Test: Binary Operations - JEE MCQ

# Test: Binary Operations - JEE MCQ

Test Description

## 10 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Binary Operations

Test: Binary Operations for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Binary Operations questions and answers have been prepared according to the JEE exam syllabus.The Test: Binary Operations MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Binary Operations below.
Solutions of Test: Binary Operations questions in English are available as part of our Mathematics (Maths) Class 12 for JEE & Test: Binary Operations solutions in Hindi for Mathematics (Maths) Class 12 course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: Binary Operations | 10 questions in 10 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) Class 12 for JEE Exam | Download free PDF with solutions
 1 Crore+ students have signed up on EduRev. Have you?
Test: Binary Operations - Question 1

### Number of binary sets on the set {p, q,r} is:​

Detailed Solution for Test: Binary Operations - Question 1

Explanation : No. of elements : 3

Total no.of binary operations on a set consisting 'n' elements is given by nn^2

= So the total no.of binary sets is 39.

Test: Binary Operations - Question 2

### * is said to be commutative in A for all a,b ε A

Test: Binary Operations - Question 3

### Given below is the table corresponding to some binary operation a * b on a set {0,1,2,3,4,5}. How many elements of this operation have an inverse?.

Detailed Solution for Test: Binary Operations - Question 3

a ∗ b = e = b ∗a,
(0,0) (1,1,) (2,2) (3,3) (4,4) (5,5) (6,6)

Test: Binary Operations - Question 4

If * and O are two binary operations defined by a * b = a + b and a O b = ab, then​

Test: Binary Operations - Question 5

The law a + b = b + a is called

Detailed Solution for Test: Binary Operations - Question 5

Commutative law, in mathematics, either of two laws relating to number operations of addition and multiplication, stated symbolically: a + b = b + a and ab = ba

Test: Binary Operations - Question 6

The number of binary operations which can be defined on the set P= {p, q} is

Detailed Solution for Test: Binary Operations - Question 6

n(A) = nn^2
=22^2
= 24
= 16

Test: Binary Operations - Question 7

Given below is binary composition table a* b = LCM of a and b on S = {1,2,3,4}. Then, from the table determine which one of these options is correct.

Detailed Solution for Test: Binary Operations - Question 7

We have ∗ is defined on the set {1,2,3,4,5}  by a∗b = LCM of a and b
Now, 3∗4 = LCM of 3 and 4=12
But, 12 does not belong to {1,2,3,4,5}.
Hence, ′∗′ is not a binary operation.

Test: Binary Operations - Question 8

Let * be any binary operation on the set R defined by a * b = a + b – ab, then the binary operation * is​

Detailed Solution for Test: Binary Operations - Question 8

Given that ο is a binary operation on Q – { – 1} defined by aοb = a + b – ab for all a,b∈Q – { – 1}.
We know that commutative property is pοq = qοp, where ο is a binary operation.
Let’s check the commutativity of given binary operation:
⇒ aοb = a + b – ab
⇒ bοa = b + a – ba = a + b – ab
⇒ b*a = a*b
∴ Commutative property holds for given binary operation ‘ο’ on ‘Q – [ – 1]’.
We know that associative property is (pοq)οr = pο(qοr)
Let’s check the associativity of given binary operation:
⇒ (aοb)οc = (a + b – ab)οc
⇒ (aοb)οc = a + b – ab + c – ((a + b – ab)×c)
⇒ (aοb)οc = a + b + c – ab – ac – ab + abc ...... (1)
⇒ aο(bοc) = aο(b + c – bc)
⇒ aο(bοc) = a + b + c – bc – (a×(b + c – bc))
⇒ a*(b*c) = a + b + c – ab – bc – ac + abc ...... (2)
From (1) and (2)
⇒ (aob)oc = ao(boc)
Hence,we can clearly say that associativity hold for the given binary operation on ‘Q – { – 1}’.
Given that ο is a binary operation on Q – { – 1} defined by aοb = a + b – ab for all a,b∈Q – { – 1}.
We know that commutative property is pοq = qοp, where ο is a binary operation.
Let’s check the commutativity of given binary operation:
⇒ aοb = a + b – ab
⇒ bοa = b + a – ba = a + b – ab
⇒ b*a = a*b
∴ Commutative property holds for given binary operation ‘ο’ on ‘Q – [ – 1]’.
We know that associative property is (pοq)οr = pο(qοr)
Let’s check the associativity of given binary operation:
⇒ (aοb)οc = (a + b – ab)οc
⇒ (aοb)οc = a + b – ab + c – ((a + b – ab)×c)
⇒ (aοb)οc = a + b + c – ab – ac – ab + abc ...... (1)
⇒ aο(bοc) = aο(b + c – bc)
⇒ aο(bοc) = a + b + c – bc – (a×(b + c – bc))
⇒ a*(b*c) = a + b + c – ab – bc – ac + abc ...... (2)
From (1) and (2)
⇒ (aob)oc = ao(boc)
Hence,we can clearly say that associativity hold for the given binary operation on ‘Q – { – 1}’.

Test: Binary Operations - Question 9

Given below is the table corresponding to some binary operation a * b on a set {0, 1,2,3,4,5}. Identify the identity element of this operation.

Test: Binary Operations - Question 10

The identity element for the binary operation * defined by a * b = ab/2, where a, b are the elements of a set of non-zero rational numbers, is​

Detailed Solution for Test: Binary Operations - Question 10

a*e = a = e*a
ae/2 = a
e = 2

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests
Information about Test: Binary Operations Page
In this test you can find the Exam questions for Test: Binary Operations solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Binary Operations, EduRev gives you an ample number of Online tests for practice

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests