Online Test — Relations and Functions
10 Questions • 20 min • Chapter MCQ
20:00
Question 1 of 10
easy
Given A = {x, y, z} and B = {1, 2}. What is n(A × A × B)?
12
18
8
27
Explanation: n(A × A × B) = n(A) × n(A) × n(B) = 3 × 3 × 2 = 18.
Question 2 of 10
medium
Which function is many-one?
f(x)=x+3
f(x)=2x−1
f(x)=x² on R
f(x)=x
Explanation: Both 2 and −2 have image 4.
Question 3 of 10
easy
Which of the following is true for the Cartesian product of empty sets?
A × ∅ = A
A × ∅ = ∅
A × ∅ = {∅}
It is undefined
Explanation: By definition, the Cartesian product of any set with an empty set is the empty set. There are no ordered pairs to form.
Question 4 of 10
medium
Which relation on A={1,2} is symmetric?
{(1,2)}
{(1,2),(2,1)}
{(1,1),(1,2)}
{(2,1)}
Explanation: Whenever (a,b) exists, (b,a) also exists.
Question 5 of 10
easy
On A={1,2,3}, the identity relation contains:
(1,1),(2,2),(3,3)
All possible ordered pairs
Only (1,1)
No ordered pair
Explanation: Identity relation contains all pairs (a,a).
Question 6 of 10
easy
The function f(x)=5 for all x is:
Identity
One-one
Constant
Onto
Explanation: Output remains fixed.
Question 7 of 10
easy
If f(x)=3x−2, then f(10) equals:
28
30
32
34
Explanation: 3×10−2=28.
Question 8 of 10
easy
A function which is not onto is called:
One-one
Into
Identity
Constant
Explanation: Into functions do not cover entire codomain.
Question 9 of 10
easy
Which of the following is an ordered pair?
{2,3}
(2,3)
[2,3]
⟨2,3⟩ and (2,3) represent the same concept, but standard notation is (2,3)
Explanation: An ordered pair is represented by (a,b).
Question 10 of 10
medium
Which of the following is one-one?
f(x)=x² on R
f(x)=5
f(x)=x+1
f(x)=|x|
Explanation: Distinct inputs give distinct outputs.