Relations And Functions Test

Relations And Functions

This is Relations and functions Test-03 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
A relation R in a set A is called universal relation, if
  • A
    if one element of A isrelated to all elements of A
  • B
    if every element of A isrelated to one element of A
  • C
    if no element of A isrelated to any element of A
  • D
    each element of A is related to every element of A
    Correct
2
A relation R in a set A is called reflexive,
  • A
    if (a, a) ∈ R, for every a ∈ A
    Correct
  • B
    if (b, a) ∈ R, for every a, b∈ A
  • C
    if (b, b) ∈ R, for every a∈ A
  • D
    if (a, b) ∈ R, for every a, b∈ A
3
A relation R in a set A is called symmetric, if
  • A
    \(\left( {{a_1},{\text{ }}{a_2}} \right) \in R{\text{ }}implies{\text{ }}that\\{\text{ }}\left( {{a_2},{\text{ }}{a_2}} \right) \in R,{\text{ }}\\for{\text{ }}all{\text{ }}{a_1},{\text{ }}{a_2} \in A\)
  • B
    \(\left( {{a_1},{\text{ }}{a_1}} \right) \in R{\text{ }}\\implies{\text{ }}that{\text{ }}\left( {{a_2},{\text{ }}{a_1}} \right) \in R,\\{\text{ }}for{\text{ }}all{\text{ }}{a_1},{\text{ }}{a_2} \in A\)
  • C
    \(\left( {{a_2},{\text{ }}{a_2}} \right) \in R{\text{ }}implies{\text{ }}that\\{\text{ }}\left( {{a_2},{\text{ }}{a_1}} \right) \in R,{\text{ }}\\for{\text{ }}all{\text{ }}{a_1},{\text{ }}{a_2} \in A\)
  • D
    \(\left( {{a_1},{\text{ }}{a_2}} \right) \in R{\text{ }}\\ implies{\text{ }}that{\text{ }}\left( {{a_2},{\text{ }}{a_1}} \right) \in R,{\text{ }}\\for{\text{ }}all{\text{ }}{a_1},{\text{ }}{a_2} \in A.\)
    Correct
4
A relation R in a set A is called transitive, if
  • A
    \(\begin{array}{*{20}{l}} {\left( {{a_1},{\text{ }}{a_2}} \right) \in R{\text{ }}implies{\text{ }}that{\text{ }}\left( {{a_1},{\text{ }}{a_3}} \right)\\ \in R,{\text{ }}for{\text{ }}all{\text{ }}{a_1},{\text{ }}{a_2},} \end{array}\)
  • B
    \(\left( {{a_1},{\text{ }}{a_2}} \right) \in R{\text{ }}and{\text{ }}\left( {{a_2},{\text{ }}{a_3}} \right) \\\in R{\text{ }}implies{\text{ }}that{\text{ }}\left( {{a_1},{\text{ }}{a_3}} \right) \in R,{\text{ }}\\for{\text{ }}all{\text{ }}{a_1},{\text{ }}{a_2},\)
    Correct
  • C
    \(\left( {{a_1},{\text{ }}a1} \right) \in R{\text{ }}and{\text{ }}\left( {{a_2},{\text{ }}{a_2}} \right) \\\in R{\text{ }}\\implies{\text{ }}that{\text{ }}\left( {a1,{\text{ }}a3} \right) \in R,{\text{ }}\\for{\text{ }}all{\text{ }}{a_1},{\text{ }}{a_2},\)
  • D
    \(\begin{array}{*{20}{l}} {\left( {{a_1},{\text{ }}{a_3}} \right)\\ \in R{\text{ }}and{\text{ }}\left( {{a_2},{\text{ }}{a_3}} \right) \in R{\text{ }}implies{\text{ }}\\that{\text{ }}\left( {a1,{\text{ }}a2} \right) \in R,\\{\text{ }}for{\text{ }}all{\text{ }}{a_1},{\text{ }}{a_2},} \end{array}\)
5
A relation R in a set A is said to be an equivalence relation if
  • A
    if R is reflexiveand transitive
  • B
    if R is reflexive and symmetric
  • C
    if R is reflexive, symmetric and transitive
    Correct
  • D
    if R is symmetric and transitive
6
Let A be the set of all students of a boys school. The relation Rin A given by R = {(a, b) : a is sister of b} is
  • A
    Empty
    Correct
  • B
    Trivial
  • C
    Reflexive
  • D
    Universal
7
Let T be the set of all triangles in a plane with R a relation in T given by \(R{\text{ }} = {\text{ }}\{ \left( {{T_1},{\text{ }}{T_2}} \right)\) : \({T_1}\) is congruent to \({T_2}\) }. Then R is
  • A
    non commutative relation
  • B
    a universal relation
  • C
    an equivalence relation
    Correct
  • D
    an empty relation
8
Let L be the set of all lines in a plane and R be the relation in L defined as R = {(L1, L2): L1 is perpendicular to L2}. Then R is
  • A
    Reflexive and symmetric but not transitive
  • B
    Symmetric but neitherreflexive nor transitive.
    Correct
  • C
    Symmetric and reflexive but not transitive
  • D
    Reflexive andtransitive but not symmetric
9
The relation R in the set Z of integers given by R = {(a, b): 2 divides a – b}(a, b) ∈Z is
  • A
    an empty relation
  • B
    an equivalence relation
    Correct
  • C
    non commutative relation
  • D
    a universal relation
10
Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Then R is
  • A
    an equivalence relation
    Correct
  • B
    an empty relation
  • C
    a universal relation
  • D
    non commutative relation
11
Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Then R is
  • A
    R is reflexive and transitive but not symmetric
    Correct
  • B
    R is reflexive and symmetric but not transitive
  • C
    R is symmetric and transitive but not reflexive.
  • D
    R is an equivalence relation.
12
Let A be a set containing n distinct elements. The number of functions that can be defined from A to A is
  • A
    none of these.
  • B
    \({2^n}\)
  • C
    \({n^n}\)
    Correct
  • D
    $\left| \!{\underline {\, n \,}} \right. $
13
The function \(f:R \to R\) given by \(f\left( x \right) = \cos \cos x\forall x \in R\) is : Neither One – one nor onto . A
  • A
    One – one and onto
  • B
    Neither One – one nor onto .
    Correct
  • C
    none of these.
  • D
    One – one
14
Let A = {1, 2, 3} and B = {2, 3, 4}, then which of the following is a function from A to B?
  • A
    {(1, 3), (2, 3), (3, 3)}
    Correct
  • B
    {(1, 2), (1, 3), (2, 3), (3, 3)}
  • C
    {(0, 3), (2, 4)}
  • D
    {(1, 2), (2, 3), (3, 4), (3, 2)}
15
The diagram given below shows that
Question 15 figure 1
  • A
    f is a function A to B.
  • B
    f is an onto function from A to B
  • C
    f is a one – one function from A to B
  • D
    f is not a function
    Correct