# CBSE Class 12 Mathematics NCERT Exemplar Solutions: Chapter 1 – Relations and Functions

Jul 3, 2018 15:01 IST
CBSE Class 12 Mathematics NCERT Exemplar Solutions: Relations and Runctions

In this article, we are providing you NCERT Exemplar Solutions for all the questions of Class 12 Mathematics Chapter 1 – Relations and Functions. The difficulty level of these questions is quite higher than the exercise questions usually given at the end of the chapter.

## About NCERT Exemplar Solutions Class 12 Maths:

All the questions of NCERT Exemplar Class 12 Maths book are very important for CBSE Class 12 Maths Board examination and other engineering entrance examinations.

Analysis of CBSE Class 12 previous year question paper shows that questions from NCERT Exemplar are frequently asked in CBSE board examination.

Questions from NCERT Exemplar Class 12 Mathematics are likely to be asked again in upcoming board exam as well as engineering entrance exams.

Types and number of questions in this chapter:

 Types Number of questions Short answer type questions 15 Long answer type questions 12 Objective type questions 20 Fillers 5 True and False 10

Few problems along with their solutions from this chapter are given follows:

Question:

Are the following set of ordered pairs functions? If so examine whether the mapping is injective or surjective.

(i) { (x, y): x is a person, y is the mother of x }.

(ii) { (a, b) : a is a person, b is an ancestor of a}.

Solution:

(i) The set of ordered pairs given here represents a function.

Here, the images of distinct elements of x under f are not distinct, so it is not injective but it is surjective.

(ii) Since, each element of domain does not have a unique image.

Therefore, the set of ordered pairs given here does not represent function.

Question:

Using the definition, prove that the function f : A b is invertible if and only if f is both one-one and onto.

Solution:

A function f :X → Y is defined to be invertible, if there exist a function g = Y → X such that gof = Ix and fog = Iy. The function is called the inverse of f and is denoted by f

We know that only bijective functions are invertible functions. A bijective function is both injective and surjective.

It means function f: X → Y is invertible iff f is a bijective function.

Question:

If the set a contains 5 elements and the set b contains 6 elements, then the number of one-one and onto mappings from a to b is

(a) 720

(b) 120

(c) 0

(d) None of these

Solution: (c)

Since, the number of elements in B is more than A.

Hence, there cannot be any one-one and onto mapping from A to B.

Question:

Every function is invertible.

Solution: False

We know that only bijective functions are invertible.

Question:

A binary operation on a set has always the identity element.

Solution: False

We have '+' is a binary operation on the set N but it has no identity element.

About NCERT Exemplar Book Class 12 Maths:

NCERT Exemplar book Class 12 Maths is published by NCERT and is a very important book for assessment purpose. Each chapter of NCERT Exemplar Class 12 Maths book starts with a brief overview of the chapter followed by solved examples and unsolved exercises.

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