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**Exercise 2.1 : ** Solutions of Questions on Page Number : **33**

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**Exercise 2.2 : ** Solutions of Questions on Page Number : **35**

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**Exercise 2.3 : ** Solutions of Questions on Page Number : **44**

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**Exercise Miscellaneous : ** Solutions of Questions on Page Number : **46**

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Next Chapter 3 : Trigonometric Functions >>
**Popular Articles**

Q1 :
**
**

If, find the values
of *x*and
*y*.

**Answer :**

It is given that.

Since the ordered pairs are equal, the corresponding elements will also be equal.

Therefore, and.

∴
*x*= 2 and
*y*= 1

Answer needs Correction? Click Here

Q2 :
**
**

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

**Answer :**

It is given that set A has 3 elements and the elements of set B are 3, 4, and 5.

⇒ Number of elements in set B = 3

Number of elements in (A x B)

= (Number of elements in A) x (Number of elements in B)

= 3 x 3 = 9

Thus, the number of elements in (A x B) is 9.

Answer needs Correction? Click Here

Q3 :
**
**

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

**Answer :**

Q4 :
**
**

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

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

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

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

**Answer :**

Q5 :
**
**

If A = {-1, 1}, find A x A x A.

**Answer :**

Q6 :
**
**

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

**Answer :**

Q7 :
**
**

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

(i) A x (B ∩C) = (A x B) ∩(A x C)

(ii) A x C is a subset of B x D

**Answer :**

Q8 :
**
**

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

**Answer :**

Q9 :
**
**

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
x B, find A and B, where
*x*, *y* and
*z* are distinct elements.

**Answer :**

Q10 :
**
**

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

**Answer :**

Q1 :
**
**

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

**Answer :**

Q2 :
**
**

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.

**Answer :**

Q3 :
**
**

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.

**Answer :**

Q4 :
**
**

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?

**Answer :**

Q5 :
**
**

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.

**Answer :**

Q6 :
**
**

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

**Answer :**

Q7 :
**
**

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

**Answer :**

Q8 :
**
**

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

**Answer :**

Q9 :
**
**

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.

**Answer :**

Q1 :
**
**

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)}

**Answer :**

Q2 :
**
**

Find the domain and range of the following real function:

(i)
*f*(*x*) =
â€“|*x*|
(ii)

**Answer :**

Q3 :
**
**

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)

**Answer :**

Q4 :
**
**

The function
'*t*'
which maps temperature in degree Celsius into temperature in
degree Fahrenheit is defined by.

Find (i) *t*(0) (ii)
*t*(28) (iii)
*t*(â€“10) (iv) The
value of C, when *t*(C) =
212

**Answer :**

Q5 :
**
**

Find the range of each of the following functions.

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

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

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

**Answer :**

Q1 :
**
**

The relation *f*
is defined by

The relation *g*is defined
by

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

**Answer :**

Q2 :
**
**

If
*f*(*x*)
= *x*^{2},
find.

**Answer :**

Q3 :
**
**

Find the domain of the function

**Answer :**

Q4 :
**
**

Find the domain and the range of the real function
*f*defined by.

**Answer :**

Q5 :
**
**

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

**Answer :**

Q6 :
**
**

Letbe a function
from **R**into
**R**. Determine the range of
*f*.

**Answer :**

Q7 :
**
**

Let *f*,
*g*: **R**
Ã¢â€ ’
**R** be defined, respectively by
*f*(*x*)
= *x* + 1,
*g*(*x*) =
2*x* â€“ 3.
Find *f*+
*g*,
*f*â€“
*g*and.

**Answer :**

Q8 :
**
**

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*.

**Answer :**

Q9 :
**
**

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.

**Answer :**

Q10 :
**
**

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.

**Answer :**

Q11 :
**
**

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

**Answer :**

Q12 :
**
**

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*.

**Answer :**

Maths - Maths : CBSE ** NCERT ** Exercise Solutions for Class 11th for ** Relations and Functions ** ( Exercise 2.1, 2.2, 2.3, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

- Maths : Chapter 3 - Trigonometric Functions Class 11
- Maths : Chapter 4 - Principle of Mathematical Induction Class 11
- Maths : Chapter 5 - Complex Numbers and Quadratic Equations Class 11
- Maths : Chapter 1 - Sets Class 11
- Maths : Chapter 9 - Sequences and Series Class 11
- Maths : Chapter 6 - Linear Inequalities Class 11
- Maths : Chapter 7 - Permutations and Combinations Class 11
- Maths : Chapter 13 - Limits and Derivatives Class 11
- Maths : Chapter 8 - Binomial Theorem Class 11

Exercise 2.1 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Exercise 2.2 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Exercise 2.3 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Exercise Miscellaneous |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Question 11 |

Question 12 |