#### Chapters

Chapter 2: Relations and Functions

Chapter 3: Trigonometric Functions

Chapter 4: Principle of Mathematical Induction

Chapter 5: Complex Numbers and Quadratic Equations

Chapter 6: Linear Inequalities

Chapter 7: Permutations and Combinations

Chapter 8: Binomial Theorem

Chapter 9: Sequences and Series

Chapter 10: Straight Lines

Chapter 11: Conic Sections

Chapter 12: Introduction to Three Dimensional Geometry

Chapter 13: Limits and Derivatives

Chapter 14: Mathematical Reasoning

Chapter 15: Statistics

Chapter 16: Probability

## Chapter 2: Relations and Functions

### NCERT solutions for Class 11 Mathematics Textbook Chapter 2 Relations and Functions Exercise 2.1 [Pages 33 - 34]

If `(x/3+1, y-2/3)=(5/3,1/3),`find the values of x and y.

If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A × B)?

If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.

State whether of the statement is true or false. If the statement is false, re-write the given statement correctly:

If P = {m, n} and Q = {n, m}, then P × Q = {(m, n), (n, m)}

True

False

State whether of the statement is true or false. If the statement is false, re-write the given statement correctly:

If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x ∈ B and y ∈ A.

True

False

State whether of the statement is true or false. If the statement is false, re-write the given statement correctly:

(iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ ϕ) = ϕ.

True

False

If A = {–1, 1}, find A × A × A.

If A × B = {(a, x), (a, y), (b, x), (b, y)}. Find A and B.

Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that A × (B ∩ C) = (A × B) ∩ (A × C)

Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that A × C is a subset of B × D

Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.

Let A and B be two sets such that n(A) = 3 and n (B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y and z are distinct elements.

The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0, 1). Find the set A and the remaining elements of A × A.

### NCERT solutions for Class 11 Mathematics Textbook Chapter 2 Relations and Functions Exercise 2.2 [Pages 35 - 36]

Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range.

Define a relation R on the set **N** of natural numbers by R = {(*x*, *y*): *y* = *x* + 5, *x* is a natural number less than 4; *x*, *y* ∈ **N**}. Depict this relationship using roster form. Write down the domain and the range.

A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(*x*, *y*): the difference between *x* and *y* is odd; *x* ∈ A, *y *∈ B}. Write R in roster form.

The given figure shows a relationship between the sets P and Q. write this relation

(i) in set-builder form (ii) in roster form.

What is its domain and range?

Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(*a*, *b*): *a*, *b* ∈ A, *b* is exactly divisible by *a*}.

(i) Write R in roster form

(ii) Find the domain of R

(iii) Find the range of R.

Determine the domain and range of the relation R defined by R = {(*x*, *x* + 5): *x* ∈ {0, 1, 2, 3, 4, 5}}.

Write the relation R = {(*x*, *x*^{3}): *x *is a prime number less than 10} in roster form.

Let A = {*x*, *y*, z} and B = {1, 2}. Find the number of relations from A to B.

Let R be the relation on **Z** defined by R = {(*a*, *b*): *a*, *b* ∈ **Z**, *a *– *b* is an integer}. Find the domain and range of R.

### NCERT solutions for Class 11 Mathematics Textbook Chapter 2 Relations and Functions Exercise 2.3 [Page 44]

Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.

(i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}

(ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}

(iii) {(1, 3), (1, 5), (2, 5)}

Find the domain and range of the given real function:

*f*(*x*) = –|*x*|

Find the domain and range of the following real function:

f(x) = `sqrt(9 - x^2)`

A function *f* is defined by *f*(*x*) = 2*x* – 5. Write down the values of

(i) *f*(0), (ii) *f*(7), (iii) *f*(–3)

The function ‘*t*’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by `t(C) = "9C"/5 + 32`

Find

(i) t(0)

(ii) t(28)

(iii) t(–10)

(iv) The value of C, when t(C) = 212.

Find the range of each of the following functions.

*f*(*x*) = 2 – 3*x*, *x* ∈ **R**, *x* > 0.

Find the range of each of the following functions.

*f*(*x*) = *x*^{2} + 2, *x*, is a real number.

Find the range of each of the following functions.

*f*(*x*) = *x*, *x* is a real number

### NCERT solutions for Class 11 Mathematics Textbook Chapter 2 Relations and Functions Exercise 2.4 [Pages 46 - 47]

The relation *f* is defined by f(x) = `{(x^2,0<=x<=3),(3x,3<=x<=10):}`

The relation* g* is defined by g(x) = `{(x^2, 0 <= x <= 2),(3x,2<= x <= 10):}`

Show that *f* is a function and* g *is not a function.

If f(x) = x^{2}, find `(f(1.1) - f(1))/((1.1 - 1))`

Find the domain of the function f(x) = `(x^2 + 2x + 1)/(x^2 - 8x + 12)`

Find the domain and the range of the real function *f* defined by `f(x)=sqrt((x-1))`

Find the domain and the range of the real function *f* defined by *f* (*x*) = |*x* – 1|.

Let `f = {(x, x^2/(1+x^2)):x ∈ R}` be a function from **R** into **R**. Determine the range of *f*.

Let *f*, *g*: **R** → **R** be defined, respectively by *f*(*x*) = *x *+ 1, *g*(*x*) = 2*x* – 3. Find *f* + *g*, *f* – *g* and `f/g`

Let *f *= {(1, 1), (2, 3), (0, –1), (–1, –3)} be a function from **Z** to **Z** defined by *f*(*x*) = *ax* + *b*, for some integers *a*, *b*. Determine *a*, *b*.

Let R be a relation from **N** to **N** defined by R = {(*a*, *b*): *a*, *b* ∈ **N** and *a* = *b*^{2}}. Are the following true?

(i) (*a*, *a*) ∈ R, for all* a *∈ **N**

(ii) (*a*, *b*) ∈ R, implies (*b*, *a*) ∈ R

(iii) (*a*, *b*) ∈ R, (*b*, *c*) ∈ R implies (*a*, *c*) ∈ R.

Justify your answer in each case.

Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and *f *= {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true?

(i) *f* is a relation from A to B (ii) *f* is a function from A to B.

Justify your answer in each case.

Let *f* be the subset of **Z** × **Z** defined by *f *= {(*ab*, *a* + *b*): *a*, *b* ∈ **Z**}. Is *f* a function from **Z** to **Z**: justify your answer.

Let A = {9, 10, 11, 12, 13} and let *f*: A → **N** be defined by *f*(*n*) = the highest prime factor of *n*. Find the range of *f*.

## Chapter 2: Relations and Functions

## NCERT solutions for Class 11 Mathematics Textbook chapter 2 - Relations and Functions

NCERT solutions for Class 11 Mathematics Textbook chapter 2 (Relations and Functions) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11 Mathematics Textbook solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11 Mathematics Textbook chapter 2 Relations and Functions are Cartesian Product of Sets, Brief Review of Cartesian System of Rectanglar Co-ordinates, Relation, Concept of Functions, Some Functions and Their Graphs, Algebra of Real Functions, Ordered Pairs, Equality of Ordered Pairs, Pictorial Diagrams, Graph of Function, Pictorial Representation of a Function, Exponential Function, Logarithmic Functions.

Using NCERT Class 11 solutions Relations and Functions exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 11 prefer NCERT Textbook Solutions to score more in exam.

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