#### Online Mock Tests

#### 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

## Solutions for Chapter 2: Relations and Functions

Below listed, you can find solutions for Chapter 2 of CBSE, Karnataka Board PUC NCERT for Class 11 Mathematics.

### NCERT solutions for Class 11 Mathematics 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 the following statement are true or false. If the statement is false, rewrite the given statement correctly.

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

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 the following statement are true or false. If the statement is false, rewrite 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* ∈ A and *y* ∈ B.

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

State whether the following statement are true or false. If the statement is false, rewrite the given statement correctly.

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

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 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 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 Chapter 2 Relations and Functions Miscellaneous Exercise [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*.

## Solutions for Chapter 2: Relations and Functions

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

Shaalaa.com has the CBSE, Karnataka Board PUC Mathematics Class 11 Mathematics CBSE, Karnataka Board PUC solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. NCERT solutions for Mathematics Class 11 Mathematics CBSE, Karnataka Board PUC 2 (Relations and Functions) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

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

Concepts covered in Class 11 Mathematics chapter 2 Relations and Functions are Cartesian Product of Sets, Brief Review of Cartesian System of Rectanglar Co-ordinates, Concept of 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 Mathematics solutions Relations and Functions exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in NCERT Solutions are essential questions that can be asked in the final exam. Maximum CBSE, Karnataka Board PUC Class 11 Mathematics students prefer NCERT Textbook Solutions to score more in exams.

Get the free view of Chapter 2, Relations and Functions Class 11 Mathematics additional questions for Mathematics Class 11 Mathematics CBSE, Karnataka Board PUC, and you can use Shaalaa.com to keep it handy for your exam preparation.