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Class 12 Maths
Relations And Functions
Quiz 2
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If f : R → R such that f(x) = 3x then what type of a function is f?
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one-one onto
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many one onto
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one-one into
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many-one into
Explanation
one-one into
If f: R → R such that f(x) = 3x – 4 then which of the following is f
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\(\frac{1}{3}\) (x + 4)
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\(\frac{1}{3}\) (x – 4)
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3x – 4
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undefined
Explanation
\(\frac{1}{3}\) (x + 4)
A = {1, 2, 3} which of the following function f: A → A does not have an inverse function
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{(1, 1), (2, 2), (3, 3)}
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{(1, 2), (2, 1), (3, 1)}
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{(1, 3), (3, 2), (2, 1)}
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{(1, 2), (2, 3), (3, 1)
Explanation
{(1, 2), (2, 1), (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
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reflexive but-not transitive
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transitive but not symmetric
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equivalence
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None of these
Explanation
equivalence
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
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symmetric but not transitive
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transitive but not symmetric
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neither symmetric nor transitive
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both symmetric and transitive
Explanation
transitive but not symmetric
The maximum number of equivalence relations on the set A = {1, 2, 3} are
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1
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2
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3
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5
Explanation
5
If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is
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reflexive
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transitive
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symmetric
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None of these
Explanation
transitive
Let us define a relation R in R as aRb if a ≥ b. Then R is
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an equivalence relation
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reflexive, transitive but not symmetric
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neither transitive nor reflexive but symmetric
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symmetric, transitive but not reflexive
Explanation
reflexive, transitive but not symmetric
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
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reflexive but not symmetric
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reflexive-but not transitive. (c) symmetric and transitive
Explanation
reflexive but not symmetric
The identity element for the binary operation * defined on Q ~ {0} as
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1
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0
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2
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None of these
Explanation
2
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
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720
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120
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0
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None of these
Explanation
0
Let A = {1, 2,3,…. n} and B = { a, b}. Then the number of surjections from A into B is
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P
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2 – 2
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2– 1
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None of these
Explanation
2
Let f : R → R be defined by f (x) = \(\frac{1}{x}\) ∀ x ∈ R. Then f is
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one-one
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onto
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bijective
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f is not defined
Explanation
f is not defined
Which of the following functions from Z into Z are bijective?
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f(x) = x³
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f(x) = x + 2
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f(x) = 2x + 1
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f{x) = x² + 1
Explanation
f(x) = x + 2
Let f: R → R be the function defined by f(x) = x³ +Then f
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(x + 5)
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(x -5)
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(5 – x)
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5 – x
Explanation
(x -5)
Let f: [0, 1| → [0, 1| be defined by
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Constant
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1 + x
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x
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None of these
Explanation
x
Let f: |2, ∞) → R be the function defined by f(x) – x² – 4x + 5, then the range of f is
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R
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[1, ∞)
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[4, ∞)
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[5, ∞)
Explanation
[1, ∞)
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
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1
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0
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\(\frac{7}{2}\)
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None of these
Explanation
None of these
Let f: R → R be defined by then f(- 1) + f (2) + f (4) is
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9
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14
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5
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None of these
Explanation
9
Let f : R → R be given by f (,v) = tan x. Then f
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\(\frac{π}{4}\)
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{nπ + \(\frac{π}{4}\) : n ∈ Z}
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does not exist
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None of these
Explanation
{nπ + \(\frac{π}{4}\) : n ∈ Z}
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