Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 5 - Relations and Functions>PRACTICE EXERCISE>Q 37

MEDIUM

NDA & NA EE

IMPORTANT

Earn 100

Consider the following statements:

$I$ . If $f (x) = x^{3}$ and $g (y) = y^{3}$ , then $f = g$ .

$II$ . Identity function is not always a bijection.

Which of the above statement(s) is / are correct?

50% studentsanswered this correctly

Important Questions on Relations and Functions

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 5 - Relations and Functions>PRACTICE EXERCISE>Q 38

If

A = \{x, y\}, B = \{2, 3\}, C = \{3, 4\}

, then what is the number of elements in

A \times (B \cup C) ?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 5 - Relations and Functions>PRACTICE EXERCISE>Q 39

If

A

is a relation on a set

R

, then which one of the following is correct?

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 5 - Relations and Functions>PRACTICE EXERCISE>Q 40

Let

N

be the set of natural numbers and

f : N \to N

be a function given by

f (x) = x + 1

for

x \in N

. Which one of the following is correct?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 5 - Relations and Functions>PRACTICE EXERCISE>Q 41

What is the range of the function

f (x) = \frac{|x|}{x}, x \neq 0 ?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 5 - Relations and Functions>PRACTICE EXERCISE>Q 42

If

A = \{1, 2\}, B = \{2, 3\}

and

C = \{3, 4\}

, then what is the cardinality of

(A \times B) \cap (A \times C) ?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 5 - Relations and Functions>PRACTICE EXERCISE>Q 43

If

A

is a finite set having

n

elements, then the number of relations which can be defined in

A

is

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 5 - Relations and Functions>PRACTICE EXERCISE>Q 44

Let

A = \{a, b, c, d\}

and

B = \{x, y, z\}

. What are the number of elements in

A \times B ?

HARD

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 5 - Relations and Functions>PRACTICE EXERCISE>Q 45

The relation

R

in the set

Z

of integers is given by

R = {(a, b) : a - b

is divisible by

5}

is