12th Standard cbse -- Maths - Relations and Functions

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Question - 1

Let R be a relation on the set L of lines defined by l1 R l2 if l1 is perpendicular to l2, then relation R is

  • A  reflexive and symmetric
  • B symmetric and transitive
  • C equivalence relation
  • D  symmetric

Question - 2

Given triangles with sides T1 : 3, 4, 5; T2 : 5, 12, 13; T3 : 6, 8, 10; T4 : 4, 7, 9 and a relation R in set of triangles defined as R = {(Δ1, Δ2) : Δ1 is similar to Δ2}. Which triangles belong to the same equivalence class?

  • A T1 and T2
  • B T2 and T3
  • C  T1 and T3
  • D T1 and T4

Question - 3

Given set A ={1, 2, 3} and a relation R = {(1, 2), (2, 1)}, the relation R will be

  • A  reflexive if (1, 1) is added
  • B  symmetric if (2, 3) is added
  • C transitive if (1, 1) is added
  • D symmetric if (3, 2) is added

Question - 4

 Given set A = {a, b, c). An identity relation in set A is

  • A  R = {(a, b), (a, c)}
  • B R = {(a, a), (b, b), (c, c)}
  • C R = {(a, a), (b, b), (c, c), (a, c)}
  • D R= {(c, a), (b, a), (a, a)}

Question - 5

A relation S in the set of real numbers is defined as xSy ⇒  x – y+ \(\sqrt3\) is an irrational number, then relation S is

  • A  reflexive
  • B  reflexive and symmetric
  • C  transitive
  • D symmetric and transitive

Question - 6

 Set A has 3 elements and the set B has 4 elements. Then the number of injective functions that can be defined from set A to set B is

  • A  144
  • B 12
  • C 24
  • D 64

Question - 7

Given a function lf as f(x) = 5x + 4, x ∈ R. If g : R → R is inverse of function ‘f then

  • A g(x) = 4x + 5
  • B  g(x) = \(\frac{5}{4x-5}\)
  • C  g(x) = \(\frac{x-4}{5}\)
  • D g(x) = 5x – 4

Question - 8

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)}. Choose the correct answer

  • A R is reflexive and symmetric but not transitive
  • B R is reflexive and transitive but not symmetric
  • C R is symmetric and transitive but not reflexive.
  • D R is an equivalence relation.

Question - 9

Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. Choose the correct answer

  • A (2, 4)∈ R
  • B (3, 8) ∈ R
  • C (6, 8)∈ R
  • D (8, 7) ∈ R

Question - 10

Let f : R ⟶ R be defined as f(x) = x4. Choose the correct answer

  • A f is one-one onto
  • B f is many-one onto
  • C f is one-one but not onto
  • D f is neither one-one nor onto
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