JEE Main Previous Year Questions (2020): Sets and Relations

# JEE Main Previous Year Questions (2020): Sets and Relations | Chapter-wise Tests for JEE Main & Advanced PDF Download

## [JEE Mains MCQs]

Q1: A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be :
(a) 63
(b) 36
(c) 54
(d) 38
Ans:
(b)
person like coffee
person like Tea
n(C) = 73
n(T) = 65
n(C  T)  100
n(C) + n(T) – n (C  T)  100
73 + 65 – x  100
38
73 – x  0  x  73
65 – x  0  x  65
38  x  65

Q2: Let  where each Xi contains 10 elements and each Yi contains 5 elements. If each element of the set T is an element of exactly 20 of sets Xi’s and exactly 6 of sets Yi’s, then n is equal to:
(a) 30
(b) 50
(c) 15
(d) 45
Ans:
(a)
= 50 sets. Given each sets having 10 elements.
So total elements = 50 × 10
sets. Given each sets having 5 elements.
So total elements = 5 × n
Now each element of set T contains exactly 20 of sets Xi.
So number of effective elements in set
Also each element of set T contains exactly 6 of sets Yi.
So number of effective elements in set

Q3: A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B. If x% of the people read both the newspapers, then a possible value of x can be:
(a) 37
(b) 65
(c) 29
(d) 55
Ans:
(d)
A ∪ B = 63 - x + x + 76 - x = 139 - x
As 139 - x ≤ 100
⇒ x ≥ 39
From venn diagram, you can see x should be less than 76 and 63 otherwise only A newspaper or only B newspaper reader will be negative number.
Intersection of x ≤ 63 and x ≤ 76 is = x ≤ 63.
∴ 39 ≤ x ≤ 63
From options possible value of x = 55.

Q4: Let R1 and R2 be two relation defined as follows:
R1 = {(a, b) ∈ R2 : a2 + b2 ∈ Q} and
R2 = {(a, b) ∈ R2 : a2 + b2 ∉ Q},
where Q is the set of all rational numbers.
Then:
(a) Neither R1 nor R2 is transitive.
(b) R2 is transitive but R1 is not transitive.
(c) R1 and R2 are both transitive.
(d) R1 is transitive but R2 is not transitive.
Ans:
(a)
For R1:

∴ R2 is not transitive.

Q5: Consider the two sets:
A2 = {m ∈ R : both the roots of x2 – (m + 1)x + m + 4 = 0 are real} and B = [–3, 5).
Which of the following is not true?
(a) A ∩ B = {–3}
(b) B – A = (–3, 5)
(c) A ∪ B = R
(d) A - B = ( − ∝ , − 3) ∪ (5, ∝ )
Ans:
(d)

Now, let's examine the options.
Option A: A ∩ B = {–3} The intersection of sets A and B would be the set of elements common to both sets. In this case, the only common element is -3. So, option A is true.
Option B: B – A = (–3, 5) The subtraction (or difference) of sets A from B is the set of elements that are in B but not in A. B is [–3, 5), and A is (-∞, -3] U [5, ∞). Subtracting A from B would leave an open interval (-3, 5), not including -3 and 5. So, option B is also true.
Option C: A ∪ B = R The union of sets A and B is the set of elements that are in A, or B, or both. Here, A U B would cover all real numbers. So, option C is true.
Option D: A - B = (-∞, -3) ∪ (5, ∞) The subtraction (or difference) of set B from A is the set of elements that are in A but not in B. B is [–3, 5), and A is (-∞, -3] U [5, ∞). Subtracting B from A would leave (-∞, -3) U [5, ∞), not including -3 and 5. But according to the convention for writing intervals, it should be (-∞, -3) U (5, ∞). So, option D is not true.

Q6: If R = {(x, y) : x, y ∈ Z, x2 + 3y2 ≤ 8} is a relation on the set of integers Z, then the domain of R–1 is:
(a) {0, 1}
(b) {–2, –1, 1, 2}
(c) {–1, 0, 1}
(d) {–2, –1, 0, 1, 2}
Ans:
(c)
Given R = {(x, y) : x, y  Z, x2 + 3y2  8}
So R = {(0,1), (0,–1), (1,0), (–1,0), (1,1), (1,-1)
(-1,1), (-1,-1), (2,0), (-2,0), (-2,0), (2,1), (2,-1), (-2,1), (-2,-1)}
R : { -2, -1, 0, 1, 2}  {-1, 0, 1}
R-1 : {-1, 0, 1}  { -2, -1, 0, 1, 2}
Domain of R–1 = {-1, 0, 1}

Q7: If A = {x ∈ R : |x| < 2} and B = {x ∈ R : |x – 2| ≥ 3}; then :
(a) A – B = [–1, 2)
(b) A ∪ B = R – (2, 5)
(c) A ∩ B = (–2, –1)
(d) B – A = R – (–2, 5)
Ans:
(d)
A : x ∈ (–2, 2);
B : x ∈ (– ∞ , –1] ∪ [5, ∞ )
⇒ B – A = R – (–2, 5)

## [JEE Mains Numericals]

Q8: Set A has m elements and set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m.n is ______.
Ans:
28
Number of subsets of A = 2m
Number of subsets of B = 2n
Given = 2m – 2n = 112
m = 7, n = 4 (27 – 24 = 112)
m × n = 7 × 4 = 28

Q9: Let X = {n ∈ N : 1 ≤ n ≤ 50}. If
A = {n ∈ X: n is a multiple of 2} and
B = {n ∈ X: n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.
Ans:
29
X = {1, 2, 3, 4, …, 50}
A = {2, 4, 6, 8, …, 50} = 25 elements
B = {7, 14, 21, 28, 35, 42, 49} = 7 elements
Here n(AB) = n(A) + n(B) – n(AB)
= 25 + 7 – 3 = 29

The document JEE Main Previous Year Questions (2020): Sets and Relations | Chapter-wise Tests for JEE Main & Advanced is a part of the JEE Course Chapter-wise Tests for JEE Main & Advanced.
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## Chapter-wise Tests for JEE Main & Advanced

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## FAQs on JEE Main Previous Year Questions (2020): Sets and Relations - Chapter-wise Tests for JEE Main & Advanced

 1. What are sets and relations in the context of JEE Main?
Ans. In JEE Main, sets and relations are important mathematical concepts that are frequently tested. A set is a collection of distinct objects, while a relation defines a connection between two sets. Understanding these concepts and their properties is essential for solving JEE Main questions related to sets and relations.
 2. How do you represent a set in mathematics?
Ans. In mathematics, a set can be represented in two ways: roster form and set-builder form. In roster form, the elements of the set are listed within curly braces, separated by commas. For example, {1, 2, 3} represents a set with elements 1, 2, and 3. In set-builder form, the set is defined using a condition. For example, {x | x is an even number} represents the set of all even numbers.
 3. What are the different types of relations?
Ans. In JEE Main, there are several types of relations that are frequently asked in questions. Some of the common types include: - Reflexive relation: A relation where every element is related to itself. - Symmetric relation: A relation where if a is related to b, then b is also related to a. - Transitive relation: A relation where if a is related to b and b is related to c, then a is also related to c. - Equivalence relation: A relation that is reflexive, symmetric, and transitive. Understanding these types of relations and their properties is crucial for solving JEE Main questions.
 4. How do you determine if a relation is an equivalence relation?
Ans. To determine if a relation is an equivalence relation, you need to check three properties: reflexivity, symmetry, and transitivity. - Reflexivity: A relation is reflexive if every element is related to itself. For example, the relation R = {(a, a), (b, b), (c, c)} is reflexive. - Symmetry: A relation is symmetric if whenever a is related to b, then b is also related to a. For example, the relation R = {(a, b), (b, a), (c, d)} is symmetric. - Transitivity: A relation is transitive if whenever a is related to b and b is related to c, then a is also related to c. For example, the relation R = {(a, b), (b, c), (a, c)} is transitive. If a relation satisfies all three properties, it is an equivalence relation.
 5. How can I practice solving JEE Main questions on sets and relations?
Ans. To practice solving JEE Main questions on sets and relations, you can refer to previous year question papers and solve them. Additionally, there are many online resources, books, and coaching materials available that provide practice questions and mock tests specifically designed for JEE Main. Regular practice and understanding the concepts thoroughly will help you improve your problem-solving skills in this topic.

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