Relations and Functions Test

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Relations and Functions Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following statement is false?

A
If A = {x, y, z} and B = {1, 2} then the number of relations from A to B is 2².

B
If R is a relation from A to B, then domain of R is a subset of A and range of R is a subset of B.

C
A subset of A × B is called a relation from the set A to set B.

D
If A = {1, 2, 3, 4} and B = {5, 6}, then the number of relations from A to B is 256.

Solution

The total number of relations that can be defined from a set A to set B is the number of possible subsets of A ´ B.

If n(A) = m and n(B) = n, then the number of relations from A to B = 2^mn.
Question 2
1 / -0

If f(x) = x² and g(x) = x are two functions from R to R then (fg)(2) is

A
2

B
8

C
1

D
4

Solution

fg(2 )= f(2).g(2) = 2².2 = 8
Question 3
1 / -0

Let A = {1, 2, 3, …, 30} and R be the relation “is one-fifth of” on A. Then the range of R is

A
{1, 2, 3, 4, 5, 6, 10, 15, 20, 25, 30}

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

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

D
{5, 10, 15, 20, 25, 30}

Solution

The range of the relation R is the set of all second elements of the ordered pair in a relation R. Here R = {(1, 5), (2, 10), (3, 15), (4, 20), (5, 25), (6, 30)}

Range is {5, 10, 15, 20, 25, 30}
Question 4
1 / -0

If n(A)=2, n(B)=2 . What is the total number of relations from A to B?

A
32

B
4

C
16

D
12

Solution

The number of relations from a set with m elements to a set with n elements is given by 2^m.n

Hence, No. of relations from A to B is 2^2x2 = 16
Question 5
1 / -0

A={1, 2, 3, 4, …, 14}. Let R be a relation from A to A defined by

R = {(a, b):3a – b = 0, a, b∈ A} then domain of R is

A
{3, 6, 9, 12}

B
{1, 2, 3}

C
{3, 6, 9}

D
{1, 2, 3, 4}

Solution

Here (a, b) ∈ R, 3a = b,

Therefore

R = {(1, 3), (2, 6), (3, 9), (4, 12)}

Domain of relation R is the set of I elements of the ordered pairs

Domain R= {1, 2, 3, 4}
Question 6
1 / -0

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

A
R⁺

B
R – {0}

C
R

D
R – {-1}

Solution

Domain of the function f is all real numbers. Since f(x) =x|x| is defined for all real values of x .
Question 7
1 / -0

If ordered pair (a + 2b, 9) = (7, 3a + 2b), then the values of a and b are

A
1, 3

B
7, 9

C
3, 1

D
9, 7

Solution

Two ordered pairs are equal, if and only if the corresponding first elements are equal and the second elements are also equal.

Hence, a + 2b = 7 and 3a + 2b = 9.

Solving the linear equations, we get

a = 1 and b = 3
Question 8
1 / -0

Which of the relations is not a function?

A
one-one

B
domain = codomain

C
one many

D
many one

Solution

For a relation to be a function one element of the domain must not be connected with more than one elements of the co-domain. Hence the answer.
Question 9
1 / -0

The graph of f(x) = x² lies in:

A
3^rd quadrant

B
1^st and 2^nd quadrant

C
3^rd and 4^th quadrant

D
1st 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 - 3

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Relations and Functions Test - 3

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Question 1

If A = {x, y, z} and B = {1, 2} then the number of relations from A to B is 22.

If R is a relation from A to B, then domain of R is a subset of A and range of R is a subset of B.

A subset of A × B is called a relation from the set A to set B.

If A = {1, 2, 3, 4} and B = {5, 6}, then the number of relations from A to B is 256.

Solution

Question 2

2

8

1

4

Solution

Question 3

{1, 2, 3, 4, 5, 6, 10, 15, 20, 25, 30}

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

{1, 2, 3, 4, 5}

{5, 10, 15, 20, 25, 30}

Solution

Question 4

32

4

16

12

Solution

Question 5

{3, 6, 9, 12}

{1, 2, 3}

{3, 6, 9}

{1, 2, 3, 4}

Solution

Question 6

R+

R – {0}

R

R – {-1}

Solution

Question 7

1, 3

7, 9

3, 1

9, 7

Solution

Question 8

one-one

domain = codomain

one many

many one

Solution

Question 9

3rd quadrant

1st and 2nd quadrant

3rd and 4th quadrant

1st quadrant

Solution

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If A = {x, y, z} and B = {1, 2} then the number of relations from A to B is 2².

R⁺

3^rd quadrant

1^st and 2^nd quadrant

3^rd and 4^th quadrant