The relation R is defined on the set of natural numbers as {(a, b): a = 2b}. Then, R is given by
  • {(2, 1), (4, 2), (6, 3),….}
  • {(1, 2), (2, 4), (3, 6),….}
  • R is not defined
  • None of these
The relation R = {(1,1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is
  • Reflexive but not symmetric
  • Reflexive but not transitive
  • Symmetric and transitive
  • Neither symmetric nor transitive
Let P = {(x, y) | x² + y² = 1, x, y ∈ R]. Then, P is
  • Reflexive
  • Symmetric
  • Transitive
  • Anti-symmetric
Let R be an equivalence relation on a finite set A having n elements. Then, the number of ordered pairs in R is
  • Less than n
  • Greater than or equal to n
  • Less than or equal to n
  • None of these
For real numbers x and y, we write xRy ⇔ x – y + √2 is an irrational number. Then, the relational R is
  • Reflexive
  • Symmetric
  • Transitive
  • None of these
Let R be a relation on the set N be defined by {(x, y) | x, y ∈ N, 2x + y = 41}. Then R is
  • Reflexive
  • Symmetric
  • Transitive
  • None of these
Which one of the following relations on R is an equivalence relation?
  • aR b ⇔ |a| = |b|
  • aR b ⇔ a ≥ b
  • aR b ⇔ a divides b
  • aR b ⇔ a < b
Let R be a relation on the set N of natural numbers denoted by nRm ⇔ n is a factor of m (i.e. n | m). Then, R is
  • Reflexive and symmetric
  • Transitive and symmetric
  • Equivalence
  • Reflexive, transitive but not symmetric
A relation R in S= {1,2,3} is defined as R= {(1, 1), (2, 3), (2, 2), (3, 3)}. Which element(s) of relation R be removed to make R an equivalence relation?
  • (1,1)
  • (2,2)
  • (3,3)
  • (2,3)
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
  • 100
R is a relation from {11,12,13} to {8,10,12} defined by y=x-3, then $R^{-1} is
  • {(8,11), (10,13)}
  • {(11,8), (13,10)}
  • {(12,12),(13,10},(8,11)}
  • None of these
Which of the following functions from Z into Z are bijections?
  • $f(x) = x^3$
  • f (x) = x + 2
  • f (x) = 2x + 1
  • $f(x)=x^2 + 1$
The relation is defined as R={(x,y) : x-y is an integer }, where $x,y \in Z$ The relation is  
  • reflexive
  • symmetric
  • transitive
  • All the above
Let f : R → R be defined by $f(x) = 3x^2 -5$ and g : R → R by $g (x) =\frac {x}{x^2 + 1}$ Then g o f is
  • $\frac {3x^2 -5}{9x^4 -30x^2 +26}$
  • $\frac {3x^2 }{9x^4 -30x^2 +26}$
  • $\frac {3x^2 +5}{9x^4 -30x^2 +26}$
  • $\frac {3x^2 -5}{9x^4 -6x^2 +26}$
Let f : R → R be the function defined by f (x) = 2x – 3  for  $x  \in  R$. then $f^{-1}$
  • $\frac {x-3}{2}$
  • $\frac {x+3}{2}$
  • $\frac {x+2}{3}$
  • None of the above
Let f: R -{n}  -> R be a function defined by $f(x)= \frac {x-m}{x-n}$ where $m \ne n$. Then
  • f is one-one onto
  • f is one-one into
  • f is many-one onto
  • f is many-one into
if g(f(x)) = |sin x| and $f(g(x))= (sin \sqrt x)^2$,then
  • $f(x) =sin^2 x$, $g(x) = \sqrt x$
  • $f(x) =sin x$, $g(x) = | x|$
  • $f(x) =x^2$, $g(x) = sin \sqrt x$
  • f and g cannot be determined
Let f : R → R be defined by $f(x) = \frac {x}{\sqrt {1+x^2}}$ then (f o f o f) (x) is
  • \frac {x}{\sqrt {1+3x^2}}$
  • \frac {x}{\sqrt {1+2x^2}}$
  • \frac {x}{\sqrt {1- x^2}}$
  • \frac {x}{\sqrt {x^2 -1}}$
if $f(x) = \frac {x-1}{x+1} , x \ne -1$ The domain of  f(f(x)) is
  • R - {1,0}
  • R - {1,0,-1}
  • R - {-1,0}
  • R - {1,0,2}
The value of  f(f(x) is
  • $\frac {-1}{x}$
  • $\frac {1}{x}$
  • $\frac {-1}{x-1}$
  • $\frac {-1}{1+x}$
0 h : 0 m : 1 s

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