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

If $$f(x) =\dfrac {1}{1-x}, x \neq 0, 1$$ 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


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 12 Commerce Maths Quiz Questions and Answers