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Maths — RELATIONS AND FUNCTIONS

50 Questions Class 11 MCQs
1
Which of the following represents a relation from set \(A=\{1,2\}\) to \(B=\{3,4\}\)?
(Exam: NCERT Class XI)
2
The number of relations from a set with 2 elements to a set with 3 elements is:
(Exam: NCERT Class XI)
3
Which of the following is a reflexive relation on \(A=\{1,2,3\}\)?
(Exam: NCERT Class XI)
4
A relation \(R\) on a set \(A\) is symmetric if:
(Exam: NCERT Class XI)
5
Which relation is transitive?
(Exam: NCERT Class XI)
6
If \(f(x)=x^2\), then \(f(-2)\) equals:
(Exam: NCERT Class XI)
7
The domain of the function \(f(x)=\sqrt{x-3}\) is:
(Exam: NCERT Class XI)
8
Which of the following is not a function?
(Exam: NCERT Class XI)
9
A function having one-one and onto properties is called:
(Exam: NCERT Class XI)
10
The range of \(f(x)=x^2\), \(x\in\mathbb{R}\), is:
(Exam: NCERT Class XI)
11
If \(f(x)=2x+1\), then \(f^{-1}(x)\) is:
(Exam: NCERT Class XI)
12
The composition \((f\circ g)(x)\) means:
(Exam: NCERT Class XI)
13
If \(f(x)=x+1\) and \(g(x)=x^2\), then \((f\circ g)(2)\) is:
(Exam: NCERT Class XI)
14
A relation that is reflexive, symmetric, and transitive is called:
(Exam: NCERT Class XI)
15
The identity function on \(\mathbb{R}\) is:
(Exam: NCERT Class XI)
16
The number of equivalence relations on a set with one element is:
(Exam: NCERT Class XI)
17
Let \(R=\{(a,b)\in \mathbb{R}^2 : a-b=0\}\). Then \(R\) is:
(Exam: NCERT Class XI)
18
The range of \(f(x)=\frac{1}{x}\), \(x\in\mathbb{R}\setminus\{0\}\), is:
(Exam: NCERT Class XI)
19
If \(f:\mathbb{R}\to\mathbb{R}\) defined by \(f(x)=x^2+1\), then \(f\) is:
(Exam: NCERT Class XI)
20
The inverse of a function exists if and only if the function is:
(Exam: NCERT Class XI)
21
If \(f(x)=ax+b\) has an inverse, then:
(Exam: NCERT Class XI)
22
Let \(A=\{1,2,3\}\). The number of symmetric relations on \(A\) is:
(Exam: JEE Main)
23
The number of equivalence relations on a set with 3 elements equals:
(Exam: JEE Main)
24
If \(f(x)=|x|\), then \(f\) is:
(Exam: JEE Main)
25
Let \(f(x)=x^3\). Then \(f^{-1}(x)\) equals:
(Exam: JEE Main)
26
If \(f\circ g=g\circ f\), then \(f\) and \(g\) are said to be:
(Exam: JEE Main)
27
Let \(f(x)=\frac{x-1}{x+1}\). Then domain of \(f^{-1}\) is:
(Exam: JEE Main)
28
The number of functions from a set of 3 elements to a set of 2 elements is:
(Exam: JEE Main)
29
The number of onto functions from a 3-element set to a 2-element set is:
(Exam: JEE Main)
30
If \(f:\mathbb{R}\to\mathbb{R}\) is defined by \(f(x)=x^2\), then \(f\) is invertible on:
(Exam: JEE Main)
31
Assertion (A): Every equivalence relation is reflexive. Reason (R): Every equivalence relation is symmetric.
(Exam: JEE Main – Assertion Reason)
32
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)
33
If \(f(x)=\ln x\), then domain of \(f\circ f\) is:
(Exam: JEE Advanced)
34
Let \(f(x)=x^2\) and \(g(x)=\sqrt{x}\). Then \((f\circ g)(x)\) equals:
(Exam: JEE Advanced)
35
The relation \(R=\{(x,y): x-y\in\mathbb{Z}\}\) on \(\mathbb{R}\) is:
(Exam: JEE Advanced)
36
If \(f(x)=x^2+x\), then minimum value of \(f(x)\) is:
(Exam: JEE Main)
37
Let \(f:\mathbb{N}\to\mathbb{N}\) be defined by \(f(x)=x+1\). Then \(f\) is:
(Exam: JEE Main)
38
The number of bijective functions from a set of 4 elements to itself is:
(Exam: JEE Main)
39
If \(f(x)=\frac{ax+b}{cx+d}\) is invertible, then:
(Exam: JEE Advanced)
40
Let \(f(x)=\sin x\). The inverse of \(f\) exists on:
(Exam: JEE Main)
41
The range of \(f(x)=\frac{1}{1+x^2}\) is:
(Exam: JEE Main)
42
If \(f(x)=x^3+1\), then \(f^{-1}(2)\) equals:
(Exam: JEE Main)
43
Let \(A=\{1,2\}\). Number of antisymmetric relations on \(A\) is:
(Exam: JEE Advanced)
44
If \(f(x)=x^2\) and domain is \(\mathbb{Z}\), then \(f\) is:
(Exam: JEE Main)
45
The relation “is parallel to” among straight lines is:
(Exam: JEE Main)
46
If \(f(x)=e^x\), then \(f^{-1}(x)\) equals:
(Exam: JEE Main)
47
The number of equivalence classes induced by relation \(x\sim y\iff x-y\) is even, on \(\mathbb{Z}\), is:
(Exam: JEE Main)
48
If \(f(x)=x|x|\), then \(f\) is:
(Exam: JEE Advanced)
49
Let \(f(x)=\tan x\). Inverse exists on:
(Exam: JEE Advanced)
50
Assertion (A): A many-one function cannot have an inverse. Reason (R): Inverse of a function must be unique.
(Exam: JEE Advanced – Assertion Reason)

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.

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