Relations And Functions Test

Relations And Functions

This is Relations and functions Test-01 for CBSE class 12 Maths.. There are 16 questions in this test with each question having around four answer choices.

Questions & Answers

1
If R is a relation from a non – empty set A to a non – empty set B, then
  • A
    \(R = A \cap B\)
  • B
    \(R = A \cup B\)
  • C
    \(R = A \times B\)
  • D
    \(R \subset A \times B.\)
    Correct
2
Let A = { 2 , 3 , 6 }. Which of the following relations on A are reflexive ?
  • A
    \({R_2}\) = { ( 2,2 ) , ( 3,3 ) , ( 3,6 ) , ( 6,3 ) }
  • B
    none of these
  • C
    \({R_1}\) = { ( 2,2 ) , ( 3,3 ) , ( 6,6 ) }
    Correct
  • D
    \({R_3}\) = { ( 2,2 ) , ( 3,6 ) , ( 2,6 ) }
3
Let R be the relation on N defined as x R y if x + 2 y = 8. The domain of R is
  • A
    {2, 4, 6, 8}
  • B
    {2, 4, 6}
    Correct
  • C
    {2, 4, 8}
  • D
    {1, 2, 3, 4}
4
Which of the following is not an equivalence relation on I, the set of integers ; x, y
  • A
    x R y x + y is an even integer
  • B
    x R y x < y
    Correct
  • C
    x R y x – y is an even integer
  • D
    x R y x = y
5
Let A = {a, b, c} and R = {(a, a), (b, b), (c, c), (b, c) } be a relation on A. Here, R is
  • A
    Transitive
  • B
    anti – symmetric
  • C
    reflexive
    Correct
  • D
    symmetric
6
R = {(1, 1), (2, 2), (1, 2), (2, 1), (2, 3)} be a relation on A, then R is
  • A
    anti symmetric
  • B
    not antisymmetric
    Correct
  • C
    symmetric
  • D
    Reflexive
7
Let A = {1, 2, 3}. Which of the following is not an equivalence relation on A ?
  • A
    {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}
  • B
    {(1, 1), (2, 2), (3, 3)}
  • C
    {(1, 1), (2, 2), (3, 3), (2, 3), (3, 2)}
  • D
    none of these.
    Correct
8
Let A = {1, 2, 3}, then the relation R = {(1, 1), (2, 2), (1, 3)} on A is
  • A
    symmetric
  • B
    none of these.
  • C
    transitive
    Correct
  • D
    reflexive
9
Let A = {1, 2, 3}, then the relation R = {(1, 1), (1, 2), (2, 1)} on A is
  • A
    symmetric
    Correct
  • B
    transitive
  • C
    none of these.
  • D
    reflexive
10
If A is a finite set containing n distinct elements, then the number of relations on A is equal to
  • A
    \({2^{{n^2}}}\)
    Correct
  • B
    n2
  • C
    2n
  • D
    none of these
11
Let A = {1, 2, 3}, then the domain of the relation R = {(1, 1), (2, 3), (2, 1)} defined on A is
  • A
    none of these.
  • B
    {1, 2, 3}
  • C
    {1, 3}
  • D
    {1, 2}
    Correct
12
Let A = {a, b, c} then the range of the relation R = {(a, b), (a, c), (b, c)} defined on A is
  • A
    {a, b, c}
  • B
    {c}
  • C
    {b, c}.
    Correct
  • D
    {a, b}
13
Number of relations that can be defined on the set A = {a, b, c, d} is
  • A
    \({2^{16}}\)
    Correct
  • B
    16
  • C
    \({4^4}\)
  • D
    24
14
Let A = {1, 2, 3, 4, 5, 6}. Which of the following partitions of A correspond to an equivalence relation on A?
  • A
    {1, 2, }, {4, 5, 6}
  • B
    {1, 3}, (2, 4, 5}, {6}
    Correct
  • C
    {1, 2, 3}, {3, 4, 5, 6}.
  • D
    {1, 2, }, {3, 4}, {2, 3, 5, 6}
15
A relation R on a non – empty set A is an equivalence relation iff it is
  • A
    reflexive, symmetric and transitive
    Correct
  • B
    reflexive
  • C
    symmetric and transitive
  • D
    none of these.
16
If I = , J = and B = , then B equals
Question 16 figure 1Question 16 figure 2Question 16 figure 3
  • A
    - I cosoption four Option A
    Correct
  • B
    I cosoption three Option B
  • C
    I cosoption one Option C
  • D
    I sin option two Option D