Class 12 Mathematics

Relation and Function

NCERT Exemplar Problems and Solution

Short Answer Type exemplar problems

Question – 1- Let A = {a, b, c} and the relation R be defined on A as follows:
R = {(a, a), (b, c), (a, b)}.
Then, write minimum number of ordered pairs to be added in R to make R reflexive and transitive.

Solution:

In order to make R reflexive, (b, b) and (c, c) will be added to R.

And in order to make R transitive, (a, c) will be added to R.

Therefore, The minimum number of order pair to be added to R will be (b, b), (c, c) and (a, c) - Answer


Question – 2 – Let D be the domain of real valued function f defined by class 12 mathematics exemplar problems and solution - relation and function1 then, write D.

Solution:

Here given D is the domain of class 12 mathematics exemplar problems and solution - relation and function2

Therefore,

class 12 mathematics exemplar problems and solution - relation and function3

Therefore, D = [– 5, 5] - Answer

Question - 3 – class 12 mathematics exemplar problems and solution - relation and function4 be defined by class 12 mathematics exemplar problems and solution - relation and function5 respectively. Then find g o f.

Solution:

class 12 mathematics exemplar problems and solution - relation and function6



Question 4 – class 12 mathematics exemplar problems and solution - relation and function7 be the function defined by class 12 mathematics exemplar problems and solution - relation and function8

Solution:

class 12 mathematics exemplar problems and solution - relation and function9

Question – 5 – If A = {a, b, c, d} and the function f = {(a, b), (b, d), (c, a), (d, c)}, write f – 1

Solution:

Given, f = {(a, b), (b, d), (c, a), (d, c)}

Therefore, f – 1 ={(b, a), (d, b), (c, a), (c, d)} Answer

Question – 6 – If class 12 mathematics exemplar problems and solution - relation and function10 is defined by class 12 mathematics exemplar problems and solution - relation and function11

Solution:

Given,

class 12 mathematics exemplar problems and solution - relation and function12

Question – 7 – Is g = {(1, 1), (2, 3, (3, 5), (4, 7)} a function? If g is described by g(x) = αx + β, then what value should be assigned to α and β?

Solution:

Given, g = {(1, 1), (2, 3, (3, 5), (4, 7)}

Therefore, each of the element of domain will be have unique image.

Consequently, g is a function.

class 12 mathematics exemplar problems and solution - relation and function13

class 12 mathematics exemplar problems and solution - relation and function14

Now, after substituting the value of α in equation (i), we get

class 12 mathematics exemplar problems and solution - relation and function15


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