NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.1, Exercise 2.2, Exercise 2.3 and Miscellaneous for CBSE First Term Exam in English Medium PDF file format as well as Video format solutions or Prashnavali 2.1 or Prashnavali 2.2 or Prashnavali 2.3 or Vividh Prashnavali 2 in Hindi Medium free for session 2022-2023. UP Board students are also using NCERT Textbooks, so they also can download UP Board Solution for Class 11 Maths Chapter 2 in Hindi Medium free. NCERT Solutions 2022-2023 and Offline Apps are updated according to NCERT Books 2022-23 following the latest CBSE Syllabus 2022-2023. All the contents are free to study online or download free in PDF format along with Offline Apps.
NCERT Solutions for Class 11 Maths Chapter 2
11th Maths Chapter 2 Solutions in English Medium
11th Maths Chapter 2 Solutions in Hindi Medium
Download 11th Maths Chapter 2 Solutions in PDF
| Class: 11 | Maths (English and Hindi Medium) |
| Chapter 2: | Relations and Functions |
11th Maths Chapter 2 Solutions
NCERT Solutions for Class 11 Maths Chapter 2 are given below updated for 2022-23. All NCERT Solutions 2022-2023 are done properly by experts removing errors, if still any mistake, please inform us. We will try to remove as soon as possible. These are appropriate for CBSE Board, Uttarakhand Board, UP Board, MP Board, Gujrat Board and all other board who are following NCERT Books based on New Updated CBSE Curriculum 2022-23.
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Class 11 Maths Chapter 2 Exercise 2.1 Solution in Videos
Class 11 Maths Exercise 2.1 and 2.2 Solution in Hindi Videos
Class 11 Maths Exercise 2.3 and Miscellaneous Solution in Hindi
Class 11 Maths Chapter 2 Miscellaneous Solution in Videos
Important Terms on Relations and Functions
1. Relation R from a non-empty set A to a non-empty set B is a subset of A × B.
2. If n(A) = p, n(B) = q then n(A × B) = pq and number of relations = 2^pq.
3. A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B.
4. Let A and B be two non-empty finite sets such that n(A) = p and n(B) = q then number of functions from A to B = q^p.
Class 11 Maths Chapter 2 Important Questions for Practice
1. If A and B are finite sets such that n(A) = 5 and n(B) = 7, then find the number of functions from A to B.
2. If A = {2, 4, 6, 9} B = {4, 6, 18, 27, 54} and a relation R from A to B is defined by R = {(a, b): a belongs to A, b belongs to B, a is a factor of b and a < b}, then find in Roster form. Also find its domain and range.
3. Determine a quadratic function (f) is defined by f(x) = ax² + bx + c. If f(0) = 6; f(2) = 11, f(–3) = 6.
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Important Questions on 11th Maths Chapter 2
If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A×B).
Number of elements in A = 3 and set B = {3,4,5}, Number of elements in B = 3 Number of elements in A×B=(Number of elements in A)×(Number of elements in B ) = 3 × 3 = 9 Hence,the number of elements in A × B is 9.
If A = {-1, 1}, find A × A × A.
A = {-1,1}, Therefore, A×A ={-1,1}×{-1,1}={(-1,-1),(-1,1),(1,-1),(1,1)} and 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,-1),(1,-1,1),(1,1,-1),(1,1,1)}
If A × B = {(a, x), (a, y), (b, x), (b, y)}. Find A and B.
A × B = {(a,x),(a,y),(b,x),(b,y)} ⇒A = {a,b} and B={x,y}
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.
The relation R from A to A is given as R = {(x, y): 3x – y = 0, where x, y ∈ A} i.e., R = {(x, y): 3x = y, where x, y ∈ A} ∴ The roster form is given by R = {(1, 3), (2, 6), (3, 9), (4, 12)} The domain of R is the set of all first elements of the ordered pairs in the relation. ∴ Domain of R = {1, 2, 3, 4} The whole set A is the co-domain of the relation R. ∴ Co-domain of R = A = {1, 2, 3… 14} The range of R is the set of all second elements of the ordered pairs in the relation. ∴ Range of R = {3, 6, 9, 12}
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.
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}
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.
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}
∴ The roster form of R = {(1, 4), (1, 6), (2, 9), (3, 4), (3, 6), (5, 4), (5, 6)}
Determine the domain and range of the relation R defined by R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}.
R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}
∴ The roster form 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}
Write the relation R = {(x, x³): x is a prime number less than 10} in roster form.
R = {(x, x³): x is a prime number less than 10}
The prime numbers less than 10 are 2, 3, 5, and 7.
∴ The roster form R = {(2, 8), (3, 27), (5, 125), (7, 343)}
Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.
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.
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.
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.
What are the core motives of chapter 2 of class 11th Maths?
In this chapter, students will study how to link pairs of objects from two sets and then introduce relations between the two objects in the pair. Finally, students will learn about special relations which will qualify to be functions. The concept of function is very significant in mathematics since it captures the idea of a mathematically precise correspondence between one quantity with the other.
The core motives of chapter 2 of class 11th Maths are to make the following things clear to the students:
- Ordered pair.
- Cartesian products of sets.
- Relations.
- Domain.
- Codomain.
- Range.
- Functions.
- Some functions and their graphs (Identity Function, Constant Function, Polynomial Function, Rational Functions, Modulus Function, Signum Function, Greatest Integer Function).
- Algebra of a real function.
Can students skip chapter 2 of class 11th Maths?
No, students can’t skip chapter 2 of class 11th Maths. Chapter 2 (Relations and Functions) of grade 11th Math is an important chapter. Students have to study Relations and Functions in class 12th Maths also. Relations and Functions (chapter 2) of class 11th Maths works as a base for Relations and Functions (chapter 1) of class 12th Maths. If students skip chapter 2 (Relations and Functions) in class 11th Maths, they will face problems in chapter 1 (Relations and Functions) of class 12th Maths.
Which questions of chapter 2 have a complete chance to come in the exams?
Chapter 2 of grade 11th Maths has 36 questions and 22 illustrations. Every year questions are asked from chapter 2 in the exams.
All the questions of this chapter are significant and can come in the terminal exams. But the most important questions of this chapter that have more chance to come in the terminal exam are questions 1, 4, 7, 8, 9, 10 of the first exercise (Ex 2.1), questions 1, 3, 4, 5, 6, 8 of the second exercise (Ex 2.2), questions 1, 2, 5 of the third exercise (Ex 2.3), questions 1, 4, 6, 9, 10, 11, 12 of the Miscellaneous exercise on chapter 2, and examples 4, 8, 10, 14, 15, 17, 19, 20, 21, 22.
How much time is required to complete chapter 2 of class 11th Maths?
Students need a maximum of 10 days to finish chapter 2 of class 11th Maths if they honestly and seriously give 1-2 hours per day to this chapter. This time also depends on student’s ability, efficiency, and working speed. This chapter is not very tough. It is easy.
