NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions (Ex 2.2)
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Mathematics is an important subject for children to study during their school years. Strong mathematical abilities can help students in a variety of ways throughout their lives. Mathematics is also essential for helping students comprehend the concepts presented in other topics like Physics, Chemistry, etc. As a result, having a strong foundation in Mathematics can help pupils succeed in other subjects as well. Many higher education courses continue the principles covered in Class 11 as well. Many of the concepts that are introduced to students in Class 11 are used in Class 12 as well as higherlevel courses of study. These are particularly crucial for people who intend to study Mathematics in college. Therefore, pupils would benefit from having a strong understanding of Mathematics in Class 11, in addition to helping them get good exam results. Many pupils find the Class 11 concepts to be interesting to learn. However, achieving high results in the annual exams requires more than just reading. The very foundation of Mathematics is practice. It takes a lot of effort to earn good grades in Mathematics, as a result. The NCERT exercises should be finished by pupils in order to fully understand the chapter. However, the exercises’ questions are not simple to answer. Some questions are extremely difficult to answer and have a tendency to confuse students. As a result, students look for solutions. Therefore, Extramarks offers NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2.
The NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2 are regarded as a very important resource for students in Class 11 to advance in their preparation for the annual examinations in Mathematics. For Class 11, the CBSE recommends the NCERT Mathematics textbook. Several other boards’ syllabi also recommend the NCERT textbook. Therefore, students from various boards as well as those from the CBSE will benefit from the NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2 given by Extramarks.
For students studying Mathematics, the internet contains a wide range of study materials. To prepare for their exams, Class 11 students may not necessarily need or benefit from all of these materials. It is crucial for pupils to study the NCERT book, since the CBSE requires all its students to use the NCERT textbooks. The Union Government established the NCERT (National Council of Educational Research and Training) to contribute to the creation of policies for enhancing school education. It was established in 1961 and provides advice to the Union and state governments on educational policy. To enhance school education in India, the NCERT carries out considerable research. Publishing textbooks for pupils is one of the NCERT’s main tasks. In order to provide students from all classes with a quality education, it also distributes newsletters, journals, and other extra resources. On its website, it also has various digital resources available for students, such as the NCERT textbooks in PDF format. The most important component of CBSE students’ preparation for their exams is reading the NCERT textbooks. Additionally, a lot of competitive exams base their course on the NCERT textbooks. Because of this, experts advise pupils to thoroughly read the NCERT textbooks. After reading, it is extremely important to do the exercises in the book. The NCERT solutions, such as the NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2, must therefore be available to pupils.
NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions (Ex 2.2) Exercise 2.2
Students who have access to the NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2 have a firm understanding of fundamental and advanced theories that boost their study even in higher classes. Students may find out more about the subjectmatter by the expertly prepared NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2 available on the Extramarks website. They can download the NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2 in PDF format from the Extramarks website.
Access NCERT Solutions for Class 11 Maths Chapter 2 – Relation and Functions
A complete answer to students’ study demands is offered by Extramarks. Although NCERT textbooks are an excellent source of study material, students still have a real concern about finding trustworthy NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2. Extramarks offers precise and indepth NCERT solutions. In addition to this, it provides a comprehensive learning solution that combines the benefits of live classrooms and learning apps to give students a seamless learning experience. Additionally, NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2 are accessible in PDF format.
Exercise 2.2
Class 11 Maths Chapter 2 Exercise 2.2 is one of the most important exercises in the chapter. Relations between two sets are thoroughly discussed in Exercise 2.2 Class 11th Maths. To help students solve this exercise, Extramarks provides NCERT Solutions Class 11 Maths Chapter 2 Exercise 2.2.
NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.2
Students frequently struggle to find the right resource to achieve their academic objectives. NCERT solutions offer the proper and necessary solution to their educational needs. For students who are preparing for their annual exams, the availability of NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2 fulfil their needs. Another advantage is that the CBSE itself recommends utilising the NCERT textbook. NCERT texts are a part of the CBSE curriculum. The textbooks contain many examrelevant and essential practise questions. These questions usually puzzle students, which lowers their confidence in the subject and the topic. Understanding the concepts from the very first topic is crucial. When trying the questions in the NCERT textbooks, students who have access to the NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2 would benefit from having a solid understanding of both basic and advanced concepts. Students can gain a solid conceptual understanding of the topic by completing it. Additionally, by matching their answers with the solutions, they can evaluate themselves and make changes.
Students preparing for the annual exams can benefit from the NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2 since they are presented in straightforward language that each student can understand. The NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2 have been written in a stepbystep format to assist students in obtaining full marks in their exams. In order to save students time and prevent them from having to look elsewhere for the concepts covered in the syllabus or the distribution of marks. The NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2 have been created in accordance with the most recent syllabus and guidelines established by the CBSE. All of the questions in the exercise are answered in the NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2, which are also totally errorfree. By repeatedly practising NCERT Solutions for Class 11 Maths Chapter 2 Exercise 2.2, students can answer such questions quickly and correctly in exams.Because they are prepared in a straightforward manner, students can utilise theNCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2 whenever and wherever they like without requiring any outside assistance.
The chapter on Relations and Functions is an essential part of competitive exams like JEE Main and JEE Advanced, in addition to the Class 11 annual exams. The results of these exams impact a student’s career because they are used to determine college admissions. Students are put under so much stress that they become overwhelmed and occasionally lose motivation. However, students may thoroughly understand the concepts and retain them for a long time by studying with the NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2 offered by Extramarks. They feel more confident while studying for numerous tests as a result. The amount of effort needed to pass the entrance exams is reduced for students who completely study the NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2 and other solutions. The NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2 thoroughly explain the solutions to assist students in passing these difficult exams. They may strengthen their basics and play a key role throughout the entire preparation period, whether it is for the annual exam or any competitive examination, with the help of the NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2.
Extramarks also provides NCERT Solutions Class 12 and NCERT Solutions Class 10 to help students in preparation for board exams. Extramarks provides NCERT Solutions for other secondary classes including NCERT Solutions Class 11, NCERT Solutions Class 9, NCERT Solutions Class 8, NCERT Solutions Class 7, NCERT Solutions Class 6, and others.
Q.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, codomain and range.
Ans.
We have:
A = {1, 2, 3,…, 14}
Relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}
= {(1, 3), (2, 6), (3, 9), (4, 12)}
Domain of Relation R = {1, 2, 3, 4}
Codomain = A
Range of relation R = {3, 6, 9, 12}
Q.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.
Ans.
R = {(x, y): y = x + 5, x is a natural number less than 4; x, y ∈N} = {(1, 6), (2, 7), (3, 8)}
Domain of R = {1, 2, 3}
Range of R = {6, 7, 8}
Q.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.
Ans.
Here, 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}
= {(1, 4), (1, 6), (2, 9), (3, 4), (3, 6), (5, 4), (5, 6)}
Which is a roster form.
Q.4 The Fig 2.7 shows a relationship between the sets P and Q. Write this relation.
(i) in setbuilder form (ii) roster form.
What is its domain and range?
Ans.
Here, P = {5, 6, 7}, Q = {3, 4, 5}
(i) The setbuilder form is R = {(x, y): y = x – 2; for x ∈P}
(ii) In roster form:
R = {(5, 3), (6, 4), (7, 5)}
Domain = {5, 6, 7}, Range = {3, 4, 5}
Q.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.
Ans.
(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}
Q.6 Determine the domain and range of the relation R defined by R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}.
Ans.
R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}} = {(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}
Q.7 Write the relation R = {(x, x^{3}): x is a prime number less than 10} in roster form.
Ans.
R = {(x, x^{3}): x is a prime number less than 10}
= {(x, x^{3}): x = 2, 3, 5, 7}
= {(2, 8), (3, 27), (5, 125), (7, 343)}
Q.8 Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.
Ans.
Since, A = {x, y, z} and B = {1, 2} So, A × B = {(x, 1), (x, 2), (y, 1), (y, 2), (z, 1), (z, 2)}
n(A × B) = 6
The number of subsets of A × B is 2^{6}. Therefore, number of relations from A into B will be 2^{6}.
Q.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
Ans.
R = {(a, b): a, b ∈ Z, a – b is an integer}
Since, a and b both are integer Z and their difference is also an integer.
Therefore, domain of R = Z
and Range of R = Z.
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FAQs (Frequently Asked Questions)
1. How can students download the NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2?
Students can download the NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2 from the Extramarks website and mobile app.
2. How can students achieve better scores in the exams by using the NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2?
The most crucial textbook for the Class 11 exams is the NCERT textbook for Mathematics. The NCERT exercises and examples are frequently used as the basis for questions. The answers to these problems are correct and simple in the NCERT Solutions For Class 11 Maths Chapter 2 Exercise 2.2. Students can earn better grades by accurately answering these questions in their exams.