Relations & Functions 50 MCQs | Class 11 Maths NCERT Chapter 2

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Maths — Relations And Functions

50 Questions Class 11 MCQs

Which of the following represents a relation from set \(A=\{1,2\}\) to \(B=\{3,4\}\)?
(Exam: NCERT Class XI)

a a. \(\{(1,3),(2,4)\}\) b b. \(\{(3,1),(4,2)\}\) c c. \(\{(1,2),(3,4)\}\) d d. \(\{(3,4)\}\)

The number of relations from a set with 2 elements to a set with 3 elements is:
(Exam: NCERT Class XI)

a a. \(6\) b b. \(8\) c c. \(2^6\) d d. \(3^2\)

Which of the following is a reflexive relation on \(A=\{1,2,3\}\)?
(Exam: NCERT Class XI)

a a. \(\{(1,1),(2,2)\}\) b b. \(\{(1,1),(2,2),(3,3)\}\) c c. \(\{(1,2),(2,3)\}\) d d. \(\{(2,2),(3,3)\}\)

A relation \(R\) on a set \(A\) is symmetric if:
(Exam: NCERT Class XI)

a a. \((a,b)\in R \Rightarrow (a,a)\in R\) b b. \((a,b)\in R \Rightarrow (b,a)\in R\) c c. \((a,a)\in R\) for all \(a\) d d. \((a,b),(b,c)\in R \Rightarrow (a,c)\in R\)

Which relation is transitive?
(Exam: NCERT Class XI)

a a. Equality b b. Inequality c c. “is friend of” d d. “is brother of”

If \(f(x)=x^2\), then \(f(-2)\) equals:
(Exam: NCERT Class XI)

a a. \(-4\) b b. \(0\) c c. \(2\) d d. \(4\)

The domain of the function \(f(x)=\sqrt{x-3}\) is:
(Exam: NCERT Class XI)

a a. \(\mathbb{R}\) b b. \(x>3\) c c. \(x\ge3\) d d. \(x\le3\)

Which of the following is not a function?
(Exam: NCERT Class XI)

a a. \(y=x^2\) b b. \(y=\sqrt{x}\) c c. \(x=y^2\) d d. \(y=|x|\)

A function having one-one and onto properties is called:
(Exam: NCERT Class XI)

a a. into b b. many-one c c. bijective d d. constant

The range of \(f(x)=x^2\), \(x\in\mathbb{R}\), is:
(Exam: NCERT Class XI)

a a. \(\mathbb{R}\) b b. \(x>0\) c c. \(x\ge0\) d d. \(x\le0\)

If \(f(x)=2x+1\), then \(f^{-1}(x)\) is:
(Exam: NCERT Class XI)

a a. \(\frac{x-1}{2}\) b b. \(\frac{x+1}{2}\) c c. \(2x-1\) d d. \(\frac{1-x}{2}\)

The composition \((f\circ g)(x)\) means:
(Exam: NCERT Class XI)

a a. \(f(x)+g(x)\) b b. \(f(g(x))\) c c. \(g(f(x))\) d d. \(f(x)g(x)\)

If \(f(x)=x+1\) and \(g(x)=x^2\), then \((f\circ g)(2)\) is:
(Exam: NCERT Class XI)

a a. \(5\) b b. \(6\) c c. \(9\) d d. \(10\)

A relation that is reflexive, symmetric, and transitive is called:
(Exam: NCERT Class XI)

a a. identity relation b b. equivalence relation c c. universal relation d d. empty relation

The identity function on \(\mathbb{R}\) is:
(Exam: NCERT Class XI)

a a. \(f(x)=1\) b b. \(f(x)=0\) c c. \(f(x)=x\) d d. \(f(x)=|x|\)

The number of equivalence relations on a set with one element is:
(Exam: NCERT Class XI)

a a. 0 b b. 1 c c. 2 d d. 3

Let \(R=\{(a,b)\in \mathbb{R}^2 : a-b=0\}\). Then \(R\) is:
(Exam: NCERT Class XI)

a a. reflexive only b b. symmetric only c c. transitive only d d. an equivalence relation

The range of \(f(x)=\frac{1}{x}\), \(x\in\mathbb{R}\setminus\{0\}\), is:
(Exam: NCERT Class XI)

a a. \(\mathbb{R}\) b b. \(\mathbb{R}^+\) c c. \(\mathbb{R}\setminus\{0\}\) d d. \((-\infty,0)\)

If \(f:\mathbb{R}\to\mathbb{R}\) defined by \(f(x)=x^2+1\), then \(f\) is:
(Exam: NCERT Class XI)

a a. one-one b b. onto c c. bijective d d. neither one-one nor onto

The inverse of a function exists if and only if the function is:
(Exam: NCERT Class XI)

a a. one-one b b. onto c c. bijective d d. many-one

If \(f(x)=ax+b\) has an inverse, then:
(Exam: NCERT Class XI)

a a. \(a=0\) b b. \(a\neq0\) c c. \(b=0\) d d. \(a=b\)

Let \(A=\{1,2,3\}\). The number of symmetric relations on \(A\) is:
(Exam: JEE Main)

a a. \(2^3\) b b. \(2^6\) c c. \(2^9\) d d. \(2^{12}\)

The number of equivalence relations on a set with 3 elements equals:
(Exam: JEE Main)

a a. 3 b b. 4 c c. 5 d d. 6

If \(f(x)=|x|\), then \(f\) is:
(Exam: JEE Main)

a a. one-one b b. onto \(\mathbb{R}\) c c. many-one d d. bijective

Let \(f(x)=x^3\). Then \(f^{-1}(x)\) equals:
(Exam: JEE Main)

a a. \(x^{1/3}\) b b. \(3x^2\) c c. \(\sqrt{x}\) d d. does not exist

If \(f\circ g=g\circ f\), then \(f\) and \(g\) are said to be:
(Exam: JEE Main)

a a. associative b b. commutative c c. distributive d d. identity

Let \(f(x)=\frac{x-1}{x+1}\). Then domain of \(f^{-1}\) is:
(Exam: JEE Main)

a a. \(\mathbb{R}\) b b. \(\mathbb{R}\setminus\{-1\}\) c c. \(\mathbb{R}\setminus\{1\}\) d d. \(\mathbb{R}\setminus\{1,-1\}\)

The number of functions from a set of 3 elements to a set of 2 elements is:
(Exam: JEE Main)

a a. 6 b b. 8 c c. 9 d d. 12

The number of onto functions from a 3-element set to a 2-element set is:
(Exam: JEE Main)

a a. 2 b b. 4 c c. 6 d d. 8

If \(f:\mathbb{R}\to\mathbb{R}\) is defined by \(f(x)=x^2\), then \(f\) is invertible on:
(Exam: JEE Main)

a a. \(\mathbb{R}\) b b. \((-\infty,0]\) c c. \([0,\infty)\) d d. both b and c

Assertion (A): Every equivalence relation is reflexive. Reason (R): Every equivalence relation is symmetric.
(Exam: JEE Main – Assertion Reason)

a a. Both A and R true, R explains A b b. Both A and R true, R does not explain A c c. A true, R false d d. A false, R true

Assertion (A): If a function has an inverse, it must be bijective. Reason (R): Only one-one functions are invertible.
(Exam: JEE Main – Assertion Reason)

a a. Both true, R explains A b b. Both true, R does not explain A c c. A true, R false d d. A false, R true

If \(f(x)=\ln x\), then domain of \(f\circ f\) is:
(Exam: JEE Advanced)

a a. \(x>0\) b b. \(x>1\) c c. \(x\ge0\) d d. \(x\neq0\)

Let \(f(x)=x^2\) and \(g(x)=\sqrt{x}\). Then \((f\circ g)(x)\) equals:
(Exam: JEE Advanced)

a a. \(x\) b b. \(|x|\) c c. \(x^2\) d d. \(\sqrt{x}\)

The relation \(R=\{(x,y): x-y\in\mathbb{Z}\}\) on \(\mathbb{R}\) is:
(Exam: JEE Advanced)

a a. reflexive only b b. symmetric only c c. transitive only d d. equivalence relation

If \(f(x)=x^2+x\), then minimum value of \(f(x)\) is:
(Exam: JEE Main)

a a. \(-\frac14\) b b. \(0\) c c. \(\frac14\) d d. \(-1\)

Let \(f:\mathbb{N}\to\mathbb{N}\) be defined by \(f(x)=x+1\). Then \(f\) is:
(Exam: JEE Main)

a a. one-one but not onto b b. onto but not one-one c c. bijective d d. neither

The number of bijective functions from a set of 4 elements to itself is:
(Exam: JEE Main)

a a. 4 b b. 12 c c. 24 d d. 16

If \(f(x)=\frac{ax+b}{cx+d}\) is invertible, then:
(Exam: JEE Advanced)

a a. \(ad-bc=0\) b b. \(ad-bc\neq0\) c c. \(a=c\) d d. \(b=d\)

Let \(f(x)=\sin x\). The inverse of \(f\) exists on:
(Exam: JEE Main)

a a. \(\mathbb{R}\) b b. \([-\pi/2,\pi/2]\) c c. \([0,2\pi]\) d d. \([-\pi,\pi]\)

The range of \(f(x)=\frac{1}{1+x^2}\) is:
(Exam: JEE Main)

a a. \((0,1]\) b b. \([0,1)\) c c. \((-\infty,1]\) d d. \([1,\infty)\)

If \(f(x)=x^3+1\), then \(f^{-1}(2)\) equals:
(Exam: JEE Main)

a a. 0 b b. 1 c c. \(-1\) d d. 2

Let \(A=\{1,2\}\). Number of antisymmetric relations on \(A\) is:
(Exam: JEE Advanced)

a a. 4 b b. 6 c c. 8 d d. 12

If \(f(x)=x^2\) and domain is \(\mathbb{Z}\), then \(f\) is:
(Exam: JEE Main)

a a. one-one b b. onto c c. many-one d d. bijective

The relation “is parallel to” among straight lines is:
(Exam: JEE Main)

a a. reflexive only b b. symmetric only c c. transitive only d d. equivalence relation

If \(f(x)=e^x\), then \(f^{-1}(x)\) equals:
(Exam: JEE Main)

a a. \(\ln x\) b b. \(\log x\) c c. \(1/x\) d d. \(x^e\)

The number of equivalence classes induced by relation \(x\sim y\iff x-y\) is even, on \(\mathbb{Z}\), is:
(Exam: JEE Main)

a a. 1 b b. 2 c c. infinite d d. 4

If \(f(x)=x|x|\), then \(f\) is:
(Exam: JEE Advanced)

a a. one-one b b. onto c c. bijective d d. many-one

Let \(f(x)=\tan x\). Inverse exists on:
(Exam: JEE Advanced)

a a. \((-\pi/2,\pi/2)\) b b. \((0,\pi)\) c c. \((-\pi,\pi)\) d d. \(\mathbb{R}\)

Assertion (A): A many-one function cannot have an inverse. Reason (R): Inverse of a function must be unique.
(Exam: JEE Advanced – Assertion Reason)

a a. Both A and R true, R explains A b b. Both true, R does not explain A c c. A true, R false d d. A false, R true

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Frequently Asked Questions

An ordered pair is a pair of elements written as \((a, b)\), where the order matters. Two ordered pairs are equal if and only if their corresponding elements are equal.

The Cartesian product of sets \(A\) and \(B\), denoted \(A \times B\), is the set of all ordered pairs \((a, b)\) where \(a \in A\) and \(b \in B\).

If set \(A\) has \(m\) elements and set \(B\) has \(n\) elements, then \(A \times B\) has \(m \times n\) elements.

A relation from set \(A\) to set \(B\) is any subset of the Cartesian product \(A \times B\).

The domain is the set of all first elements of the ordered pairs belonging to the relation.

The range is the set of all second elements of the ordered pairs of a relation.

The codomain is the set from which the second elements of ordered pairs are taken, regardless of whether all elements appear in the relation or not.

A relation that contains no ordered pair is called an empty relation.

A relation that contains all possible ordered pairs of a Cartesian product is called a universal relation.

An identity relation on a set \(A\) consists of all ordered pairs \((a, a)\) for every \(a \in A\).

A relation is reflexive if every element of the set is related to itself, i.e., \((a, a)\) belongs to the relation for all \(a\).

A relation is symmetric if whenever \((a, b)\) belongs to the relation, \((b, a)\) also belongs to it.

A relation is transitive if whenever \((a, b)\) and \((b, c)\) belong to the relation, then \((a, c)\) must also belong to it.

A relation that is reflexive, symmetric, and transitive is called an equivalence relation.

An equivalence class is the set of all elements related to a given element under an equivalence relation.

Relations & Functions

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Maths — Relations And Functions

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Relations & Functions

MCQ Bank Snapshot

Why Practise These MCQs?

Topic-wise MCQ Breakdown

Must-Know Formulae Before You Start

MCQ Solving Strategy

⚠ Common Traps & Errors

Difficulty Ladder

Continue Your Preparation

Maths — Relations And Functions

Frequently Asked Questions

Q 01 What is an ordered pair?

Q 02 What is the Cartesian product of two sets?

Q 03 How many elements are there in a Cartesian product?

Q 04 What is a relation in mathematics?

Q 05 What is the domain of a relation?

Q 06 What is the range of a relation?

Q 07 What is the codomain of a relation?

Q 08 What is an empty relation?

Q 09 What is a universal relation?

Q 10 What is an identity relation?

Q 11 What is a reflexive relation?

Q 12 What is a symmetric relation?

Q 13 What is a transitive relation?

Q 14 What is an equivalence relation?

Q 15 What are equivalence classes?

Recent Posts

Relations and Functions – Learning Resources

Detailed Notes

True / False

NCERT Solutions

Practice Advance MCQs

Let's Connect