Relations And Functions Test

Relations And Functions

This is Relations and functions Test-02 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
Let \(R{\text{ }} = {\text{ }}\{ \left( {x,{\text{ }}y} \right):{x^2}\; + {\text{ }}{y^2}\; = {\text{ }}1\) and x, y \( \in \) R} be a relation in R. The relation R is
  • A
    anti – symmetric
  • B
    reflexive
  • C
    transitive
  • D
    symmetric
    Correct
2
The void relation ( a subset of A x A ) on a non empty set A is :
  • A
    Transitive and symmetric
    Correct
  • B
    transitive
  • C
    Anti symmetric
  • D
    Reflexive
3
If \(n{\text{ }} \geqslant {\text{ }}2\) , then the number of onto mappings or surjections that can be defined from { 1,2,3,4,………..,n} onto {1,2} is
  • A
    \({2^n}--{\text{ }}2\)
    Correct
  • B
    \({2^n} + {\text{ }}2\)
  • C
    \({2^n}\)
  • D
    2n
4
If A = { 1, 2, 3}, then the relation R = {(1, 2), (2, 3), (1, 3) in A is
  • A
    transitive only
    Correct
  • B
    symmetric only
  • C
    none of these
  • D
    symmetric and transitive only
5
If A = { 1, 2, 3}, then the relation R = {(1, 2), (2, 3), (1, 3) in A is
  • A
    none of these
  • B
    transitive only
    Correct
  • C
    symmetric only
  • D
    symmetric and transitive only
6
A relation R from C to R is defined by x Ry if f |x| = y. Which of the following is correct?
  • A
    (2 + 3 i)R13
  • B
    iR1
    Correct
  • C
    (1 + i)R2
  • D
    3R(–3)
7
If R is a relation from a set A to a set B and S is a relation from B to C, then the relation \(S{\text{ }}^\circ \) R.
  • A
    none of these
  • B
    Is from A to C
    Correct
  • C
    does not exist
  • D
    Is from C to A
8
The binary operation * defined on the set of integers as \(a*b = \left| {a - b} \right| - 1\)is:
  • A
    Associative
  • B
    None of these.
  • C
    commutative
    Correct
  • D
    Not commutative
9
R is a relation from { 11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation \({R^{ - 1}}\)
  • A
    {(8, 11), (9, 12), (10, 13)}
  • B
    {(11, 8), (13, 10)}
  • C
    {(8, 11), (10, 13)}
    Correct
  • D
    none of these
10
For real numbers x and y, we define x Ry if \(fx - y + \sqrt 2 \) f x – y +√2 is an irrational number. The relation R is
  • A
    transitive
  • B
    none of these
  • C
    reflexive
    Correct
  • D
    symmetric
11
Given the relation R = {(1, 2), (2, 3)} on eht set {1, 2, 3}, the minimum number of ordered pairs which when added to R make it an equivalence
  • A
    8
  • B
    6
  • C
    5
  • D
    7
    Correct
12
Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relations on the set A = {1, 2, 3, 4}. the relation R is
  • A
    transitive
  • B
    a function
    Correct
  • C
    not symmetric
  • D
    Reflexive
13
In Z , the set of integers , inverse of – 7 , w.r.t. ‘ * ‘ defined by a*b = a +b + 7 for all \(a,b \in Z\) ,is
  • A
    -14
  • B
    7
  • C
    14
  • D
    -7
    Correct
14
A Relation is a
  • A
    universal set
  • B
    Cartesian product of two sets
    Correct
  • C
    power set
  • D
    null set
15
A relation R in a set A is called empty relation if
  • A
    if every element of A isrelated to one element of A
  • B
    if one element of A isrelated to all elements of A
  • C
    if no element of A isrelated to any element of A
    Correct
  • D
    if every element of A isrelated to any element of A