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CBSE Questions for Class 12 Commerce Maths Relations And Functions Quiz 5 - MCQExams.com

If f(x)=11x,x0,1 then the graph of the function y=f[f{f(x)}] for x>1  is
  • a straight line
  • a circle
  • an ellipse
  • a pair of straight lines
Let f : R \rightarrow  R, g : R \rightarrow R be two function such that
f(x) = 2x-  3, g(x) = x^3 + 5
The function (fog)^{1}(x) is equal to.
  • \left ( \dfrac {x+7}{2} \right )^{1/3}
  • \left (x- \dfrac {7}{2} \right )^{1/3}
  • \left ( \dfrac {x-2}{7} \right )^{1/3}
  • \left ( \dfrac {x-7}{2} \right )^{1/3}
If f(x) = 3x -  5, \,\,then\,\, f^{-1}(x).
  • is given by \dfrac {1}{3x-5}
  • is given by \dfrac {x+5}{3}
  • does not exist because f is not one-one
  • does not exist because f is not onto
If f : [0, \Pi ] \rightarrow  [-1, 1], f(x) = cosx, then f is.
  • one-one
  • onto
  • one-one onto
  • none of these
If f(x) = \left\{\begin{matrix} 1&x \in Q \\ 0 &x \notin  Q\end{matrix}\right. then fof(\sqrt 3 ) is equal to
  • 0
  • 1
  • \sqrt 3
  • none of these
If functions f\left ( x \right ) and g\left ( x \right ) are defined on R\rightarrow R such that
f(x)=x+3, x \in   rational
          =4x, x \in irrational
g(x)=x+\sqrt{5}, x\in irrational
       =-x, x \in rational
then \left ( f-g \right )\left ( x \right ) is
  • one-one & onto
  • neither one-one nor onto
  • one-one but not onto
  • onto but not one-one
If \displaystyle f\left ( x \right )=\left ( 1-x^{3} \right )^{\frac{1}{3}}, then find fof(x)
  • \dfrac1x
  • x
  • x^2
  • x^3
Let f(x) =\frac {ax+b} {cx+d}. Then fof(x) = x provided that.
  • d =- a
  • d = a
  • a = b = c = d = 1
  • a = b = 1
If \displaystyle f(x)=2x^{3}+7x-5\, and\, g(x)=f^{-1}(x) then g' (4) is equal to
  • \displaystyle \frac{1}{13}
  • \displaystyle \frac{1}{103}
  • \displaystyle \frac{1}{4}
  • non existent
If \displaystyle R=R^{-1} then the relation R is ________
  • reflexive
  • symmetric
  • anti-symmetric
  • transitive
Let \displaystyle f\left ( x \right )=\frac{3}{2}+\sqrt{x-\frac{3}{4}} be a function and g\left ( x \right ) be another function such that g\left ( f\left ( x \right ) \right )=x, then the value of g\left ( 20 \right ) will be
  • 333
  • 335
  • 338
  • 343
If f(x) + f(1-x) = 10 then the value of \displaystyle f\left ( \frac{1}{10} \right )+f\left ( \frac{2}{10} \right )+.........+f\left ( \frac{9}{10} \right )
  • is 45
  • is 50
  • is 90
  • Cannot be determined
If f (x) = 2x - 1 and g (x) = 3x + 2, then find (fog) (x) :
  • 2 (3x + 1)
  • 2 ( 3x + 2)
  • 3 (2x + 1 )
  • 3 ( 3x + 1 )
If f(x) = -x^2+1, g(x) = -\sqrt[3]{x} then (gofogofogogog) (x) is.
  • an odd function
  • an even function
  • a polynomial function
  • an identity function
If the function f(x) = x^3 + e^{x/2} and g(x) = f^{-1}(x); then the value of g'(1) is
  • 2
  • -2
  • 1
  • 0
If f(x)=2x-1 and g(x)=3x+2  then find (fog) (x)
  • 2(3x+1)
  • 2(3x+2)
  • 3(2x+1)
  • 3(3x+1)
If f(x) = 2x+1 and g(x) = 3x-5 then find \left ( fog \right )^{-1}\left ( 0 \right )
  • 5/3
  • 3/2
  • 2/3
  • 3/5
If X = {2,3,5,7,11} and Y = {4,6,8,9,10} then find the number of one-one functions from X to Y
  • 720
  • 120
  • 24
  • 12
Find \left( f\circ g \right) \left( 3 \right) when f\left( x \right) =7x-6 and g\left( x \right) =5{ x }^{ 2 }-7x-6.
  • -36
  • 1014
  • -90
  • 120
If R is a relation from a set A to the set B and S is a relation from B to C, then the relation SoR
  • is from C to A
  • does not exist
  • is from A to C
  • None of these
If f = {(1,3) (2,1) (3,4) (4,2)} and g = {(1,2) (2,3) (3,4) (4,1)} then find n(fog)
  • 12
  • 16
  • 4
  • 5
What is the relation for the following diagram?

456168.PNG
  • R =\{(2, 5), (2, 6), (3, 7)\}
  • R = \{(1, 5), (2, 6), (3, 7)\}
  • R =\{(1, 5), (2, 6), (1, 7)\}
  • R = \{(1, 5), (2, 6), (2, 7)\}
Which of the following do(es) not belong to A \times B for the sets A = \{1, 2\} and B =\{0, 2\}?
  • R = \{(1, 0), (2, 2)\}
  • R = \{(1, 1), (2, 1)\}
  • R = \{(1, 0), (1, 2)\}
  • R = \{(1, 2), (2, 2)\}
What is the relation for the set A =\{-1, 0, 3\} and B =\{1, 2, 3\} ?
  • R =\{(-1, 1), (1, 2), (3, 3)\}
  • R = \{(-1, 1), (0, 2), (3, 3)\}
  • R = \{(-1, 1), (2, 2), (3, 3)\}
  • R = \{(-1, 1), (0, 2), (-1, 3)\}
If f: R\rightarrow R be given by f(x) = (3 - x^{3})^{ {1}/{3}}, then find f(f (x)) is

  • x^{{1}/{3}}
  • x^{3}
  • x 
  • 3 - x^{3}
If f:R\rightarrow R and g:R\rightarrow R are defined by f\left( x \right) =\left| x \right| and g\left( x \right) =\left[ x-3 \right] for x\in R, then
g\left( f\left( x \right)  \right) :\left\{ -\dfrac { 8 }{ 5 } < x < \dfrac { 8 }{ 5 }  \right\} is equal to
[.] is Greatest integer function
  • \left\{ 0,1 \right\}
  • \left\{ 1,2 \right\}
  • \left\{ -3,-2 \right\}
  • \left\{ 2,3 \right\}
If R be the set of all real numbers and f:R\rightarrow R is given by f\left( x \right)=3{ x }^{ 2 }+1. Then, the set f^{ -1 }\left( \left[ 1,6 \right]  \right) is
  • \left\{ -\sqrt { \dfrac { 5 }{ 3 } } ,0,\sqrt { \dfrac { 5 }{ 3 } } \right\}
  • \left[ -\sqrt { \dfrac { 5 }{ 3 } } ,\sqrt { \dfrac { 5 }{ 3 } } \right]
  • \left[ -\sqrt { \dfrac { 1 }{ 3 } } ,\sqrt { \dfrac { 1 }{ 3 } } \right]
  • \left( -\sqrt { \dfrac { 5 }{ 3 } } ,\sqrt { \dfrac { 5 }{ 3 } } \right)
Let R be the set of real numbers and the functions f: R \rightarrow R and g: R\rightarrow R be defined by f(x) = x^{2} + 2x - 3 and g(x) = x + 1. Then the value of x for which f(g(x)) = g(f(x)) is
  • -1
  • 0
  • 1
  • 2
Let f:R\rightarrow R be such that f is injective and f(x)f(y)=f(x+y) for all x,y\in R, if f(x), f(y) and f(z) are in GP, then x,y and z are in
  • AP always
  • GP always
  • AP depending on the values of x,y and z
  • GP depending on the values of x,y and z
Find the number of binary operations on the set \left \{a, b\right \} 

  •  10
  • 16
  • 20
  • 8
Let Q be the set of all rational numbers in [0, 1] and f : [0, 1]\rightarrow [0, 1] be defined by f(x)=\begin{cases}x&for&x\in Q\\ 1-x&for&x\notin Q\end{cases}
Then the set S=\{x\in [0, 1]: (f\, o \, f)(x)=x\} is equal to
  • [0, 1]
  • Q
  • [0, 1] - Q
  • (0, 1)
If f(x)={2}^{100}x+1, g(x)={3}^{100}x+1, then the set of real numbers x such that f\left\{ g(x) \right\} =x is
  • empty
  • a singleton
  • a finite set with more than one element
  • infinite
In three element group \{e, a, b\} where e is the identity, a^5b^4 is equal to 
  • a
  • e
  • ab
  • b
Find the value of {f}^{-1}(1.5) if f(x)=\sqrt [ 3 ]{ { x }^{ 3 }+1 } .
  • 3.4
  • 2.4
  • 1.3
  • 1.5
If f(x)\, =\, (p\, -\, x^n)^{1/n},\, p\, >\, 0 and n is a positive integer, then f(f(x)) =
  • x
  • x^n
  • p^{1/n}
  • p\, -\, x^n
Which of the following is a subgroup of the group G = \left \{1, 2, 3, 4, 5, 6\right \} under \otimes_{7}.
(\otimes_7: under multiplication modulo 7)
  • \left \{2, 6, 1\right \}
  • \left \{1, 2, 4\right \}
  • \left \{5, 4, 2\right \}
  • \left \{2, 3, 1\right \}
If f: R\rightarrow R^{+} and g: R^{+} \rightarrow R are such that g(f(x)) = |\sin x| and f(g(x)) = (\sin \sqrt {x})^{2}, then a possible choice for f and g is
  • f(x) = x^{2} , g(x) = \sin \sqrt {x}
  • f(x) = \sin x, g(x) = |x|
  • f(x) = \sin^{2}x, g(x) = \sqrt {x}
  • f(x) = x^{2}, g(x) = \sqrt {x}
If \displaystyle { Q }_{ 1 } is the set of all relations other than 1 with the binary operation \displaystyle \ast  defined by \displaystyle a\ast b=a+b-ab for all a, b \in \displaystyle Q_1, then the identity in \displaystyle { Q }_{ 1 } with respect to \displaystyle { Q }_{ 1 } is
  • 1
  • 0
  • -1
  • 2
In Z, the set of all integers, the inverse of -7 w.r.t. defined by a\times b=a+b+7 for all a, b, \in Z is : 
  • -14
  • 7
  • 14
  • -7
f(x) = x^{2} + d and g(x) = 2x^{2}, where d is a constant. If \dfrac {f(g(2))}{f(2)} = 4, find the value of d.
  • 16
  • 5
  • 22
  • 18
If f(g(a)) = 0  where g(x) = \dfrac {x}{4} + 2 and f(x) = |x^{2} - 3|, find the possible value of a.
  • -8+4\sqrt{3}
  • -(8+4\sqrt{3})
  • 6
  • 18
If p(x) = \dfrac{x}{x-2} and q(x) = \sqrt{9-x}, find the value of (p\circ  q)(5)
  • 0
  • \dfrac{8}{7}
  • 2
  • Undefined
If f(x) = \sqrt{x} and g(x) = \sqrt{x^2+4}, calculate the value of f(g(2)).
  • 0
  • 1.41
  • 1.68
  • 2.45
  • 2.83
If f(x) = 2x and f(f(x)) = x + 1, then the value of x is
  • \dfrac {1}{3}
  • 1
  • 2
  • 3
  • 5
Find the value of  g(f(2)), if f(x) = e^{x} and g(x) = \dfrac {x}{2}
  • 2.7
  • 3.7
  • 4.2
  • 5.4
  • 6.1
If h(x)={x}^{3}+x and g(x)=2x+3, then calculate g(h(2)).
  • 7
  • 10
  • 17
  • 19
  • 23
If f(x) = x^{2} - 10 and g(x) = 4x + 3, calculate the value of f(g(2)).
  • -24
  • -21
  • 12
  • 27
  • 111
If f(x) = x^2 and g(x) = 2x, calculate the value of f(g(-3))-g(f(-3)).
  • 54
  • 18
  • 0
  • -18
  • -54
The above figure shows the graph of the function f(x), the value of f(f(3)) is:
493615.jpg
  • -4
  • -2
  • 0
  • 1
  • 3
Find the correct expression for \displaystyle f\left( g\left( x \right)  \right)  if \displaystyle f(x)=4x+1 and \displaystyle g\left( x \right) ={ x }^{ 2 }-2  
  • \displaystyle -{ x }^{ 2 }+4x+1
  • \displaystyle { x }^{ 2 }+4x-1
  • \displaystyle 4{ x }^{ 2 }-7
  • \displaystyle 4{ x }^{ 2 }-1
  • \displaystyle 16{ x }^{ 2 }+8x-1
0:0:1


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Practice Class 12 Commerce Maths Quiz Questions and Answers