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 then, write D.

Solution:

Here given D is the domain of

Therefore,

Therefore, D = [– 5, 5] - Answer

Question - 3 – be defined by respectively. Then find g o f.

Solution:

Question 4 – be the function defined by

Solution:

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 is defined by

Solution:

Given,

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.

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

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