Relations And Functions Test

Relations And Functions

This is Relations and functions Test-09 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
A binary operation ∗ on a set A is a
  • A
    multiplies ALL elements by a scalar
  • B
    function ∗ \(:{\text{ }}a + 4,a \in R\)
  • C
    adds 1 to all elements of A
  • D
    function ∗ \(:{\text{ }}A{\text{ }} \times {\text{ }}A{\text{ }} \to {\text{ }}A\)
    Correct
2
A binary operation ∗ on the set X is called commutative, if
  • A
    a ∗ b = b ∗ a for every a, \(b \in X\)
    Correct
  • B
    * is Transitive for every a, \(b \in X\)
  • C
    a + b = b – a for every a, \(b \in X\)
  • D
    ∗ is open for every a, \(b \in X\)
3
If A is a set an element e ∈A is called identity for the operation ∗, if
  • A
    a ∗ e = a ≠ e ∗ a, \(\forall a \in A.\)
  • B
    a ∗ e = a = e ∗ a, \(\exists \;a \in A\)
  • C
    a ∗ e = e = e ∗ a, \(\forall a \in A.\)
  • D
    a ∗ e = a = e ∗ a, \(\forall a \in A.\)
    Correct
4
An element a \( \in A\) is said to be invertible with respect to the operation ∗, if there exists
  • A
    An element b in A such that a ∗ b∗ b = e = b ∗ a
  • B
    An element b in A such that a ∗ b = e = b ∗ a
    Correct
  • C
    An element b in A such that a ∗ b∗ b = e∗ a = b ∗ a∗ a
  • D
    An element b in A such that a ∗ b∗ a = e = b ∗ a
5
Division operation of on the set R∗ of nonzero real numbers is
  • A
    not a binary operation
  • B
    a unary operation
  • C
    a binary operation
    Correct
  • D
    Commutative
6
\( * :{\text{ }}R{\text{ }} \times {\text{ }}R{\text{ }} \to {\text{ }}R\) given by \(\left( {a,{\text{ }}b} \right){\text{ }} \to {\text{ }}a{\text{ }} + {\text{ }}4{b^2}\) is a
  • A
    unary operation
  • B
    binary operation
    Correct
  • C
    ternary operation
  • D
    not well defined
7
\( + :{\text{ }}R{\text{ }} \times {\text{ }}R{\text{ }} \to {\text{ }}R\) and\( \times :{\text{ }}R{\text{ }} \times {\text{ }}R{\text{ }} \to {\text{ }}R\) × : R × R → R are
  • A
    commutative operations
    Correct
  • B
    non associative operations
  • C
    non transitive operations
  • D
    not commutative operations
8
\( * :{\text{ }}R{\text{ }} \times {\text{ }}R{\text{ }} \to {\text{ }}R\) defined by a ∗ b = a + 2b is
  • A
    Commutative
  • B
    not well defined
  • C
    not commutative
    Correct
  • D
    a unary operation
9
\( * :{\text{ }}R{\text{ }} \times {\text{ }}R{\text{ }} \to {\text{ }}R\) defined by a ∗ b = a + 2b is
  • A
    not well defined
  • B
    a unary operation
  • C
    Commutative
  • D
    Not associative
    Correct
10
∗ defined on the set {1, 2, 3, 4, 5} by a ∗ b = L.C.M. of a and b is
  • A
    not a binary operation
    Correct
  • B
    a unary operation
  • C
    not well defined
  • D
    a binary operation
11
Let ∗ be the binary operation on N defined by a ∗ b = H.C.F. of a and b.∗ is
  • A
    commutative but not associative
  • B
    not commutative
  • C
    both commutative and associative
    Correct
  • D
    not associative
12
Let ∗ be a binary operation on the set Q of rational numbers defined by \(a * b{\text{ }} = {\text{ }}{a^2} + {\text{ }}{b^2}\) , then∗is
  • A
    commutative
    Correct
  • B
    both commutative and associative
  • C
    Associative
  • D
    not commutative
13
Let ∗ be a binary operation on the set Q of rational numbers defined by a ∗ b = a + ab, then∗ is
  • A
    not commutative
  • B
    both commutative and associative
  • C
    associative
  • D
    commutative
    Correct
14
Let ∗ be a binary operation on the set Q of rational numbers defined by \(a * b{\text{ }} = \;{\left( {a{\text{ }}--{\text{ }}b} \right)^2}\) then∗ is
  • A
    not commutative
  • B
    both commutative and associative
  • C
    associative
  • D
    commutative
    Correct
15
Let ∗ be a binary operation on the set Q of rational numbers defined by a ∗ b =\(\frac{{ab}}{4}\), then∗ is
  • A
    both commutative and associative
  • B
    not commutative
  • C
    associative
  • D
    commutative
    Correct