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Sets, Relations and Functions: JEE Main Previous Year Questions (2021-2026)
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JEE Main Previous Year Questions (2021-2026):
Sets, Relations and Functions
(January 2026)
Sets, Relations
Q1: Let R be a relation defined on the set {1, 2, 3, 4} × {1, 2, 3, 4} by
R = {((a, b), (c, d)) : 2 a + 3 b = 3 c + 4 d }.
Then the number of elements in R is
(a) 6
(b) 15
(c) 12
(d) 18
Ans: (c)
Sol:
let A = {1, 2, 3, 4}
R is defined on A × A such that since
R = {((a, b), (c, d)) : 2a + 3b = 3c + 4d}
since a , b , c , d ? A
Page 2
JEE Main Previous Year Questions (2021-2026):
Sets, Relations and Functions
(January 2026)
Sets, Relations
Q1: Let R be a relation defined on the set {1, 2, 3, 4} × {1, 2, 3, 4} by
R = {((a, b), (c, d)) : 2 a + 3 b = 3 c + 4 d }.
Then the number of elements in R is
(a) 6
(b) 15
(c) 12
(d) 18
Ans: (c)
Sol:
let A = {1, 2, 3, 4}
R is defined on A × A such that since
R = {((a, b), (c, d)) : 2a + 3b = 3c + 4d}
since a , b , c , d ? A
Let possible values of 2a + 3b = L1 and possible values of 3c + 4d = L2
Common values of Common values of 2a + 3b = 3c + 4d
7, 10, 11, 13, 14, 15, 16, 17, 18, 20
value 7, 10, 13, 15, 16, 17, 18, 20
occurs 1 time in L1 and 1 time in L2
e.g value 7 occurs 1 time in L1 & 1 time in L2 total = 1 × 1 = 1
so, total number of these types of elements in R = 8 --- (1)
value 11 and 14 occurs 2 times in L1 and 1 time in L2
Page 3
JEE Main Previous Year Questions (2021-2026):
Sets, Relations and Functions
(January 2026)
Sets, Relations
Q1: Let R be a relation defined on the set {1, 2, 3, 4} × {1, 2, 3, 4} by
R = {((a, b), (c, d)) : 2 a + 3 b = 3 c + 4 d }.
Then the number of elements in R is
(a) 6
(b) 15
(c) 12
(d) 18
Ans: (c)
Sol:
let A = {1, 2, 3, 4}
R is defined on A × A such that since
R = {((a, b), (c, d)) : 2a + 3b = 3c + 4d}
since a , b , c , d ? A
Let possible values of 2a + 3b = L1 and possible values of 3c + 4d = L2
Common values of Common values of 2a + 3b = 3c + 4d
7, 10, 11, 13, 14, 15, 16, 17, 18, 20
value 7, 10, 13, 15, 16, 17, 18, 20
occurs 1 time in L1 and 1 time in L2
e.g value 7 occurs 1 time in L1 & 1 time in L2 total = 1 × 1 = 1
so, total number of these types of elements in R = 8 --- (1)
value 11 and 14 occurs 2 times in L1 and 1 time in L2
e.g value 11 occurs 2 time in L1 & 1 time in L2 total
elements in R is 2 × 1 = 2
so total number these type of elements = 2 + 2 = 4 --- (2)
total number of elements in R = 8+4 = 12
Q2: Consider two sets A = {x ? Z : | (| x - 3| - 3) | = 1} and
Then the number of onto functions f : A ? B is equal to :
(a) 32
(b) 81
(c) 79
(d) 62
Ans: (d)
Sol:
Page 4
JEE Main Previous Year Questions (2021-2026):
Sets, Relations and Functions
(January 2026)
Sets, Relations
Q1: Let R be a relation defined on the set {1, 2, 3, 4} × {1, 2, 3, 4} by
R = {((a, b), (c, d)) : 2 a + 3 b = 3 c + 4 d }.
Then the number of elements in R is
(a) 6
(b) 15
(c) 12
(d) 18
Ans: (c)
Sol:
let A = {1, 2, 3, 4}
R is defined on A × A such that since
R = {((a, b), (c, d)) : 2a + 3b = 3c + 4d}
since a , b , c , d ? A
Let possible values of 2a + 3b = L1 and possible values of 3c + 4d = L2
Common values of Common values of 2a + 3b = 3c + 4d
7, 10, 11, 13, 14, 15, 16, 17, 18, 20
value 7, 10, 13, 15, 16, 17, 18, 20
occurs 1 time in L1 and 1 time in L2
e.g value 7 occurs 1 time in L1 & 1 time in L2 total = 1 × 1 = 1
so, total number of these types of elements in R = 8 --- (1)
value 11 and 14 occurs 2 times in L1 and 1 time in L2
e.g value 11 occurs 2 time in L1 & 1 time in L2 total
elements in R is 2 × 1 = 2
so total number these type of elements = 2 + 2 = 4 --- (2)
total number of elements in R = 8+4 = 12
Q2: Consider two sets A = {x ? Z : | (| x - 3| - 3) | = 1} and
Then the number of onto functions f : A ? B is equal to :
(a) 32
(b) 81
(c) 79
(d) 62
Ans: (d)
Sol:
Page 5
JEE Main Previous Year Questions (2021-2026):
Sets, Relations and Functions
(January 2026)
Sets, Relations
Q1: Let R be a relation defined on the set {1, 2, 3, 4} × {1, 2, 3, 4} by
R = {((a, b), (c, d)) : 2 a + 3 b = 3 c + 4 d }.
Then the number of elements in R is
(a) 6
(b) 15
(c) 12
(d) 18
Ans: (c)
Sol:
let A = {1, 2, 3, 4}
R is defined on A × A such that since
R = {((a, b), (c, d)) : 2a + 3b = 3c + 4d}
since a , b , c , d ? A
Let possible values of 2a + 3b = L1 and possible values of 3c + 4d = L2
Common values of Common values of 2a + 3b = 3c + 4d
7, 10, 11, 13, 14, 15, 16, 17, 18, 20
value 7, 10, 13, 15, 16, 17, 18, 20
occurs 1 time in L1 and 1 time in L2
e.g value 7 occurs 1 time in L1 & 1 time in L2 total = 1 × 1 = 1
so, total number of these types of elements in R = 8 --- (1)
value 11 and 14 occurs 2 times in L1 and 1 time in L2
e.g value 11 occurs 2 time in L1 & 1 time in L2 total
elements in R is 2 × 1 = 2
so total number these type of elements = 2 + 2 = 4 --- (2)
total number of elements in R = 8+4 = 12
Q2: Consider two sets A = {x ? Z : | (| x - 3| - 3) | = 1} and
Then the number of onto functions f : A ? B is equal to :
(a) 32
(b) 81
(c) 79
(d) 62
Ans: (d)
Sol:
So set B = {3, 4}
Let n(A) & n(B) be number of elements in set A and B respectively
n(A) = 6, n(B) = 2
Number of onto function f : A ? B is
= Total function - Into function
Total function = (n(B))
n(A)
= 2 6
number of Into function can be find using inclusion-exclusion principle
Number of into function =
2
C
1
(1)
6
2
C
1
(1)
6
= only one image or range left from set B.
Number of onto function = 2
6
-
2
C
1
(1)
6
= 64 - 2 = 62
Q3: Let A = {0, 1, 2, … ,9}. Let R be a relation on A defined by (x, y) ? R if and only if | x -
y | is a multiple of 3.
Given below are two statements :
Statement I : n (R) = 36.
Statement II : R is an equivalence relation.
In the light of the above statements, choose the correct answer from the options given
below :
(a) Statement I is correct but Statement II is incorrect
(b) Both Statement I and Statement II are correct
Read MoreFAQs on Sets, Relations and Functions: JEE Main Previous Year Questions (2021-2026)
| 1. What's the difference between a relation and a function in JEE Maths? |  |
Ans. A relation is any set of ordered pairs connecting elements from two sets, while a function is a special relation where each input maps to exactly one output. In JEE problems, functions must pass the vertical line test-no element in the domain repeats with different range values. Understanding this distinction is critical for solving domain-codomain questions that frequently appear in JEE Main.
| 2. How do I find the domain and range of functions in JEE previous year papers? | |
Ans. Domain comprises all input values where the function is defined; range contains all possible outputs. For polynomial functions, domain is typically all real numbers. For rational functions, exclude values making the denominator zero. For square roots, ensure the radicand is non-negative. JEE Main consistently tests these restrictions through algebraic and graphical methods across multiple years.
| 3. What are the key properties of sets I need to memorise for JEE exams? | |
Ans. Essential set properties include commutative laws (A∪B = B∪A), associative laws, distributive laws, De Morgan's laws, and complement rules. Cardinality (number of elements) and subset relationships are tested frequently. Master Venn diagram representations to visualise union, intersection, and complement operations-these visual tools help solve complex set theory problems in JEE Advanced and Main efficiently.
| 4. Why do inverse functions and composition of functions confuse me in JEE? | |
Ans. Inverse functions exist only for one-to-one functions (injective); composition f(g(x)) requires the range of g to be within the domain of f. Many students mix up notation and operation order-f⁻¹(x) isn't 1/f(x). JEE repeatedly tests whether composed functions are valid and whether finding inverses is possible, making clarity on these prerequisites essential for accuracy.
| 5. Which set relations and functions concepts appear most often in JEE Main question banks? | |
Ans. Equivalence relations (reflexive, symmetric, transitive properties), injective-surjective-bijective function classifications, and composite functions dominate JEE Main papers. Domain-range questions paired with function behaviour analysis appear consistently. Function transformations and inverse function existence also feature heavily. Referring to EduRev's compiled previous year questions, mind maps, and MCQ tests helps identify high-frequency patterns specific to your exam year.
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