Relations and Functions Test

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Relations and Functions Test - 2

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Weekly Quiz Competition

Question 1
1 / -0

For the relation R= {(1,2),(2,3),(4,5),(3,6)} ,

The domain is

A
{1,3,5,6}

B
{1,2,3,4}

C
{1,2,3,4,5,6}

D
{2,3,5,6}

Solution

The domain of a relation is the set of all first entries in the ordered pairs of the relation.
Question 2
1 / -0

Which of the following relations is not a function?

A
R= {(2,1), (4,4)(3,1),(5,1)}

B
R= {(1,2), (3,4),(2,1),(5,1)}

C
R= {(1,2), (3,4)(2,1),(5,2)}

D
R={(1,2), (1,4)(3,1),(5,1)}

Solution

For a relation to be a function, every element of the domain must be connected to a unique element of the co-domain. In this case, (d) has the element 1 being connected to two different elements 2 and 4.Thus, it’ can’t be a function.
Question 3
1 / -0

f(x) = x is called

A
an identity function

B
inverse function

C
step function

D
a constant function

Solution

In this function every element x is mapped with itself; hence it’s the identity function.
Question 4
1 / -0

Let R be a relation defined as

R = {(x, y): y = 2x, x is natural number < 5} then Range of R is given as ,

A
{1, 2, 3, 4}

B
{2, 4, 6, 8, 10}

C
N

D
{2, 4, 6, 8}

Solution

R = {(x, y): y = 2x, x is natural number < 5}

Relation R in roster form is { (1,2),(2,4),(3,6),(4,8)}

Range of relation R is the set of II elements of the ordered pairs

{ (1,2),(2,4),(3,6),(4,8)} So range is {2, 4, 6, 8}
Question 5
1 / -0

If n(A) = 3 and n(B) =4 then find the number of elements in the power set of A × B

A
24

B
8

C
64

D
4096

Solution

As n( A × B) = 12 and so n( P( A × B)) = 2¹² = 4096
Question 6
1 / -0

If f and g are two functions over real numbers defined as f(x) = 3x + 1, g(x) = x² + 2, then find f-g

A
x²+1

B
x²+1-3x

C
3x + x²

D
3x – x²-1

Solution

f - g = (3x + 1) – (x² + 2) = 3x – x²-1
Question 7
1 / -0

A relation R defined on the set A = {1,2,3,5} as

{(x, y): x+y >10: x,y ∈ A }is

A
Identity relation

B
Zero relation

C
Universal relation

D
Empty relation

Solution

Here R = {(x, y): x + y >10: x, y ∈ A }

Sum of none of the two elements of A is more than 10 and hence R is an empty relation.
Question 8
1 / -0

If A × B = {(x, a), (x, b), (y,a), (y, b)} then A =

A
{a,b}

B
{x,a}

C
{x,x,y,y}

D
{x,y}

Solution

Given A × B = {(x, a), (x, b), (y, a), (y, b)}

Set A is represented by the first elements of ordered pairs so

A = {x, y}
Question 9
1 / -0

Find the domain of the function f(x) = x |x|

A
R – {-1}

B
R

C
R⁺

D
R – {0}

Solution

Domain of the function f is all real numbers. Since f(x) =x|x| is defined for all real values of x .
Question 10
1 / -0

The graph of f(x) = x² lies in:

A
1^st and 2^nd quadrant

B
1st quadrant

C
3^rd and 4^th quadrant

D
3^rd quadrant

Solution

In the graph of f(x) = x², f will take only positive values. Hence graph will lie above x-axis. Hence, 1^st and 2^ndquadrant.

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Relations and Functions Test - 2

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Relations and Functions Test - 2

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Question 1

{1,3,5,6}

{1,2,3,4}

{1,2,3,4,5,6}

{2,3,5,6}

Solution

Question 2

R= {(2,1), (4,4)(3,1),(5,1)}

R= {(1,2), (3,4),(2,1),(5,1)}

R= {(1,2), (3,4)(2,1),(5,2)}

R={(1,2), (1,4)(3,1),(5,1)}

Solution

Question 3

an identity function

inverse function

step function

a constant function

Solution

Question 4

{1, 2, 3, 4}

{2, 4, 6, 8, 10}

N

{2, 4, 6, 8}

Solution

Question 5

24

8

64

4096

Solution

Question 6

x2+1

x2+1-3x

3x + x2

3x – x2-1

Solution

Question 7

Identity relation

Zero relation

Universal relation

Empty relation

Solution

Question 8

{a,b}

{x,a}

{x,x,y,y}

{x,y}

Solution

Question 9

R – {-1}

R

R+

R – {0}

Solution

Question 10

1st and 2nd quadrant

1st quadrant

3rd and 4th quadrant

3rd quadrant

Solution

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x²+1

x²+1-3x

3x + x²

3x – x²-1

R⁺

1^st and 2^nd quadrant

3^rd and 4^th quadrant

3^rd quadrant