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