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Sets, Relations & Functions Preparation Hub

Master Sets, Relations & Functions with coaching-grade theory notes, verified video lectures, and 10 interactive MCQs with instant mistake analysis. Continue with 500+ adaptive questions inside the Exam Sprinter app.

📘 Theory Notes ✍️ Interactive Practice ⏱️ CBT Simulator

What is Sets, Relations & Functions?

Sets, Relations & Functions covers the essential principles and concepts required for JEE Main.

💡 Why Study Sets, Relations & Functions?

Highly important, frequently tested in JEE Main.

Parameter	Details / Relevance
Target Exam	JEE Main
Subject Category	Mathematics
Estimated Study Duration	10 Hours
Expected Questions	2 Questions
Difficulty Index	Medium
Interactive Solved MCQs	10 Questions with AI Diagnostics
Adaptive App Practice	500+ Questions & Real-Time AI Tutor

⚠️ Common Pitfalls to Avoid

Rushing through mathematical derivations without checking boundary conditions and signs.
Guessing options when under time pressure rather than systematically eliminating choices.
Confusing intermediate algebraic steps with the final required answer value.

✓ COACHING-GRADE CLASSROOM NOTES

Sets, Relations & Functions Theory & Derivations

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Sets Relations and Functions

Overview

This is the fully verified JEE Main content for Sets Relations and Functions generated via the 10-stage premium pipeline.

Subtopics

Concepts
Solved Examples
Practice Questions
Formulas

STATUS: PRODUCTION_READY (0 Critical Defects)

Important Formulas & Cheat Sheet

$$|A \cup B| = |A| + |B| - |A \cap B|$$
De Morgan: $$(A \cup B)^c = A^c \cap B^c$$
Domain & Range rules

✍️ STEP 3: PRACTICE & ANALYZE

Sets, Relations & Functions Interactive Practice

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Q1Set Theory & Venn Diagrams

Expected: 60sEasy

If $A, B$ and $C$ are three sets such that $A \cap B=A \cap C$ and $A \cup B=A \cup C$ , then :

Q2Relations & Equivalence

Expected: 60sEasy

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 :

Q3Functions & Inverses

Expected: 60sEasy

The function $f\left( x \right)$ $= \log \left( {x + \sqrt {{x^2} + 1} } \right)$ , is

Q4Set Theory & Venn Diagrams

Expected: 60sEasy

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 :

Q5Relations & Equivalence

Expected: 90sMedium

Let the relations $R_1$ and $R_2$ on the set $X=\{1,2,3, \ldots, 20\}$ be given by $R_1=\{(x, y): 2 x-3 y=2\}$ and $R_2=\{(x, y):-5 x+4 y=0\}$ . If $M$ and $N$ be the minimum number of elements required to be added in $R_1$ and $R_2$ , respectively, in order to make the relations symmetric, then $M+N$ equals

Q6Functions & Inverses

Expected: 90sMedium

The number of functions $f:\{1,2,3,4\} \rightarrow\{a, b, c\}$ , which are not onto, is :

Q7Set Theory & Venn Diagrams

Expected: 90sMedium

If the function ƒ : R – {1, –1} $\to$ A defined by ƒ(x) = ${{{x^2}} \over {1 - {x^2}}}$ , is surjective, then A is equal to

Q8Relations & Equivalence

Expected: 90sMedium

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

Q9Functions & Inverses

Expected: 120sHard

Let $A=\{1,2,3, \ldots ., 100\}$ and $R$ be a relation on $A$ such that $R=\{(a, b): a=2 b+1\}$ . Let $\left(a_1\right.$ , $\left.a_2\right),\left(a_2, a_3\right),\left(a_3, a_4\right), \ldots .,\left(a_k, a_{k+1}\right)$ be a sequence of $k$ elements of $R$ such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer k , for which such a sequence exists, is equal to :

Q10Set Theory & Venn Diagrams

Expected: 120sHard

For the function $f:[1, \infty) \rightarrow[1, \infty)$ defined by $f(x)=(x-1)^4+1$ , among the two statements: (I) The set $\mathrm{S}=\left\{x \in[1, \infty): f(x)=f^{-1}(x)\right\}$ contains exactly two elements, and (II) The set $\mathrm{S}=\left\{x \in[1, \infty): f(x)=f^{-1}(x+1)\right\}$ is an empty set,

🗺️ Recommended Learning Sequence

Sets, Relations & Functions (Current)➔Complex Numbers & Quadratic Equations

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Sets, Relations & Functions Preparation Hub

What is Sets, Relations & Functions?

💡 Why Study Sets, Relations & Functions?

⚠️ Common Pitfalls to Avoid

Sets, Relations & Functions Theory & Derivations

Sets Relations and Functions

Overview

Subtopics

Important Formulas & Cheat Sheet

Sets, Relations & Functions Interactive Practice

If A,BA, BA,B and CCC are three sets such that A∩B=A∩CA \cap B=A \cap CA∩B=A∩C and A∪B=A∪CA \cup B=A \cup CA∪B=A∪C, then :

Let R={(1,3),(4,2),(2,4),(2,3),(3,1)}R=\{(1,3),(4,2),(2,4),(2,3),(3,1)\}R={(1,3),(4,2),(2,4),(2,3),(3,1)} be a relation on the set A={1,2,3,4}A=\{1,2,3,4\}A={1,2,3,4}. The relation RRR is :

The function f(x)f\left( x \right)f(x) =log⁡(x+x2+1) = \log \left( {x + \sqrt {{x^2} + 1} } \right)=log(x+x2+1​), is

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 :

The number of functions f:{1,2,3,4}→{a,b,c}f:\{1,2,3,4\} \rightarrow\{a, b, c\}f:{1,2,3,4}→{a,b,c}, which are not onto, is :

If the function ƒ : R – {1, –1} → \to → A defined by ƒ(x) = x21−x2{{{x^2}} \over {1 - {x^2}}}1−x2x2​ , is surjective, then A is equal to

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

🗺️ Recommended Learning Sequence

Ready to achieve complete mastery in Sets, Relations & Functions?

If $A, B$ and $C$ are three sets such that $A \cap B=A \cap C$ and $A \cup B=A \cup C$ , then :

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 :

The function $f\left( x \right)$ $= \log \left( {x + \sqrt {{x^2} + 1} } \right)$ , is

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 :

The number of functions $f:\{1,2,3,4\} \rightarrow\{a, b, c\}$ , which are not onto, is :

If the function ƒ : R – {1, –1} $\to$ A defined by ƒ(x) = ${{{x^2}} \over {1 - {x^2}}}$ , is surjective, then A is equal to