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Test: Introduction to Relations (April 15) - JEE MCQ


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10 Questions MCQ Test - Test: Introduction to Relations (April 15)

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Test: Introduction to Relations (April 15) - Question 1

Let a relation T on the set R of real numbers be T = {(a, b) : 1 + ab < 0, a, ∈ R}. Then from among the ordered pairs (1, 1), (1, 2), (1, -2), (2, 2), the only pair that belongs to T is________.​

Detailed Solution for Test: Introduction to Relations (April 15) - Question 1

Since T is a set of real number for it's given ordered pairs we have a condition provided that is 1 + ab is less than zero. so in the given option c if we put order of a and b then it satisfy our given condition

Test: Introduction to Relations (April 15) - Question 2

If A = {1, 3, 5, 7} and we define a relation R = {(a, b), a, b ∈ A: |a - b| = 8}. Then the number of elements in the relation R is

Detailed Solution for Test: Introduction to Relations (April 15) - Question 2

Clearly there is no pair in set A whose difference is 8 or -8.
so D is the correct option.

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Test: Introduction to Relations (April 15) - Question 3

If A = {1, 3, 5, 7} and define a relation, such that R = {(a, b) a, b ∈ A : |a + b| = 8}. Then how many elements are there in the relation R

Detailed Solution for Test: Introduction to Relations (April 15) - Question 3

Number of relations would be 4 as.. 1 + 7,7 + 1, 3 + 5, 5 + 3 all are equal to 8

Test: Introduction to Relations (April 15) - Question 4

If A = {1, 2, 3, 4} and B = {1, 3, 5} and R is a relation from A to B defined by(a, b) ∈ element of R ⇔ a < b. Then, R = ?

Detailed Solution for Test: Introduction to Relations (April 15) - Question 4

A = {1, 2, 3, 4} 
B = {1, 3, 5}
(a, b) ∈ element of R ⇔ a < b for all a ∈ A, b ∈ B
(a, b) pairs satisfying the condition of R are:
(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)
So, 
R = {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}

Test: Introduction to Relations (April 15) - Question 5

Let A = {1, 2, 3, 4} and B = {x, y, z}. Then R = {(1, x), (2, z), (1, y), (3, x)} is​

Detailed Solution for Test: Introduction to Relations (April 15) - Question 5

Let a set of A = (1, 2, 3, 4) and set B (x, y, z) so. set A of all elements in set B then the relation of A to B

Test: Introduction to Relations (April 15) - Question 6

If R be a relation “less than” from set A = {1, 2, 3, 4} to B = {1, 3, 5}, i.e. (a, b) ∈ R if a < b, if (b, a) ∈ R-1elements in R-1 are​

Detailed Solution for Test: Introduction to Relations (April 15) - Question 6

A = {1, 2, 3, 4} 
B = {1, 3, 5} 
(a, b) ∈ R if a < b 
(b, a) ∈ R - 1
R - 1 will have all (b, a) pairs where b < a, for all b ∈ B, a ∈ A
R - 1 = {(3, 1), (3, 2), (5, 1), (5, 2), (5, 3), (5, 4)}

Test: Introduction to Relations (April 15) - Question 7

Let R be a relation on a finite set A having n elements. Then, the number of relations on A is​

Detailed Solution for Test: Introduction to Relations (April 15) - Question 7

Number of relations on A = 

Step-by-step explanation:

If there are n elements in set A then the total number of ordered pairs in the set A × A = n²

In other words A × A will have n² elements.

We also know that if a set has N elements then the number of subsets of A are 2n

Therefore, for A × A there can as many relations as the number of subsets of A × A

The number of subsets of A × A = 

Therefore the number of relations = 

Test: Introduction to Relations (April 15) - Question 8

A situation in which significant power is distributed among three or more states is known as what?

Detailed Solution for Test: Introduction to Relations (April 15) - Question 8

Definition of Multipolar system: A multipolar system is a system in which power is distributed at least among 3 significant poles concentrating wealth and/or military capabilities and able to block or disrupt major political arrangements threatening their major interests.

Test: Introduction to Relations (April 15) - Question 9

Let R be an equivalence relation on Z, the set of integers.

R = {(a, b): a,b ∈ Z and a – b is a multiple of 3} The Equivalence class of [1] is​

Detailed Solution for Test: Introduction to Relations (April 15) - Question 9

Correct Answer :- d

Explanation : R = (a,b) : 3 divides (a-b)

⇒(a−b) is a multiple of 3.

To find equivalence class 1, put b=1

So, (a−0) is a multiple of 3

⇒ a is a multiple of 3

So, In set z of integers, all the multiple

of 3 will come in equivalence

class {1}

Hence, equivalence class {1} = {3x+1}

{-5,-2,1,4,7}

Test: Introduction to Relations (April 15) - Question 10

Which one of the following relations on set of real numbers is an equivalence relation?

Detailed Solution for Test: Introduction to Relations (April 15) - Question 10

If |a| = |b | then |b| = |a| so this is symmetric as well as reflexive and if |a| = |b| and |b| = |c| then |c| = |a| then it is transitive as well so it is an equivalence relation.

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