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Previous year question hub

Sets And Relations - Algebra - Mathematics Previous Year Questions

Practice Sets And Relations - Algebra - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

110Papers
19Years
121Questions
1Topics

Sets And Relations question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Sets And Relations. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 88 72.7%
Easy 22 18.2%
Hard 11 9.1%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 86 71.1%
Numerical Answer Type (NAT) 35 28.9%

Subject weightage

Top subjects by unique question coverage.

Mathematics
121 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
121 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Sets And Relations
121 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

JEE MAIN 2026 ONLINE 21ST JANUARY EVENING SHIFT
2 Qs
JEE MAIN 2026 ONLINE 22ND JANUARY EVENING SHIFT
2 Qs
JEE MAIN 2026 ONLINE 23RD JANUARY EVENING SHIFT
2 Qs
JEE Main 2026 (Online) 2nd April Evening Shift
1 Qs
JEE Main 2026 (Online) 5th April Evening Shift
1 Qs
JEE Main 2026 (Online) 6th April Evening Shift
1 Qs
JEE Main 2026 (Online) 8th April Evening Shift
1 Qs
JEE MAIN 2026 ONLINE 21ST JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 22ND JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 23RD JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 24TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 22ND JANUARY MORNING SHIFT
2 Qs
JEE MAIN 2025 ONLINE 23RD JANUARY EVENING SHIFT
2 Qs
JEE MAIN 2025 ONLINE 7TH APRIL MORNING SHIFT
2 Qs
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 23RD JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 24TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 24TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 28TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 29TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 29TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 2ND APRIL EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 2ND APRIL MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 3RD APRIL EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 3RD APRIL MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 4TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 4TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 7TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 8TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 6TH APRIL MORNING SHIFT
2 Qs
JEE MAIN 2024 ONLINE 1ST FEBRUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 1ST FEBRUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 27TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 27TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 29TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 29TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 30TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 31ST JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 31ST JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 4TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 6TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 8TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT
2 Qs
JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 10TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 11TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 11TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 12TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 13TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 1ST FEBRUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 1ST FEBRUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 24TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 24TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 25TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 29TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 30TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 31ST JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 31ST JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 6TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 8TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 8TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 26TH JUNE MORNING SHIFT
2 Qs
JEE MAIN 2022 ONLINE 29TH JULY MORNING SHIFT
2 Qs
JEE MAIN 2022 ONLINE 24TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 25TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 26TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 27TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 28TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 28TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 28TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 29TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH JULY EVENING SHIFT
2 Qs
JEE Main 2021 (Online) 24th February Morning Shift
1 Qs
JEE Main 2021 (Online) 26th February Morning Shift
1 Qs
JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 16TH MARCH MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 17TH MARCH MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 18TH MARCH EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 26TH AUGUST MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 31ST AUGUST MORNING SHIFT
1 Qs
JEE MAIN 2020 ONLINE 2ND SEPTEMBER MORNING SLOT
1 Qs
JEE MAIN 2020 ONLINE 3RD SEPTEMBER EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 3RD SEPTEMBER MORNING SLOT
1 Qs
JEE MAIN 2020 ONLINE 4TH SEPTEMBER EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 4TH SEPTEMBER MORNING SLOT
1 Qs
JEE MAIN 2020 ONLINE 5TH SEPTEMBER MORNING SLOT
1 Qs
JEE MAIN 2020 ONLINE 6TH SEPTEMBER MORNING SLOT
1 Qs
JEE MAIN 2020 ONLINE 7TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 9TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 12TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 12TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2018 OFFLINE
1 Qs
JEE MAIN 2018 ONLINE 15TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2016 ONLINE 10TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2015 OFFLINE
1 Qs
AIEEE 2012
1 Qs
AIEEE 2011
1 Qs
AIEEE 2010
1 Qs
AIEEE 2009
1 Qs
AIEEE 2008
1 Qs
AIEEE 2006
1 Qs
AIEEE 2005
1 Qs
AIEEE 2004
1 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
JEE Main 2026 (Online) 2nd April Evening Shift20261View paper
JEE Main 2026 (Online) 5th April Evening Shift20261View paper
JEE Main 2026 (Online) 6th April Evening Shift20261View paper
JEE Main 2026 (Online) 8th April Evening Shift20261View paper
JEE MAIN 2026 ONLINE 21ST JANUARY EVENING SHIFT20262View paper
JEE MAIN 2026 ONLINE 21ST JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 22ND JANUARY EVENING SHIFT20262View paper
JEE MAIN 2026 ONLINE 22ND JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 23RD JANUARY EVENING SHIFT20262View paper
JEE MAIN 2026 ONLINE 23RD JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 24TH JANUARY MORNING SHIFT20261View paper
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 22ND JANUARY MORNING SHIFT20252View paper
JEE MAIN 2025 ONLINE 23RD JANUARY EVENING SHIFT20252View paper
JEE MAIN 2025 ONLINE 23RD JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 24TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 24TH JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 28TH JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 29TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 29TH JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 2ND APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 2ND APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 3RD APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 3RD APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 4TH APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 4TH APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 7TH APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 7TH APRIL MORNING SHIFT20252View paper
JEE MAIN 2025 ONLINE 8TH APRIL EVENING SHIFT20251View paper
JEE MAIN 2024 ONLINE 1ST FEBRUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 1ST FEBRUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 27TH JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 27TH JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 29TH JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 29TH JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 30TH JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 31ST JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 31ST JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 4TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 6TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 6TH APRIL MORNING SHIFT20242View paper
JEE MAIN 2024 ONLINE 8TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 10TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 11TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 11TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 12TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 13TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT20232View paper
JEE MAIN 2023 ONLINE 1ST FEBRUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 1ST FEBRUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 24TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 24TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 25TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 29TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 30TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 31ST JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 31ST JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 6TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 8TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 8TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2022 ONLINE 24TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 26TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 26TH JUNE MORNING SHIFT20222View paper
JEE MAIN 2022 ONLINE 27TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JULY MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JULY MORNING SHIFT20222View paper
JEE MAIN 2022 ONLINE 29TH JUNE MORNING SHIFT20221View paper
JEE Main 2021 (Online) 24th February Morning Shift20211View paper
JEE Main 2021 (Online) 26th February Morning Shift20211View paper
JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 16TH MARCH MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 17TH MARCH MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 18TH MARCH EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 26TH AUGUST MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH JULY EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 31ST AUGUST MORNING SHIFT20211View paper
JEE MAIN 2020 ONLINE 2ND SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 3RD SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 3RD SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 4TH SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 4TH SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 5TH SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 6TH SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 7TH JANUARY EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 9TH JANUARY EVENING SLOT20201View paper
JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH APRIL EVENING SLOT20191View paper
JEE MAIN 2018 OFFLINE20181View paper
JEE MAIN 2018 ONLINE 15TH APRIL MORNING SLOT20181View paper
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT20181View paper
JEE MAIN 2016 ONLINE 10TH APRIL MORNING SLOT20161View paper
JEE MAIN 2015 OFFLINE20151View paper
AIEEE 201220121View paper
AIEEE 201120111View paper
AIEEE 201020101View paper
AIEEE 200920091View paper
AIEEE 200820081View paper
AIEEE 200620061View paper
AIEEE 200520051View paper
AIEEE 200420041View paper

All Sets And Relations previous year questions

Practice every matching question in batches of 20, with every available option.

1
2004 · Mathematics · Algebra · Sets And Relations
AIEEE 2004
Let $R=\{(1,3),(4,2),(2,4),(2,3),(3,1)\}$ be a relation on the set $A=\{1,2,3,4\}$. The relation $R$ is :
A
a function
B
transitive
C
not symmetric
D
reflexive
Open complete paper
2
2005 · Mathematics · Algebra · Sets And Relations
AIEEE 2005
Let $R=\{(3,3),(6,6),(9,9),(12,12),(6,12)$, $(3,9),(3,12),(3,6)\}$ be a relation on the set $A=\{3,6,9,12\}$. The relation is :
A
reflexive and symmetric only
B
an equivalence relation
C
reflexive only
D
reflexive and transitive only
Open complete paper
3
2006 · Mathematics · Algebra · Sets And Relations
AIEEE 2006
Let $W$ denote the words in the English dictionary. Define the relation $R$ by

$R=\{(x, y) \in W \times W \mid$ the words $x$ and $y$ have at least one letter in common}. Then, $R$ is
A
reflexive, symmetric and not transitive
B
reflexive, symmetric and transitive
C
reflexive, not symmetric and transitive
D
not reflexive, symmetric and transitive
Open complete paper
4
2008 · Mathematics · Algebra · Sets And Relations
AIEEE 2008
Let R be the real line. Consider the following subsets of the plane \(R \times R\) :
$$S = \left\{ {(x,y):y = x + 1\,\,and\,\,0 < x < 2} \right\}$$
\(T = \left\{ {(x,y): x - y\,\,\,is\,\,an\,\,{\mathop{\rm int}} eger\,} \right\}\),

Which one of the following is true ?

A
Neither S nor T is an equivalence relation on R
B
Both S and T are equivalence relation on R
C
S is an equivalence relation on R but T is not
D
T is an equivalence relation on R but S is not
Open complete paper
5
2009 · Mathematics · Algebra · Sets And Relations
AIEEE 2009
If $A, B$ and $C$ are three sets such that $A \cap B=A \cap C$ and $A \cup B=A \cup C$, then :
A
$A=C$
B
$B=C$
C
$A \cap B=\phi$
D
$A=B$
Open complete paper
6
2010 · Mathematics · Algebra · Sets And Relations
AIEEE 2010
Consider the following relations

$R=\{(x, y) \mid x, y$ are real numbers and $x=w y$ for some rational number $w\}$;

$S=\left\{\left(\frac{m}{n}, \frac{p}{q}\right) \mid m, n, p\right.$ and $q$ are integers such that $n, q \neq 0$ and $q m=p m\}$. Then
A
$R$ is an equivalence relation but $S$ is not an equivalence relation
B
Neither $R$ nor $S$ is an equivalence relation
C
$S$ is an equivalence relation but $R$ is not an equivalence relation
D
$R$ and $S$ both are equivalence relations
Open complete paper
7
2011 · Mathematics · Algebra · Sets And Relations
AIEEE 2011
Let $R$ be the set of real numbers.

Statement I : $A=\{(x, y) \in R \times R: y-x$ is an integer $\}$ is an equivalence relation on $R$.

Statement II : $ B=\{(x, y) \in R \times R: x=\alpha y$ for some rational number $\alpha\}$ is an equivalence relation on $R$.
A
Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
B
Statement I is true, Statement II is false.
C
Statement I is false, Statement II is true.
D
Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
Open complete paper
8
2012 · Mathematics · Algebra · Sets And Relations
AIEEE 2012
Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y \(\subseteq\) X, Z \(\subseteq\) X and Y \(\cap\) Z is empty, is :
A
35
B
25
C
53
D
52
Open complete paper
9
2015 · Mathematics · Algebra · Sets And Relations
JEE MAIN 2015 OFFLINE
Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A $\times$ B , each having atleast three elements are
A
219
B
256
C
275
D
510
Open complete paper
10
2016 · Mathematics · Algebra · Sets And Relations
JEE MAIN 2016 ONLINE 10TH APRIL MORNING SLOT
Let P = {\(\theta\) : sin\(\theta\) \(-\) cos\(\theta\) = \(\sqrt 2 \,\cos \theta\)}

and Q = {\(\theta\) : sin\(\theta\) + cos\(\theta\) = \(\sqrt 2 \,\sin \theta\)} be two sets. Then
A
P \(\subset\) Q and Q \(-\) P \(\ne\) \(\phi\)
B
Q \(\not\subset\) P
C
P \(\not\subset\) Q
D
P = Q
Open complete paper
11
2018 · Mathematics · Algebra · Sets And Relations
JEE MAIN 2018 OFFLINE
Two sets A and B are as under :

A = {(\(a\), b) \(\in\) R \(\times\) R : |\(a\) - 5| < 1 and |b - 5| < 1};

B = {(\(a\), b) \(\in\) R \(\times\) R : 4(\(a\) - 6)2 + 9(b - 5)2 \(\le\) 36 };

Then
A
neither A \(\subset\) B nor B \(\subset\) A
B
B \(\subset\) A
C
A \(\subset\) B
D
A \(\cap\) B = \(\phi\) ( an empty set )
Open complete paper
12
2018 · Mathematics · Algebra · Sets And Relations
JEE MAIN 2018 ONLINE 15TH APRIL MORNING SLOT
Consider the following two binary relations on the set A = {a, b, c} :
R1 = {(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)} and
R2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}.
Then :
A
both R1 and R2 are not symmetric.
B
R1 is not symmetric but it is transitive.
C
R2 is symmetric but it is not transitive.
D
both R1 and R2 are transitive.
Open complete paper
13
2018 · Mathematics · Algebra · Sets And Relations
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT
Let N denote the set of all natural numbers. Define two binary relations on N as R = {(x, y) \(\in\) N \(\times\) N : 2x + y = 10} and R2 = {(x, y) \(\in\) N \(\times\) N : x + 2y = 10}. Then :
A
Range of R1 is {2, 4, 8).
B
Range of R2 is {1, 2, 3, 4}.
C
Both R1 and R2 are symmetric relations.
D
Both R1 and R2 are transitive relations.
Open complete paper
14
2019 · Mathematics · Algebra · Sets And Relations
JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT
In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is
A
42
B
102
C
1
D
38
Open complete paper
15
2019 · Mathematics · Algebra · Sets And Relations
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT
Let A, B and C be sets such that \(\phi\) \(\ne\) A \(\cap\) B \(\subseteq\) C. Then which of the following statements is not true ?
A
If (A – B) \(\subseteq\) C, then A \(\subseteq\) C
B
B \(\cap\) C \(\ne\) \(\phi\)
C
(C \(\cup\) A) \(\cap\) (C \(\cup\) B) = C
D
If (A – C) \(\subseteq\) B, then A \(\subseteq\) B
Open complete paper
16
2019 · Mathematics · Algebra · Sets And Relations
JEE MAIN 2019 ONLINE 12TH JANUARY EVENING SLOT
Let Z be the set of integers.
If A = {x \(\in\) Z : 2(x + 2) (x2 \(-\) 5x + 6) = 1} and
B = {x \(\in\) Z : \(-\) 3 < 2x \(-\) 1 < 9},
then the number of subsets of the set A \(\times\) B, is
A
212
B
218
C
210
D
215
Open complete paper
17
2019 · Mathematics · Algebra · Sets And Relations
JEE MAIN 2019 ONLINE 12TH JANUARY MORNING SLOT
Let S = {1, 2, 3, … , 100}. The number of non-empty subsets A of S such that the product of elements in A is even is :
A
250 – 1
B
250 (250 \(-\) 1)
C
2100 \(-\) 1
D
250 + 1
Open complete paper
18
2019 · Mathematics · Algebra · Sets And Relations
JEE MAIN 2019 ONLINE 9TH APRIL EVENING SLOT
Two newspapers A and B are published in a city. It is known that 25% of the city populations reads A and 20% reads B while 8% reads both A and B. Further, 30% of those who read A but not B look into advertisements and 40% of those who read B but not A also look into advertisements, while 50% of those who read both A and B look into advertisements. Then the percentage of the population who look into advertisement is :-
A
13.5
B
13
C
12.8
D
13.9
Open complete paper
19
2020 · Mathematics · Algebra · Sets And Relations
JEE MAIN 2020 ONLINE 2ND SEPTEMBER MORNING SLOT
If R = {(x, y) : x, y \(\in\) Z, x2 + 3y2 \(\le\) 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}
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20
2020 · Mathematics · Algebra · Sets And Relations
JEE MAIN 2020 ONLINE 3RD SEPTEMBER EVENING SLOT
Let R1 and R2 be two relation defined as follows :
R1 = {(a, b) \(\in\) R2 : a2 + b2 \(\in\) Q} and
R2 = {(a, b) \(\in\) R2 : a2 + b2 \(\notin\) 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.
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