If f : R → R such that f(x) = 3x then what type of a function is f?
  • one-one onto
  • many one onto
  • one-one into
  • many-one into
If f: R → R such that f(x) = 3x – 4 then which of the following is f
  • \(\frac{1}{3}\) (x + 4)
  • \(\frac{1}{3}\) (x – 4)
  • 3x – 4
  • undefined
A = {1, 2, 3} which of the following function f: A → A does not have an inverse function
  • {(1, 1), (2, 2), (3, 3)}
  • {(1, 2), (2, 1), (3, 1)}
  • {(1, 3), (3, 2), (2, 1)}
  • {(1, 2), (2, 3), (3, 1)
Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a congruent to b ∀ a, b ∈ T. Then R is
  • reflexive but-not transitive
  • transitive but not symmetric
  • equivalence
  • None of these
Consider the non-empty set consisting of children is a family and a relation R defined as aRb If a is brother of b. Then R is
  • symmetric but not transitive
  • transitive but not symmetric
  • neither symmetric nor transitive
  • both symmetric and transitive
The maximum number of equivalence relations on the set A = {1, 2, 3} are
  • 1
  • 2
  • 3
  • 5
If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is
  • reflexive
  • transitive
  • symmetric
  • None of these
Let us define a relation R in R as aRb if a ≥ b. Then R is
  • an equivalence relation
  • reflexive, transitive but not symmetric
  • neither transitive nor reflexive but symmetric
  • symmetric, transitive but not reflexive
Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is
  • reflexive but not symmetric
  • reflexive-but not transitive. (c) symmetric and transitive
The identity element for the binary operation * defined on Q ~ {0} as
  • 1
  • 0
  • 2
  • None of these
If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is
  • 720
  • 120
  • 0
  • None of these
Let A = {1, 2,3,…. n} and B = { a, b}. Then the number of surjections from A into B is
  • P
  • 2 – 2
  • 2– 1
  • None of these
Let f : R → R be defined by f (x) = \(\frac{1}{x}\) ∀ x ∈ R. Then f is
  • one-one
  • onto
  • bijective
  • f is not defined
Which of the following functions from Z into Z are bijective?
  • f(x) = x³
  • f(x) = x + 2
  • f(x) = 2x + 1
  • f{x) = x² + 1
Let f: R → R be the function defined by f(x) = x³ +Then f
  • (x + 5)
  • (x -5)
  • (5 – x)
  • 5 – x
Let f: [0, 1| → [0, 1| be defined by
  • Constant
  • 1 + x
  • x
  • None of these
Let f: |2, ∞) → R be the function defined by f(x) – x² – 4x + 5, then the range of f is
  • R
  • [1, ∞)
  • [4, ∞)
  • [5, ∞)
Let f: N → R be the function defined by f(x) = \(\frac{2x-1}{2}\) and g: Q → R be another function defined by g (x) = x +Then (g 0 f) \(\frac{3}{2}\) is
  • 1
  • 0
  • \(\frac{7}{2}\)
  • None of these
Let f: R → R be defined by then f(- 1) + f (2) + f (4) is
  • 9
  • 14
  • 5
  • None of these
Let f : R → R be given by f (,v) = tan x. Then f
  • \(\frac{π}{4}\)
  • {nπ + \(\frac{π}{4}\) : n ∈ Z}
  • does not exist
  • None of these
0 h : 0 m : 1 s

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