Relations and Functions Test

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Relations and Functions Test - 2

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Weekly Quiz Competition

Question 1
1 / -0

Let A and B be two given sets, then in order to define a relation on these two sets which of the following must hold?

A
Relation can be defined between any two sets

B
One of them should be non-empty

C
Both of them should be non-empty

D
There must be some connection between these two sets
Question 2
1 / -0

If, f is a function from A to B, then for a ∈ A and c, d ∈ B, f(a) = c and also f(a) = d, then

A
c > d

B
c < d

C
c = d

D
c ≠ d
Question 3
1 / -0

Which of the following relations is/are function(s)?

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

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

C
R = {(1, 2), (2, 3), (1, 4), (4, 5), (5, 6), (6, 7)}

D
All of the above
Question 4
1 / -0

If set A = {1, 4, 8, 2} and set B = {3, 6}, then which of the following is A × B?

A
{3, 12, 24, 6, 6, 24, 48, 12}

B
{(1, 3), (4, 3), (8, 3), (2, 3), (1, 6), (4, 6), (8, 6), (2, 6)}

C
{3, 12, 24, 6, 48,12}

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

If there are p elements in set A and q elements in set B, then number of elements in A ´ B are always equal to

A
pq

B
p^q

C
p + q

D
None of these
Question 6
1 / -0

Which of the following is a relation from set A = {1, 6, 8} to set B = {3, 6, 9}?

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

B
R = {(6, 6)}

C
R = {(8, 1), (8, 9)}

D
All of the above
Question 7
1 / -0

If f (x) = tan x, −π2<x<π2 and g (x) = √ 1−x2 , then domain of fog is

A
[- 1, 1]

B
[−π4,π4]

C
(- 1, 1)

D
(−π/2,π/2)

Solution

fog(x)=f(g(x))=f(√1−x²)

⇒fog(x)=tan√ 1−x²

and it is defined if

1−x²≥0

⇒x²≤1

⇒−1≤x≤1
Question 8
1 / -0

Which of the following statements are true?

a. Every real function has a graph.
b. Graph of a real function is a subset of R².
c. Graph of a quadratic polynomial is always a parabola.
d. The graph of a general polynomial does not have a break in it.

A
a, b and d

B
a, c and d

C
b, c and d

D
all of the above

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Relations and Functions Test - 2

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Relations and Functions Test - 2

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Question 1

Relation can be defined between any two sets

One of them should be non-empty

Both of them should be non-empty

There must be some connection between these two sets

Question 2

c > d

c < d

c = d

c ≠ d

Question 3

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

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

R = {(1, 2), (2, 3), (1, 4), (4, 5), (5, 6), (6, 7)}

All of the above

Question 4

{3, 12, 24, 6, 6, 24, 48, 12}

{(1, 3), (4, 3), (8, 3), (2, 3), (1, 6), (4, 6), (8, 6), (2, 6)}

{3, 12, 24, 6, 48,12}

{(3, 1), (3, 4), (3, 8), (3, 2), (6, 1), (6, 4), (6, 8), (6, 2)}

Question 5

pq

pq

p + q

None of these

Question 6

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

R = {(6, 6)}

R = {(8, 1), (8, 9)}

All of the above

Question 7

[- 1, 1]

[−π4,π4]

(- 1, 1)

(−π/2,π/2)

Solution

Question 8

a, b and d

a, c and d

b, c and d

all of the above

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