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Class 12 Maths
Relations And Functions
Quiz 1
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If f(x) = f (x) ⇒ x= x∀ xx∈ A then the function f: A → B is
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one-one
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one-one onto
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onto
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many one
Explanation
one-one
What type of a relation is R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} on the set A – {1, 2, 3, 4}
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Reflexive
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Transitive
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Symmetric
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None of these
Explanation
None of these
If an operation is defined by a* b = a² + b², then (1 * 2) * 6 is
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12
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28
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61
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None of these
Explanation
61
Consider the binary operation * on a defined by x * y = 1 + 12x + xy, ∀ x, y ∈ Q, then 2 * 3 equals
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31
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40
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43
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None of these
Explanation
31
The range of the function f(x) = \(\sqrt{(x-1)(3-x)}\) is
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[1, 3]
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[0, 1]
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[-2, 2]
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None of these
Explanation
[1, 3]
If f: R → R defined by f(x) = 2x + 3 then f
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None of these
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2x – 3
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\(\frac{x-3}{2}\)
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\(\frac{x+3}{2}\)
Explanation
\(\frac{x-3}{2}\)
The function f(x) = log (x² + \(\sqrt{x^2+1}\) ) is
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even function
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odd function
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Both
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None of these
Explanation
even function
Let E = {1, 2, 3, 4} and F = {1, 2} Then, the number of onto functions from E to F is
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14
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16
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12
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8
Explanation
14
If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C. then
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A = B
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A = C
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B = C
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A ∩ B = d
Explanation
B = C
Let A = {1, 2}, how many binary operations can be defined on this set?
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8
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10
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16
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20
Explanation
16
If A = (1, 2, 3}, B = {6, 7, 8} is a function such that f(x) = x + 5 then what type of a function is f?
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Many-one onto
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Constant function
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one-one onto
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into
Explanation
one-one onto
Let function R → R is defined as f(x) = 2x³ – 1, then ‘f’ is
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2x³ + 1
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(2x)³ + 1
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(1 – 2x)³
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(\(\frac{1+x}{2}\))
Explanation
(\(\frac{1+x}{2}\))
Let the functioin ‘f’ be defined by f (x) = 5x² + 2 ∀ x ∈ R, then ‘f’ is
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onto function
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one-one, onto function
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one-one, into function
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many-one into function
Explanation
many-one into function
A relation R in human being defined as, R = {{a, b) : a, b ∈ human beings : a loves A} is-
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reflexive
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symmetric and transitive
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equivalence
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None of these
Explanation
equivalence
If f(x) + 2f (1 – x) = x² + 2 ∀ x ∈ R, then f(x) =
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x² – 2
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1
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\(\frac{1}{3}\) (x – 2)²
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None of these
Explanation
\(\frac{1}{3}\) (x – 2)²
The period of sin² θ is
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π²
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π
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2π
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\(\frac{π}{2}\)
Explanation
π
If the function f(x) = x³ + e
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1
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2
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3
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4
Explanation
2
What type of relation is ‘less than’ in the set of real numbers?
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only symmetric
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only transitive
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only reflexive
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equivalence
Explanation
only transitive
If A = [1, 2, 3}, B = {5, 6, 7} and f: A → B is a function such that f(x) = x + 4 then what type of function is f?
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into
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one-one onto
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many-onto
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constant function
Explanation
one-one onto
f: A → B will be an into function if
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range (f) ⊂ B
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f(a) = B
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B ⊂ f(a)
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f(b) ⊂ A
Explanation
range (f) ⊂ B
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