Class 11 Maths Chapter 2 Relations And Functions Exercise 2.2 Solutions in English Medium

Class 11 Maths Chapter 2 Relations And Functions Exercise 2.2 Solutions in English Medium

 

Free NCERT Solutions for Class 11 Maths Chapter 2 Relations And Functions Exercise 2.2 prepared by expert Mathematics teacher as per CBSE (NCERT) books guidelines.

 

Free  NCERT Solutions for Class 11 Math’s Chapter 2  Relations And Functions Exercise 2.1, Exercise 2.2, Exercise 2.3 and Miscellaneous Exercise in English Medium for CBSE.

 



NCERT Maths Class 11 Chapter 2 Relations And Functions. Just click on the Exercise wise links given below to practice the Maths solutions for the respective exercise.

Exercise 2.1Click here
Exercise 2.2Click here
Exercise 2.3Click here




Class 11 Maths Chapter 2 Relations And Functions Exercise 2.2 Solutions in English Medium

 


 

EXERCISE : 2.2

Exercise 2.2 Class 11 Maths Question no 1

        1.    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, co domain and range .

Solution :

Given: A = {1, 2, 3, …….., 14}

 

The ordered pairs which satisfy 3x – y=0  are (1, 3), (2, 6), (3, 9) and (4, 12).

       ∴ R = {(1, 3), (2, 6), (3, 9), (4, 12)}

Domain = {1, 2, 3, 4}

Range = {3, 6, 9, 12}

Co-domain = {1, 2, 3, ….., 14}

 

Exercise 2.2 Class 11 Maths Question no 2

        2.    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.

Solution :

R = {(x, y): y = x + 5, x is a natural number less than 4, x, y∈ N}

The natural numbers less than 4 are 1, 2, and 3.

∴ R = {(1, 6), (2, 7), (3, 8)}

The domain of R is the set of all first elements of the ordered pairs in the relation.

∴ Domain of R = {1, 2, 3}

The range of R is the set of all second elements of the ordered pairs in the relation.

∴ Range of R = {6, 7, 8}

 

Exercise 2.2 Class 11 Maths Question no 3

 3.   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.

Solution :

A = {1, 2, 3, 5} and B = {4, 6, 9}

R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}

∴R = {(1, 4), (1, 6), (2, 9), (3, 4), (3, 6), (5, 4), (5, 6)}

 

Exercise 2.2 Class 11 Maths Question no 4

4.  Figure shows a relationship between the sets  P and Q. Write this relation:

(i) in set-builder form

(ii) roster form

Solution :

According to the given figure, P = {5, 6, 7}, Q = {3, 4, 5}

(i)                           R = {(x, y): y = x – 2; x ∈ P} or R = {(x, y): y = x – 2 for x = 5, 6, 7}

 

(ii)                         R = {(5, 3), (6, 4), (7, 5)}

Domain of R = {5, 6, 7}

Range of R = {3, 4, 5}

Exercise 2.2 Class 11 Maths Question no 5

5.  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.

Solution :

A = {1, 2, 3, 4, 6}, R = {(a, b): a, b ∈ A, b is exactly divisible by a}

(i)                           R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (6, 6)}

 

(ii) Domain of R = {1, 2, 3, 4, 6}

(iii) Range of R = {1, 2, 3, 4, 6}

 

Exercise 2.2 Class 11 Maths Question no 6

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

Solution :

R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}

∴ R = {(0, 5), (1, 6), (2, 7), (3, 8), (4, 9), (5, 10)}

∴Domain of R = {0, 1, 2, 3, 4, 5}

Range of R = {5, 6, 7, 8, 9, 10}

 

Exercise 2.2 Class 11 Maths Question no 7

7.  Write the relation R = {(x, x3) : x is a prime number less than 10} in roster form .

Solution :

R = {(x, x3) : x is a prime number less than 10} The prime numbers less than 10 are 2, 3, 5, and 7.

∴R = {(2, 8), (3, 27), (5, 125), (7, 343)}

 

 

Exercise 2.2 Class 11 Maths Question no 8

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

Solution :     

It is given that A = {x, y, z} and B = {1, 2}.

∴ A × B = {(x, 1), (x, 2), (y, 1), (y, 2), (z, 1), (z, 2)}

Since n(A × B) = 6, the number of subsets of A × B is 26.

Therefore, the number of relations from A to B is 26.

 

 

Exercise 2.2 Class 11 Maths Question no 9

9. 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 .

Solution :-

R = {(a, b): a, b ∈ Z, a – b is an integer}

It is known that the difference between any two integers is always an integer.

∴Domain of R = Z

Range of R = Z



 


Published  By Lokesh Das



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CLASS 11 English MEDIUM NCERT SOLUTIONS. CLASS 11 MATHEMATICS SOLUTIONS IN ENGLISH MEDIUM. CLASS 11 MATHEMATICS RELATIONS AND FUNCTIONS CHAPTER SOLUTIONS IN ENGLISH MEDIUM. CLASS 11 MATHS  RELATIONS AND FUNCTIONS EXERCISE 2.2 SOLUTIONS IN ENGLISH MEDIUM.

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