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NCERT Exemplar Class 12 Maths Chapter 1 Solutions: Relations and Functions

NCERT Exemplar Class 12 Maths Solutions Chapter 1 ‘Relations and Functions’ cover the basics of different types of relations and functions along with some advanced topics. To give you a gist, this chapter of NCERT Exemplar Class 12 Maths has problems related to types of functions like onto and one-one, types of relations like empty and equivalence relations, the composition of functions, Invertible functions, and binary operations.

NCERT Exemplar Class 12 Maths Chapter 1 has a total of 62 questions that are spread in 5 sections touching all the parts of relations and functions. The questions are of various kinds which help you get a complete revision with the help of short and long type questions, objective type questions, fill in the blanks and true/false kind of questions.

Instasolv has created solutions to these NCERT Exemplar problems in detailed and easy steps for you to follow. By following the techniques of the experts at Instasolv, you can better your grades in CBSE at the same time and have an edge while taking various competitive exams such as JEE.

Important Topics for NCERT Maths Exemplar Solutions Class 12 Chapter 1

  • Relation: Given an ordered pair of inputs and outputs, relation defines how the input is related to the output. E.g.: In a class, if we take names of each student and their heights then the pair (name, height) is a kind of relation.
  • Functions – A function is a special type of relation which has a one-to-one relation between input and output. So for every input, a function says that there can be only one output. All functions are relations but not all relations are functions.  
  • DomainThe input values or starting points in the ordered pair is the domain, so in the above example of (name, height), names from the domain.
  • RangeThe output values or ending points in the ordered pair is the range, so in the above example of (name, height), heights form the range.
  • Types of relations
    • Empty relationA void or empty relation is when no relation exists between elements of a set. 

If set S = {4,5,6} then relation R ={a,b} where |a-b| > 3 is an empty relation. 

R = φ ⊂ S × S

    • Universal relation – It is also called full relation where each element of the set is related.

Set S = {boys in class 5}, relation R={a,b} where |a+b| > 10 cms. Here relation R is a universal relation since boys in class 5 are all greater in height than 10 cms.

R = S x S

    • Reflexive relation – For a relation, when in a set every element maps to itself then that relation is called a reflexive relation. For example: 

S = {set of real numbers}, and R = {x,x} where x = x

Since every real number is equal to itself, R here is a reflexive relation. 

(x,x) R

    • Symmetric relation – If in a set, a relation R holds for an ordered pair (x,y) and it also holds for pair (y,x) then that is called asymmetric relation. Example:

Set S = {4,5} and relation R = {(4,5), (5,4)} then R is a symmetric relation.

xRy => yRx, where x,y ∈ S

    • Transitive relation – In a set S, a relation R is a transitive relation if (x,y) ∈ R and (y,z) ∈ R implies (x,z) ∈ R

xRy and yRz => xRz where x,y,z S

    • Equivalence relation – A relation which is reflexive, symmetric, and transitive is an equivalence relation. A relation {is equal to} is an equivalence relation on a set S{x,y,z) since:
      • x = x (reflexive)
      • x = y then y = x (symmetric)
      • x = y, and y = z, then x = z (transitive)
  • Types of Functions
    • Injective functionAlso known as one-one function, it implies that every element y in a co-domain has at most a single x in the domain.

If f: A -> B then f (a1) = f(a2) ⇒ a1 = a2 ∀ a1, a2 ∈ X.

    • Surjective function – Also known as onto function, it implies that every element y in a co-domain has at least one x in the domain.

 If f: A -> B then b ∈ B, ∃ a ∈ A such that f(a) = b.

    • Bijective function – A function which is both injective and surjective is called a bijective function. 
    • Identity function – A function f is an identity function If in a set S, if each element has its own image i.e. f(x) = x.
    • Invertible function – If f1 : A -> B and there exists another function f2: B -> A such that f2(f1) = IA and f1(f2) = IB then f2 is inverse of f1 and denoted as f1-1
    • Binary operations – Binary operations like addition, subtraction, multiplication, and exponential can be performed on 2 elements of a set to result in another element of the same set. So a binary operation * on a non-empty set S are functions from S x S to S.
    • Composite function – When you combine 2 or more functions in a way that output of one function becomes the input of another then that is called the composition of functions. This means that the range or y values of one function become the domain or x values of the next function. 

(f1 o f2)(x) = f1(f2(x))

Discussion of Exercises of NCERT Exemplar Class 12 Maths Solutions Chapter 1

  1. The first set of questions is short answer types with 15 questions. They test you on the different types of relations, how to write the domain of a function, finding the inverse of a function, and how to find different types of functions given mappings.
  2. The second set is a long answer type with 12 questions. You are given a set and they need to find different relations on that set, finding the domain and range of a given relation, problems on different types of functions and relations.
  3. The third set of questions is objective type with 20 questions. This is a recap of all the important aspects of relations and functions.
  4. The fourth set of questions is fill in the blanks type with 5 questions. They are based on the inverse of a function and composite functions.
  5. The fifth set is a true and false type with 10 questions touching all the areas of relation and function like their types, composition of functions and invertible functions.
  6. The NCERT Exemplar for Class 12 have materials on all the topics which come in CBSE and other engineering and medical exams. These questions require you to employ a high order of thinking on the different levels of complexity of the problems.

Why Use NCERT Maths Exemplar Solutions Class 12 Chapter 1 by Instasolv?

Instasolv makes sure that the questions are solved by the subject matter experts in a step by step manner. This NCERT Exemplar helps students immensely in getting a sound knowledge of the topic of the NCERT Class 12 Maths chapter with their detailed solutions. The free of cost solutions not only provide solutions but you will also find many tips and shortcuts to the problem to help you manage your time better during the exam.