NCERT Solutions for Class 11 Mathematics Chapter 2 Relations and Functions
NCERT Solutions for Class 11 Mathematics Chapter 2 Relations and Functions
NCERT Solutions for Class 11 Mathematics Chapter 2 Relations and Functions
This worksheet provides complete and accurate NCERT Solutions for Class 11 Mathematics Chapter 2 Relations and Functions. This chapter introduces students to the concepts of relations and functions, which are essential for understanding advanced mathematics. Students learn how to form ordered pairs, Cartesian products, and define relations and functions along with their properties. This chapter is important as it builds the foundation for topics like calculus and algebra. The worksheet follows the NCERT structure and provides clear, step-by-step answers to all exercises to support effective learning and revision.
Chapter summary: stories, poems & themes
This chapter is purely concept-based and does not include stories or poems. It focuses on mathematical understanding through definitions, examples, and problem-solving exercises. Students work with ordered pairs, relations, domain, codomain, and range, and identify whether a relation is a function. The chapter also includes reasoning-based and activity-based questions that help students build logical thinking skills.
What this NCERT chapter covers?
• Understanding ordered pairs and Cartesian products
• Formation and representation of relations
• Identifying domain, codomain, and range
• Understanding functions and their properties
• Differentiating between relations and functions
• Solving problems based on function values and operations
• Logical reasoning through true/false and verification questions
How to use these NCERT solutions?
Students should first attempt all questions independently to build problem-solving skills. After solving, they can refer to these solutions to verify their answers and understand correct methods. Parents and teachers can guide students using these answers as per NCERT standards. The solutions are arranged in the same order as the NCERT textbook, making it easier for students to revise systematically and prepare for exams.
Student tips & learning tricks
• Clearly understand the difference between relation and function
• Always identify domain and range carefully
• Practice writing ordered pairs correctly
• Check whether each input has exactly one output to identify functions
• Avoid confusion between codomain and range
• Practice solving problems step-by-step for better accuracy
Why NCERT solutions are important?
NCERT Solutions are important because they follow the CBSE curriculum and help students understand concepts in a structured way. They ensure that students use the correct methods and mathematical language expected in exams. These solutions strengthen conceptual clarity, improve accuracy, and build confidence. Regular practice helps students perform better in school exams and competitive tests.
Complete answer key – NCERT solutions
EXERCISE 2.1
1.
x = 2
y = 3
2.
(i) False
Correct statement: P × Q = {(m,n), (m,m), (n,n), (n,m)}
(ii) True
(iii) True
3.
(i) A × (B ∩ C) = {(1,5), (1,6), (2,5), (2,6)}
(A × B) ∩ (A × C) = {(1,5), (1,6), (2,5), (2,6)}
(ii) A × C = {(1,5), (1,6), (2,5), (2,6)}
B × D = {(1,5), (1,6), (1,7), (1,8), (2,5), (2,6), (2,7), (2,8), (3,5), (3,6), (3,7), (3,8), (4,5), (4,6), (4,7), (4,8)}
Hence, A × C ⊂ B × D
4.
Number of elements = 92
5.
G × H = {(7,5), (7,4), (7,2), (8,5), (8,4), (8,2)}
H × G = {(5,7), (5,8), (4,7), (4,8), (2,7), (2,8)}
6.
A × A × A = {(–1,–1,–1), (–1,–1,1), (–1,1,–1), (–1,1,1), (1,–1,–1), (1,–1,1), (1,1,–1), (1,1,1)}
7.
A = {a, b}
B = {x, y}
8.
A × B = {(1,3), (1,4), (2,3), (2,4)}
Subsets:
φ
{(1,3)}
{(1,4)}
{(2,3)}
{(2,4)}
{(1,3),(1,4)}
{(1,3),(2,3)}
{(1,3),(2,4)}
{(1,4),(2,3)}
{(1,4),(2,4)}
{(2,3),(2,4)}
{(1,3),(1,4),(2,3)}
{(1,3),(1,4),(2,4)}
{(1,3),(2,3),(2,4)}
{(1,4),(2,3),(2,4)}
{(1,3),(1,4),(2,3),(2,4)}
Total subsets = 16
9.
A = {x, y, z}
B = {1, 2}
10.
A = {–1, 0, 1}
A × A = {(–1, –1), (–1, 0), (–1, 1), (0, –1), (0, 0), (0, 1), (1, –1), (1, 0), (1, 1)}
Remaining elements of A × A (excluding given pairs (–1, 0) and (0, 1)):
{(–1, –1), (–1, 1), (0, –1), (0, 0), (1, –1), (1, 0), (1, 1)}
11.
Domain = {1, 2, 3, 4}
Codomain = {1, 2, 3, ..., 14}
Range = {3, 6, 9, 12}
12.
R = {(1,6), (2,7), (3,8)}
Domain = {1, 2, 3}
Range = {6, 7, 8}
13.
(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 = {1, 2, 3, 4, 6}
(iii) Range = {1, 2, 3, 4, 6}
EXERCISE 2.2
1.
R = {(1,4), (1,6), (1,9), (2,4), (2,6), (2,9), (3,4), (3,6), (3,9), (5,4), (5,6), (5,9)}
2.
(i) R = {(x, y): y = x + 1}
(ii) R = {(1,2), (2,3), (3,4), (4,5)}
Domain = {1, 2, 3, 4}
Range = {2, 3, 4, 5}
3.
Domain = {0, 1, 2, 3, 4, 5}
Range = {5, 6, 7, 8, 9, 10}
4.
(i) Function
Domain = {2, 5, 8, 11, 14, 17}
Range = {1}
(ii) Function
Domain = {2, 4, 6, 8, 10, 12, 14}
Range = {1, 2, 3, 4, 5, 6, 7}
(iii) Not a function
5.
R = {(2,8), (3,27), (5,125), (7,343)}
6.
Number of relations = 2⁶ = 64
7.
Domain = Z
Range = Z
EXERCISE 2.3
1.
(i) Domain = R
Range = R
(ii) Domain = R
Range = R
2.
(i) f(0) = –5
(ii) f(7) = 9
(iii) f(–3) = –11
MISCELLANEOUS EXERCISE
1.
f is a function
g is not a function
2.
(i) 32
(ii) 82.4
(iii) 14
(iv) 100
3.
(i) Range = (–∞, 2)
(ii) Range = [2, ∞)
(iii) Range = R
4.
Answer = 1 2
5.
Domain = R – {2, –2}
6.
Domain = R
Range = {–1, 1}
7.
Domain = R
Range = (–∞, 0)
8.
Range = (–1, 1)
9.
(f + g)(x) = 3x – 2
(f – g)(x) = –x + 4
(f/g)(x) = (x + 1)/(2x – 3)
10.
a = 2
b = –1
11.
(i) False
(ii) False
(iii) False
12.
(i) True
(ii) False
13.
Not a function
14.
Range = {3, 5, 11, 13}
Get complete NCERT Solutions for Class 11 Mathematics Relations and Functions chapter and strengthen your understanding of key concepts with accurate answers.