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Test: Relations & Functions- 1


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25 Questions MCQ Test Mathematics (Maths) Class 12 | Test: Relations & Functions- 1

Test: Relations & Functions- 1 for JEE 2022 is part of Mathematics (Maths) Class 12 preparation. The Test: Relations & Functions- 1 questions and answers have been prepared according to the JEE exam syllabus.The Test: Relations & Functions- 1 MCQs are made for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Relations & Functions- 1 below.
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Test: Relations & Functions- 1 - Question 1

If R is a relation from a non – empty set A to a non – empty set B, then

Detailed Solution for Test: Relations & Functions- 1 - Question 1

Let A and B be two sets. Then a relation R from set A to set B is a subset of A × B. Thus, R is a relation from A to B ⇔ R ⊆ A × B.

Test: Relations & Functions- 1 - Question 2

The range of the function f(x) = 7-x Px-3 is 

Detailed Solution for Test: Relations & Functions- 1 - Question 2

Here, 0 ≤ x- 3 ≤ 7 - x  
⇒0 ≤ x - 3 and x - 3 ≤ 7 - x
By solvation, we will get 3 ≤ x ≤ 5
So x = 3,4,5 find the values of 7-x Px - 3 by substituting the values of x

Test: Relations & Functions- 1 - Question 3

Let R be the relation over the set of straight lines of a plane such that l1 R l2 ⇔ l1 ⊥ l2. Then, R is

Detailed Solution for Test: Relations & Functions- 1 - Question 3

To be reflexive, a line must be perpendicular to itself, but which is not true. So, R is not reflexive
For symmetric, if  l1 R l2 ⇒ l1 ⊥ l2.
⇒  l2 ⊥ l1 ⇒ l1 R l2 hence symmetric
For transitive,  if l1 R l2 and l2 R l3
⇒ l1 R l2  and l2 R l3  does not imply that l1 ⊥ l3 hence not transitive.

Test: Relations & Functions- 1 - Question 4

The diagram given below shows that 

Detailed Solution for Test: Relations & Functions- 1 - Question 4

Because, the element b in the domain A has no image in the co-domain B.

Test: Relations & Functions- 1 - Question 5

Which of the following is an even function?

Detailed Solution for Test: Relations & Functions- 1 - Question 5

Because, f(- x) = f(x) is the necessary condition for a function to be an even function, which is only satisfied by x2+ sin2x .

Test: Relations & Functions- 1 - Question 6

The binary relation S = Φ (empty set) on set A = {1, 2, 3} is

Detailed Solution for Test: Relations & Functions- 1 - Question 6

Reflexive : A relation is reflexive if every element of set is paired with itself. Here none of the element of A is paired with themselves, so S is not reflexive.
Symmetric : This property says that if there is a pair (a, b) in S, then there must be a pair (b, a) in S. Since there is no pair here in S, this is trivially true, so S is symmetric.
Transitive : This says that if there are pairs (a, b) and (b, c) in S, then there must be pair (a,c) in S. Again, this condition is trivially true, so S is transitive.

Test: Relations & Functions- 1 - Question 7

The void relation (a subset of A x A) on a non empty set A is:

Detailed Solution for Test: Relations & Functions- 1 - Question 7

The relation { } ⊂ A x A on a is surely not reflexive. However, neither symmetry nor transitivity is contradicted. So { } is a transitive and symmetry relation on A.

Test: Relations & Functions- 1 - Question 8

A relation R in a set A is called reflexive,

Detailed Solution for Test: Relations & Functions- 1 - Question 8

A relation R on a non empty set A is said to be reflexive if fx Rx for all x ∈ R, Therefore, R is reflexive.

Test: Relations & Functions- 1 - Question 9

The domain of the function f = {(1, 3), (3, 5), (2, 6)} is

Detailed Solution for Test: Relations & Functions- 1 - Question 9

The domain in ordered pair (x,y) is represented by x-coordinate. Therefore, the domain of the given function is given by : {1, 3, 2}.

Test: Relations & Functions- 1 - Question 10

The domain of the function 

Detailed Solution for Test: Relations & Functions- 1 - Question 10

x - 1 ≥ 0 and 6 – x ≥ 0 ⇒ 1 ≤ x ≤ 6.

Test: Relations & Functions- 1 - Question 11

Let R be the relation on N defined as x R y if x + 2 y = 8. The domain of R is

Detailed Solution for Test: Relations & Functions- 1 - Question 11

As x R y if x + 2y = 8, therefore, domain of the relation R is given by x = 8 – 2y ∈ N.
When y = 1, 
⇒ x = 6 ,when y = 2, 
⇒ x = 4, when y = 3, 
⇒ x = 2.
therefore domain is {2, 4, 6}.

Test: Relations & Functions- 1 - Question 12

If n ≥ 2, then the number of onto mappings or surjections that can be defined from {1, 2, 3, 4, ……….., n} onto {1, 2} is

Detailed Solution for Test: Relations & Functions- 1 - Question 12

The number of onto functions that can be defined from a finite set A containing n elements onto a finite set B containing 2 elements = 2− 2.

Test: Relations & Functions- 1 - Question 13

A relation R in a set A is called symmetric, if

Detailed Solution for Test: Relations & Functions- 1 - Question 13

A relation R on a non empty set A is said to be symmetric if fx Ry ⇔ yRx, for all x , y ∈ R .

Test: Relations & Functions- 1 - Question 14

The range of  is 

Detailed Solution for Test: Relations & Functions- 1 - Question 14

We have , 



Therefore, range of f(x) is {-1}.

Test: Relations & Functions- 1 - Question 15

The function f(x) = sin x2 is

Detailed Solution for Test: Relations & Functions- 1 - Question 15

For even function: f(-x) = f(x) , 
therefore, f(− x)
 = sin (− x)2 = sin x2 = f(x).

Test: Relations & Functions- 1 - Question 16

Which of the following is not an equivalence relation on I, the set of integers ; x, y

Detailed Solution for Test: Relations & Functions- 1 - Question 16

If R is a relation defined by xRy : ifx ⩽ y, then R is reflexive and transitive But, it is not symmetric. Hence, R is not an equivalence relation.

Test: Relations & Functions- 1 - Question 17

If A = {1, 2, 3}, then the relation R = {(1, 2), (2, 3), (1, 3) in A is

Detailed Solution for Test: Relations & Functions- 1 - Question 17

A relation R on a non empty set A is said to be transitive if fxRy and y Rz ⇒ xRz, for all x ∈ R. Here, (1, 2) and (2, 3) belongs to R implies that (1, 3) belongs to R.

Test: Relations & Functions- 1 - Question 18

A relation R in a set A is called transitive, if

Detailed Solution for Test: Relations & Functions- 1 - Question 18

A relation R on a non empty set A is said to be transitive if fx Ry and yRz ⇒ x Rz, for all x ∈ R.

Test: Relations & Functions- 1 - Question 19

The range of the function f(x) =|x−1| is

Detailed Solution for Test: Relations & Functions- 1 - Question 19

We have, f(x) = |x−1|, which always gives non-negative values of f(x) for all x ∈ R.Therefore range of the given function is all non-negative real numbers i.e. [0,∞).

Test: Relations & Functions- 1 - Question 20

The range of the function   is

Detailed Solution for Test: Relations & Functions- 1 - Question 20

As the denominator of the function  is a modulus function i.e.

Test: Relations & Functions- 1 - Question 21

Let A = {a, b, c} and R = {(a, a), (b, b), (c, c), (b, c)} be a relation on A. Here, R is

Detailed Solution for Test: Relations & Functions- 1 - Question 21

Correct Answer :- b

Explanation:- A = {a, b, c} and R = {(a, a), (b, b), (c, c), (b, c)}

Any relation R is reflexive if fx Rx for all x ∈ R. Here ,(a, a), (b, b), (c, c) ∈ R. Therefore , R is reflexive.

For the transitive, in the relation R there should be (a,c)

Hence it is not transitive.

Test: Relations & Functions- 1 - Question 22

A relation R from C to R is defined by x Ry iff |x| = y. Which of the following is correct?

Detailed Solution for Test: Relations & Functions- 1 - Question 22

Test: Relations & Functions- 1 - Question 23

A relation R in a set A is said to be an equivalence relation if

Detailed Solution for Test: Relations & Functions- 1 - Question 23

A relation R on a non empty set A is said to be reflexive iff xRx for all x ∈ R . .
A relation R on a non empty set A is said to be symmetric if fx Ry ⇔ y Rx, for all x , y ∈ R .
A relation R on a non empty set A is said to be transitive if fx Ry and y Rz ⇒ x Rz, for all x ∈ R.
An equivalence relation satisfies all these three properties.

Test: Relations & Functions- 1 - Question 24

Let f: R → R be a mapping such that f(x) = . Then f is

Test: Relations & Functions- 1 - Question 25

Which of the following is a polynomial function?

Detailed Solution for Test: Relations & Functions- 1 - Question 25

A polynomial function has all exponents as integral whole numbers. 

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