2 + b^2, what is the value of (−3) ∗ 2?- a)1
- b)4
- c)13
- d)18
Correct answer is option 'C'. Can you explain this answer?
If the binary operation ∗ is defined as a ∗ b = a^2 + b^2, what is the value of (−3) ∗ 2?
a)
1
b)
4
c)
13
d)
18
|
Ifedayo Adekoya answered |
Understanding the Operation
The binary operation defined here is a ∗ b = a^2 + b^2. This means that when we perform the operation between two numbers, we square each number and then add the results together.
Applying the Operation
To find the value of (-3) ∗ 2, we will substitute -3 for 'a' and 2 for 'b' in the operation:
- a = -3
- b = 2
Now we calculate:
Step 1: Square the Values
- (-3)^2 = 9
- (2)^2 = 4
Step 2: Add the Squares
Now we sum the squared values:
- 9 + 4 = 13
Final Result
Thus, (-3) ∗ 2 = 13.
Conclusion
The value of (-3) ∗ 2 is 13, which corresponds to option 'C'. This demonstrates how the defined operation works by utilizing the properties of squaring and addition.
The binary operation defined here is a ∗ b = a^2 + b^2. This means that when we perform the operation between two numbers, we square each number and then add the results together.
Applying the Operation
To find the value of (-3) ∗ 2, we will substitute -3 for 'a' and 2 for 'b' in the operation:
- a = -3
- b = 2
Now we calculate:
Step 1: Square the Values
- (-3)^2 = 9
- (2)^2 = 4
Step 2: Add the Squares
Now we sum the squared values:
- 9 + 4 = 13
Final Result
Thus, (-3) ∗ 2 = 13.
Conclusion
The value of (-3) ∗ 2 is 13, which corresponds to option 'C'. This demonstrates how the defined operation works by utilizing the properties of squaring and addition.
Let * be a binary operation on a set, and a be any element in the set. If there exists an element b such that a * b = a, then b is called:- a)identity element
- b)inverse element
- c)commutative element
- d)associative element
Correct answer is option 'B'. Can you explain this answer?
Let * be a binary operation on a set, and a be any element in the set. If there exists an element b such that a * b = a, then b is called:
a)
identity element
b)
inverse element
c)
commutative element
d)
associative element
|
Sun Ray Institute answered |
If there exists an element b such that a * b = a, then b is called the inverse element of a.
The set of real numbers under the operation ∗, defined as a ∗ b = a2 − b2, is closed. Which property does the operation satisfy?- a)Associative
- b)Commutative
- c)Identity
- d)Inverse
Correct answer is option 'A'. Can you explain this answer?
The set of real numbers under the operation ∗, defined as a ∗ b = a2 − b2, is closed. Which property does the operation satisfy?
a)
Associative
b)
Commutative
c)
Identity
d)
Inverse
|
|
Sun Ray Institute answered |
The operation ∗ is closed under the set of real numbers, which means for any real numbers a and b, a ∗ b is also a real number. Therefore, the operation satisfies the closure property.
Which of the following is a commutative binary operation?- a)Addition of real numbers
- b)Subtraction of real numbers
- c)Multiplication of real numbers
- d)Division of real numbers
Correct answer is option 'A'. Can you explain this answer?
Which of the following is a commutative binary operation?
a)
Addition of real numbers
b)
Subtraction of real numbers
c)
Multiplication of real numbers
d)
Division of real numbers
|
|
Sun Ray Institute answered |
The addition of real numbers satisfies the commutative property, where a + b = b + a for any real numbers a and b.
For a binary operation * on a set, if a * b = b * a for all elements a and b in the set, the operation is said to be:- a)commutative
- b)associative
- c)distributive
- d)transitive
Correct answer is option 'A'. Can you explain this answer?
For a binary operation * on a set, if a * b = b * a for all elements a and b in the set, the operation is said to be:
a)
commutative
b)
associative
c)
distributive
d)
transitive
|
|
Sun Ray Institute answered |
If a * b = b * a for all elements a and b in the set, the operation is said to be commutative.
Let @ be a binary operation on the set of integers defined by a @ b = |a - b|. Which property does this operation satisfy?- a)Associative
- b)Commutative
- c)Distributive
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
Let @ be a binary operation on the set of integers defined by a @ b = |a - b|. Which property does this operation satisfy?
a)
Associative
b)
Commutative
c)
Distributive
d)
None of the above
|
|
Sun Ray Institute answered |
The operation @ is commutative because a @ b = b @ a for all integers a and b.
Which of the following is not a binary operation on the set of integers?- a)Division
- b)Subtraction
- c)Multiplication
- d)Addition
Correct answer is option 'A'. Can you explain this answer?
Which of the following is not a binary operation on the set of integers?
a)
Division
b)
Subtraction
c)
Multiplication
d)
Addition
|
|
Sun Ray Institute answered |
Division is not a binary operation on the set of integers because division by zero is not defined.
Let ⊗ be a binary operation on the set of rational numbers defined by a ⊗ b = ab + a. What is the identity element for this operation?- a)0
- b)1
- c)-1
- d)2
Correct answer is option 'B'. Can you explain this answer?
Let ⊗ be a binary operation on the set of rational numbers defined by a ⊗ b = ab + a. What is the identity element for this operation?
a)
0
b)
1
c)
-1
d)
2
|
|
Sun Ray Institute answered |
For an element e to be an identity element, it should satisfy a ⊗ e = a for all elements a. By substituting a = 1 and e = 1 into the given expression, we get 1 ⊗ 1 = 1(1) + 1 = 1 + 1 = 2 ≠ 1. Hence, there is no identity element for this operation.
If the binary operation ∗ is defined as a ∗ b = a3 − b3, what is the value of 4 ∗ (−2)?- a)56
- b)72
- c)16
- d)−8
Correct answer is option 'B'. Can you explain this answer?
If the binary operation ∗ is defined as a ∗ b = a3 − b3, what is the value of 4 ∗ (−2)?
a)
56
b)
72
c)
16
d)
−8
|
|
Sun Ray Institute answered |
Substituting the values, 4 ∗ (−2) = 4^3 − (−2)^3 = 64 − (−8) = 64 + 8 = 72.
For a binary operation ∗ on a set, if a ∗ b = b for all elements a and b, what property does the operation satisfy?- a)Identity
- b)Inverse
- c)Commutative
- d)Distributive
Correct answer is option 'A'. Can you explain this answer?
For a binary operation ∗ on a set, if a ∗ b = b for all elements a and b, what property does the operation satisfy?
a)
Identity
b)
Inverse
c)
Commutative
d)
Distributive
|
|
Sun Ray Institute answered |
The property where a binary operation ∗ satisfies a ∗ b = b for all elements a and b is known as the identity property.
If the binary operation ∗ is defined as a ∗ b = a − b, what is the value of (−3) ∗ (−5)?- a)8
- b)−8
- c)2
- d)−2
Correct answer is option 'C'. Can you explain this answer?
If the binary operation ∗ is defined as a ∗ b = a − b, what is the value of (−3) ∗ (−5)?
a)
8
b)
−8
c)
2
d)
−2
|
|
Sun Ray Institute answered |
Substituting the values, (−3) ∗ (−5) = (−3) − (−5) = −3 + 5 = 2.
Let * be a binary operation on the set of real numbers defined by a * b = 2a - b. What is the value of 3 * (4 * 2)?- a)0
- b)-5
- c)5
- d)7
Correct answer is option 'A'. Can you explain this answer?
Let * be a binary operation on the set of real numbers defined by a * b = 2a - b. What is the value of 3 * (4 * 2)?
a)
0
b)
-5
c)
5
d)
7
|
|
Sun Ray Institute answered |
3 * (4 * 2) = 3 * (2(4) - 2) = 3 * (8 - 2) = 3 * 6 = 2(3) - 6 = 6 - 6 = 0. Hence, the answer is 0.
Given the binary operation *, defined as a * b = 2a + b, what is the value of 3 * (−4)?- a)−5
- b)−2
- c)2
- d)5
Correct answer is option 'C'. Can you explain this answer?
Given the binary operation *, defined as a * b = 2a + b, what is the value of 3 * (−4)?
a)
−5
b)
−2
c)
2
d)
5
|
|
Sun Ray Institute answered |
Substituting the values, 3 * (−4) = 2(3) + (−4) = 6 − 4 = 2.
What is the result of the binary operation ⊕ on the set {1, 2, 3}, defined as a ⊕ b = a + b − ab?- a){0, 1, 2}
- b){−2, −1, 0}
- c){0, 1, 3}
- d){−2, 0, 2}
Correct answer is option 'C'. Can you explain this answer?
What is the result of the binary operation ⊕ on the set {1, 2, 3}, defined as a ⊕ b = a + b − ab?
a)
{0, 1, 2}
b)
{−2, −1, 0}
c)
{0, 1, 3}
d)
{−2, 0, 2}
|
|
Sun Ray Institute answered |
Substituting the values, we get the following results:
1 ⊕ 1 = 1 + 1 − 1(1) = 1
1 ⊕ 2 = 1 + 2 − 1(2) = 1
1 ⊕ 3 = 1 + 3 − 1(3) = 0
2 ⊕ 1 = 2 + 1 − 2(1) = 1
2 ⊕ 2 = 2 + 2 − 2(2) = 0
2 ⊕ 3 = 2 + 3 − 2(3) = −1
3 ⊕ 1 = 3 + 1 − 3(1) = 0
3 ⊕ 2 = 3 + 2 − 3(2) = −1
3 ⊕ 3 = 3 + 3 − 3(3) = 3
Therefore, the result of the operation ⊕ is {0, 1, 3}.
1 ⊕ 1 = 1 + 1 − 1(1) = 1
1 ⊕ 2 = 1 + 2 − 1(2) = 1
1 ⊕ 3 = 1 + 3 − 1(3) = 0
2 ⊕ 1 = 2 + 1 − 2(1) = 1
2 ⊕ 2 = 2 + 2 − 2(2) = 0
2 ⊕ 3 = 2 + 3 − 2(3) = −1
3 ⊕ 1 = 3 + 1 − 3(1) = 0
3 ⊕ 2 = 3 + 2 − 3(2) = −1
3 ⊕ 3 = 3 + 3 − 3(3) = 3
Therefore, the result of the operation ⊕ is {0, 1, 3}.
Which of the following is an example of an associative binary operation?- a)a + b = b + a
- b)a − b = b − a
- c)a × b = b × a
- d)a ÷ b = b ÷ a
Correct answer is option 'C'. Can you explain this answer?
Which of the following is an example of an associative binary operation?
a)
a + b = b + a
b)
a − b = b − a
c)
a × b = b × a
d)
a ÷ b = b ÷ a
|
|
Sun Ray Institute answered |
The operation of multiplication (×) satisfies the associative property, where a × (b × c) = (a × b) × c for any numbers a, b, and c.
Consider the binary operation ⊕ defined on the set of natural numbers by a ⊕ b = a2 - b2. Which property does this operation satisfy?- a)Associative
- b)Commutative
- c)Distributive
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
Consider the binary operation ⊕ defined on the set of natural numbers by a ⊕ b = a2 - b2. Which property does this operation satisfy?
a)
Associative
b)
Commutative
c)
Distributive
d)
None of the above
|
|
Sun Ray Institute answered |
The operation ⊕ does not satisfy the properties of associativity or commutativity.
Consider the binary operation * defined on the set of integers by a * b = a + 2b. What is the result of (3 * 2) * 4?- a)18
- b)15
- c)21
- d)24
Correct answer is option 'B'. Can you explain this answer?
Consider the binary operation * defined on the set of integers by a * b = a + 2b. What is the result of (3 * 2) * 4?
a)
18
b)
15
c)
21
d)
24
|
|
Sun Ray Institute answered |
(3 * 2) * 4 = (3 + 2(2)) * 4 = (3 + 4) * 4 = 7 * 4 = 7 + 2(4) = 7 + 8 = 15
Consider the binary operation ○ defined on the set of rational numbers by a ○ b = ab - b. Which property does this operation satisfy?- a)Associative
- b)Commutative
- c)Distributive
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
Consider the binary operation ○ defined on the set of rational numbers by a ○ b = ab - b. Which property does this operation satisfy?
a)
Associative
b)
Commutative
c)
Distributive
d)
None of the above
|
|
Sun Ray Institute answered |
The operation ○ does not satisfy the properties of associativity or commutativity.
Consider the binary operation ∘ defined on the set of real numbers by a ∘ b = a2 + 2ab + b2. What is the value of 2 ∘ (3 ∘ 4)?- a)49
- b)81
- c)2601
- d)169
Correct answer is option 'C'. Can you explain this answer?
Consider the binary operation ∘ defined on the set of real numbers by a ∘ b = a2 + 2ab + b2. What is the value of 2 ∘ (3 ∘ 4)?
a)
49
b)
81
c)
2601
d)
169
|
|
Sun Ray Institute answered |
2 ∘ (3 ∘ 4) = 2 ∘ (32 + 2(3)(4) + 42) = 2 ∘ (9 + 24 + 16) = 2 ∘ 49 = 22 + 2(2)(49) + 492 = 2601.
Let * be a binary operation on the set of integers defined by a * b = a + b + ab. Which property does this operation satisfy?- a)Associative
- b)Commutative
- c)Distributive
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
Let * be a binary operation on the set of integers defined by a * b = a + b + ab. Which property does this operation satisfy?
a)
Associative
b)
Commutative
c)
Distributive
d)
None of the above
|
|
Sun Ray Institute answered |
The operation * does not satisfy the properties of associativity or commutativity.
Chapter doubts & questions for Binary Operations - Mathematics for JAMB 2025 is part of JAMB exam preparation. The chapters have been prepared according to the JAMB exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for JAMB 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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