Are these practice questions for Relations and Functions based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 11 - Science Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Relations and Functions free?

Yes. Every chapter includes free practice questions for Class 11 - Science students to get you started.

What types of questions are included?

The practice set for Relations and Functions mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Relations and Functions for full coverage.

How many practice questions are there for Relations and Functions?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Relations and Functions Class 11 Mathematics Practice Questions with Answers

easy

State the condition for two ordered pairs

(x_1, y_1)

and

(x_2, y_2)

to be equal.

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easy

Define the Cartesian product of two non-empty sets A and B.

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easy

Given the function

f(x) = \frac{2x+1}{x-3}

, calculate

f(5)

.

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easy

If

P = \{a, b\}

and

Q = \{1, 2, 3\}

, list the elements of

P \times Q

and

Q \times P

. State whether

P \times Q

is equal to

Q \times P

.

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easy

If set A has 4 elements and set B = {x, y, z}, calculate the number of elements in A × B and the total number of possible relations from A to B.

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easy

Let

A = \{1, 2, 3\}

and

B = \{a, b\}

. Design two distinct functions,

f_1

and

f_2

, from

A

to

B

such that the range of

f_1

is

\{a\}

and the range of

f_2

is

\{a, b\}

. Justify why both are valid functions.

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easy

If

(\frac{x}{2} + 3, y - 4) = (5, 1)

, calculate the values of

x

and

y

.

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easy

Name the function

f: \mathbf{R} \rightarrow \mathbf{R}

defined by

f(x) = k

, where

k

is a real number.

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easy

If

(a+2, 9) = (5, b-1)

, find the values of

a

and

b

.

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medium

Examine if the relation

R = \{(2, 1), (4, 2), (6, 3), (8, 4), (6, 5)\}

is a function. Provide a clear reason for your answer.

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medium

If

A = \{1, 2, 3\}

and

B = \{a, b\}

, calculate

A \times B

and

B \times A

.

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medium

A relation R is defined on the set

A = \{1, 2, 3, 4, 5, 6\}

by

R = \{(x, y) : y = x + 2\}

. Write R in roster form and determine its domain and range. The codomain is A.

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medium

If a set A has 3 elements and a set B has 4 elements, how many relations can be defined from set A to set B?

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medium

Propose a real function

f(x)

whose domain is

\mathbb{R} - \{-2, 2\}

and whose range is

(0, \infty)

.

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medium

If

A = \{-1, 0, 1\}

, list the elements of the set

A \times A

.

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medium

Let R be a relation on the set of natural numbers

\mathbf{N}

defined by

R = \{(x, y) : y = x^2, x \text{ is a prime number less than 10}\}

. Calculate the range of R.

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medium

Evaluate whether the relation

f: \mathbb{N} \to \mathbb{N}

defined by

f(n) = n + (-1)^n

represents a valid function.

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medium

Given

A = \{x, y, z\}

and

B = \{1, 2\}

. Let

R_1 = \{(x, 1), (y, 2), (z, 1)\}

and

R_2 = \{(x, 1), (y, 1), (x, 2)\}

. Evaluate both

R_1

and

R_2

to determine if they can be considered functions from

A

to

B

. Provide a detailed justification for each case.

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medium

Let

A = \{1, 2, 3, ..., 10\}

. Formulate a relation

R

on

A

defined by

R = \{(x, y) : y = 2x - 1\}

. (i) Express

R

as a set of ordered pairs. (ii) Find the domain, codomain, and range of

R

. (iii) Critique whether

R

qualifies as a function from

A

to

A

. If not, modify the domain of

R

to the largest possible subset of

A

for which it would be a function. Justify your modifications.

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medium

Identify which of the following relations are functions. Give a reason for your answer. (i)

R_1 = \{(a,1), (b,2), (c,1)\}

where the domain is

\{a, b, c\}

. (ii)

R_2 = \{(x,5), (y,6), (x,7)\}

where the domain is

\{x, y\}

.

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medium

Justify whether the relation

R

on the set

\mathbb{Z}

of integers, defined as

R = \{(a, b) : |a - b| \le 1\}

, is reflexive, symmetric, or transitive.

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medium

Justify if the relation

R = \{(x, y) : x, y \in \mathbb{Z}, xy \ge 0\}

is a function from

\mathbb{Z}

to

\mathbb{Z}

.

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medium

Let a relation R be defined from

A = \{2, 3, 4, 5\}

to

B = \{3, 6, 7, 10\}

by

R = \{(x, y) : x \text{ divides } y\}

. Write R in roster form. Also, find its domain and range.

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medium

Describe the Identity Function and the Signum Function. For each function, state its domain, range, and provide its definition.

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medium

Define a function from a set A to a set B. Explain the two key conditions that a relation must satisfy to be a function. Provide one example of a relation that is a function and one that is not, explaining your reasoning.

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medium

Explain the difference between the range and the codomain of a relation from a non-empty set A to a non-empty set B.

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medium

Let R be a relation on the set of natural numbers

\mathbf{N}

defined by

R = \{(x, y) : y = 2x + 1, x \text{ is a natural number and } x \le 3\}

. List the elements of R and state its domain and range.

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medium

Design a function

f: \mathbb{R} \to \mathbb{R}

and another function

g: \mathbb{R} \to \mathbb{R}

such that

(f+g)(x)

is defined for all

x \in \mathbb{R}

, but the domain of

(\frac{f}{g})(x)

is

\mathbb{R} - \{k\}

for some integer

k

. Define

f(x)

,

g(x)

,

(f+g)(x)

, and

(\frac{f}{g})(x)

, and explicitly state their domains.

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medium

Analyze the function

f(x) = \frac{x^2 + 2x + 1}{x^2 - x - 6}

. (i) Factorize the denominator. (ii) Use this to determine the domain of the function

f

. (iii) Calculate

f(0)

and

f(-1)

.

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medium

If

f(x) = 2x - 5

and

g(x) = x^2 + 1

are two real functions, calculate

(f+g)(x)

,

(fg)(x)

, and

(\frac{f}{g})(x)

.

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medium

Propose a function

f: \mathbb{Z} \to \mathbb{Z}

such that its range is the set of all non-negative integers,

\mathbb{W} = \{0, 1, 2, ...\}

. Prove that your proposed relation is indeed a function with the specified range.

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medium

Let

A = \{1, 2\}

,

B = \{3, 4\}

, and

C = \{4, 5\}

. Demonstrate that

A \times (B \cup C) = (A \times B) \cup (A \times C)

.

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hard

Let

f(x) = x^2

and

g(x) = \sqrt{x-1}

. Evaluate the domains of the functions

f+g

,

f-g

,

fg

, and

\frac{f}{g}

. Justify how the domain of the combined function is determined in each case.

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hard

Let

A = \{1, 2, 3, 4, 5\}

and

R

be the relation on

A

defined by

R = \{(a, b) : b = a^2 - 1\}

. (i) Write

R

in roster form. (ii) Find the domain, codomain, and range of

R

. (iii) Represent

R

using an arrow diagram. (iv) Examine if

R

is a function from

A

to

A

. Justify your answer.

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hard

Calculate the domain and range of the real function

f(x) = \sqrt{25 - x^2}

.

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hard

Let

f(x) = \frac{1}{\sqrt{x - |x|}}

. Critique the possibility of defining this function for any real number

x

. Determine its domain and justify your conclusion.

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hard

Given

A \times B = \{(a, x), (b, y), (a, y), (b, x)\}

. (i) Identify the sets A and B. (ii) State the value of

n(A \times B)

. (iii) List all possible subsets of A. (iv) How many relations can be defined from set B to set A?

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hard

Let

f(x) = 3x - 2

and

g(x) = x^2

be two real functions. Define the following functions: (i)

(f+g)(x)

(ii)

(f-g)(x)

(iii)

(fg)(x)

(iv)

(\frac{f}{g})(x)

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hard

Critique the statement: "If

n(A) = m

and

n(B) = n

, then the number of non-empty relations from A to B is

2^{mn} - 1

." Is this always true? Justify your answer.

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hard

The Cartesian product

A \times A

has 9 elements, among which are found

(1, 0)

and

(2, 1)

. Find the set A and the remaining elements of

A \times A

.

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hard

Formulate a piecewise function

f(x)

with three distinct linear pieces, such that its domain is

\mathbb{R}

and its range is

[0, \infty)

. The function should not be the modulus function.

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hard

A function

f: \mathbf{R} \rightarrow \mathbf{R}

is defined by

f(x) = \begin{cases} 1 - x, & x < 1 \ 0, & x = 1 \ x - 1, & x > 1 \end{cases}

. (i) Calculate

f(-2)

. (ii) Calculate

f(1)

. (iii) Calculate

f(5)

. (iv) Analyze the function and determine its range.

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hard

Let

A = \{1, 2, 3, 4, 5\}

. A relation R is defined on set A as

R = \{(a, b) : b = a+1, a,b \in A\}

. (i) Express R in roster form. (ii) State the domain of R. (iii) State the range of R. (iv) State the codomain of R. (v) Explain if R is a function on A.

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hard

Formulate a relation on the set

A = \{1, 2, 3\}

that is reflexive and symmetric but not transitive.

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hard

Prove that for any two non-empty sets A and B,

A \times B = B \times A

if and only if

A = B

. Justify each step of your proof.

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Relations and FunctionsClass 11 Mathematics Practice Questions