CBSE Questions for Class 11 Commerce Applied Mathematics Functions Quiz 12 - MCQExams.com

If $$P(S)$$ denotes the set of all subsets of a given set S, then the number of one-to-one functions from the set $$S=\{1,2,3\}$$ to he set $$P(S)$$
  • $$24$$
  • $$8$$
  • $$336$$
  • $$320$$
$$\begin{aligned} \text { If } A & = \{ x | x / 2 \in Z , 0 \leq x \leq 10 \} \\ B & = \{ x | x \text { is one digit prime } \} \\ C & = \{ x | x / 3 \in N , x \leq 12 \} \end{aligned}$$,
Then $$A \cap ( B \cup C )$$ is equal to-
  • $$\{ 2,6 \}$$
  • $$\{3,6,12 \}$$
  • $$\{ 2,6,12 \}$$
  • $$\{ 6,8 \}$$
The function $$f:N\rightarrow N $$ defined by $$f\left( x \right) =x-5\left[ \dfrac { x }{ 5 }  \right]$$, where $$N$$ is the set of natural numbers and $$[x]$$ denotes the greatest integer less then or equal to $$x$$ is
  • One-one and onto
  • One-one but not onto
  • Onto but not one-one
  • Neigher one-one nor onto
Let $$f:R\rightarrow R$$ is defined as $$f(x)=\begin{cases} 2x+{ \alpha  }^{ 2 },\ x \ge 2 \\ \frac { \alpha x }{ 2 } +10,\ x <2 \end{cases}$$. If $$f(x)$$ is onto function then set of values of $$\alpha$$ is
  • $$[1,4]$$
  • $$[-2,3]$$
  • $$(0,3]$$
  • $$[2,5]$$
The domain of the function $$f ( x ) = \underbrace { \log _ { 2 } \log _ { 2 } \log _ { 2 } \dots \log _ { 2 } x } _ { n times }$$ is
  • $$( - \infty , - 2 ) \cup [ 4 , \infty )$$
  • $$( - \infty , - 2 ] \cup [ 4 , \infty )$$
  • $$( - \infty , - 2 ) \cup ( 4 , \infty ]$$
  • none of these
The domain of definition of the function $$y=\dfrac { 325 }{ 197 } \left[ \dfrac { \sqrt { { x }^{ 2 }-1 }  }{ \sqrt { { x-1 } }  }  \right] $$
  • $$\left(1,\infty\right)$$
  • $$\left[1,\infty\right)$$
  • Set of all real numbers
  • $$\left(-\infty,-1\right)\cup \left( 1,\infty \right) $$
Let $$X=\left\{a_{1},a_{2},a_{3},a_{4},a_{5},a_{6}\right\}$$ & $$Y=\{b_{1},b_{2},b_{3}\}$$ the number of function $$f$$ from $$X$$ to $$Y$$ such that it is onto and there are exactly three elements $$x$$ in $$X$$ such that $$f(x)=b_{1}$$ is
  • $$75$$
  • $$100$$
  • $$120$$
  • $$90$$
The domain of $$f(x)=\log_{x}\log_{2}\left(\dfrac {1}{x-1/2}\right)$$ is 
  • $$\left(\dfrac {1}{2},1\right) \cup \left(1,\dfrac {3}{2}\right)$$
  • $$\left(\dfrac {1}{2},\dfrac {3}{2}\right)$$
  • $$\left[\dfrac {1}{2},\dfrac {3}{2}\right]$$
  • $$\left(\dfrac {1}{2},\dfrac {3}{2}\right]$$
The number of non-bijective mappings that can be defined from $$A={1,2,7}$$ to itself is
  • $$21$$
  • $$27$$
  • $$6$$
  • $$9$$
The number of linear functions which map from $$[-1, 1]$$ onto $$[0, 2]$$ is 
  • $$0$$
  • $$1$$
  • $$2$$
  • $$infinite$$
Let $$f : R \rightarrow (-1,1)$$ be defined as $$f(x)=\dfrac {e^{x}-e^{-x}}{e^{x}+e^{-x}}$$ then $$f$$ is
  • One-one onto
  • One-one into
  • Many-one onto
  • Many-one-into
Domain of the function
$$f ( x ) = \frac { 1 } { \sqrt { 4 x - \left| x ^ { 2 } - 10 x + 9 \right| } }$$ is
  • $$( 7 - \sqrt { 40 } , 7 + \sqrt { 40 } )$$
  • $$( 0,7 + \sqrt { 40 } )$$
  • $$( 7 - \sqrt { 40 } , \infty )$$
  • None of these
If $$f:Z\rightarrow Z, f(n)=\begin{cases} n+1;\quad n\quad is\quad even \\ n-3;\quad n\quad is\quad odd \end{cases}$$ is $$ f$$ is ...........
  • only one one
  • only Onto
  • one one & Onto both
  • Neither one one nor Onto
The complete set of values of $$x$$ for which the function $$f(x)=2\tan^{-1}x+\sin^{-1} \dfrac{2x}{1+x^{2}}$$ behaves like a constant function with positive output is equal to
  • $$x \in [-1,1]$$
  • $$[1,\infty)$$
  • $$(-\infty,1]$$
  • $$(-\infty, -1] \cup [1,\infty)$$
The function f:$$R\rightarrow R$$ defined by f(x)=x-[x],$$\forall x\epsilon R\quad is$$
  • one-one
  • onto
  • Both one-one and onto
  • neither one-one nor onto
If $$f:R\rightarrow R\quad defined\quad by\quad f\left( x \right) =\frac { { e }^{ { x }^{ 2 } }-{ e }^{ { -x }^{ 2 } } }{ { e }^{ x^{ 2 } }+{ e }^{ { -x }^{ 2 } } } ,\quad then\quad f\quad is$$
  • one-one but not onto
  • not one-one but onto
  • one-one and onto
  • neither one-one noronto
$$f (x) = x^4 - 10x^3 + 35x^2 - 50x + c$$ is a constant. the number of real roots of . f (x) = 0 and 
f'' (x) = 0 are respectively 
  • 1 , 0
  • 3, 2
  • 1 , 2
  • 3 , 0
If $$y^2 = ax^2 +bx+c$$, then $$y^2 \dfrac{d^2y}{dx^2}$$ is
  • a constant function
  • a function of x only
  • a function of y only
  • a function of both x and y
The domain of the real valued function $$f(x)$$ for which $$4^{f(x)+4^{1-f(x)}}= 4^{x}$$ is 
  • $$(-1,1)$$
  • $$(-\infty ,1)$$
  • $$[1,\infty)$$
  • R
The function $$f:R\rightarrow R$$ defined by $$f\left(x\right)=6^ {x}+6$$ is
  • one-one and onto
  • many-one and onto
  • one-one and into
  • mauny-one and into
Let n(A) = 4 and n(B) =Then the number of one - one  functions from A to B is 
  • 120
  • 360
  • 24
  • none of these
$$f(x)$$ is
  • One-one and onto
  • One-one and into
  • Many-one and onto
  • Many-one and into
The domain of the function $$f(x) = \log_{10}[1-\log_{10}(x^{2}-5x+16)]$$ is
  • $$(2,3)$$
  • $$[2,3]$$
  • $$(2,3]$$
  • $$[2,3)$$
The domain of the definition of the function $$y\left(x\right)$$ given by the equation $$2^ {x}+2^ {y}$$ is
  • $$0 < x \le 1$$
  • $$0\le x\le 1$$
  • $$-\infty < x \le 0$$
  • $$-\infty < x < 1$$
If $$fxln\left(1+\dfrac{1}{x}\right)dx=p(x)ln\left(1+\dfrac{1}{x}\right)+\dfrac{1}{2}x-\dfrac{1}{2}ln(1+x)+c$$, being arbitary costant, then
  • $$p(X)=\dfrac{1}{2}x^{2}$$
  • $$p(x)=0$$
  • $$p(x)=1$$
  • $$none\ of\ these$$
The domain of $$\frac{x+1}{\sqrt{x^{2}-5x+6}}$$ is
  • R-{2,3}
  • $$(3,\infty )$$
  • $$(-\infty ,\infty )$$
  • $$(-\infty, 2)\cup (3,\infty )$$
Consider the function $$f\left( x \right) ={ e }^{ x }$$ and $$g\left( x \right)=\sin ^{ -1 }{ x } $$, then which of the following is/are necessarily true.
  • Domain of $$gof =$$ Domain of $$f$$
  • Range of $$gof\ \subset$$ Range of $$g$$
  • Domain of $$gof$$ is $$\left( -\infty ,0 \right) $$
  • Range of $$gof$$ is $$\left( -\dfrac{\pi}{2} ,0 \right) $$
If $$f(x)=\frac { \alpha x }{ x+1 } $$, where $$x\neq -1$$ and (fof) (x) = x, then $$\alpha =$$
  • $$\sqrt { 2 } $$
  • $$-\sqrt { 2 } $$
  • $$1$$
  • $$-1$$
Let N be the set of natural numbers and two functions f and g be defined as
and g(n)=$$n-{ \left( -1 \right)  }^{ n }$$ then fog is:
  • one-one but not onto
  • onto but not one-one
  • neither one-one nor into
  • both one-one and onto
let $$f:R\rightarrow R$$ be a function defined by $$f(x)=\frac { { x }^{ 2 }-3x+4 }{ { x }^{ 2 }+3x+4 }$$ then f is
  • one-one but not onto
  • onto but not one
  • onto as well as one-one
  • neither onto nor one-one
Let $$f:R\rightarrow R$$  defined by $$f\left( x \right) =\frac { { e }^{ { x }^{ 2 } }-{ e }^{ -x^{ 2 } } }{ { e }^{ x^{ 2 } }+{ e }^{ { -x }^{ 2 } } } ,$$ then
  • f(x) is one-one but not onto
  • f(x) is neither one-one nor onto
  • f(x) is many one but onto
  • f(x) is one-one and onto
The function $$f:R\rightarrow R$$ defined by $$f\left( x \right) =\frac { { e }^{ \left| x \right|  }-{ e }^{ -x } }{ { e }^{ x }+{ e }^{ -x } } $$ is
  • One-One and onto
  • One-one but not onto
  • Not one-one but onto
  • Neither one-one nor onto
$$f:N\rightarrow N\quad where\quad f\left( x \right) =x-{ (-1) }^{ x }$$, then 'f' is
  • one-one and into
  • many- one and into
  • one-one and onto
  • many-one and onto
Let f(x+y)=f f(x) f(y) and  f(x) =1+x g(x) G(x), where $$\underset { x\rightarrow 0 }{ lim } g\left( x \right) =a and \underset { x\rightarrow 0 }{ lim } G\left( x \right) =b,$$ then f' (x) is equal to
  • 1+ab
  • ab
  • f(x)
  • ab f(x)
Let (X) be a function satisfying f' (X) = f (X) with f (0) = 1 and g (X) be a function that satisfies f (X) + g (x) = $${ x }^{ 2 },$$ Then the value of the integral $$\int _{ 0 }^{ 1 }{ f } (x)\quad g\quad (x)\quad dx,\quad is$$
  • $$e-\frac { { e }^{ 2 } }{ 2 } -\frac { 5 }{ 2 } $$
  • $$e+\frac { { e }^{ 2 } }{ 2 } -\frac { 3 }{ 2 } $$
  • $$e-\frac { { e }^{ 2 } }{ 2 } -\frac { 3 }{ 2 } $$
  • $$e+\frac { { e }^{ 2 } }{ 2 } +\frac { 5 }{ 2 } $$
l qt f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g be the function satisfying f(x)+g(x)=$$X^{2}$$, the value of the integral $$\int _{ 0 }^{ 1 }{ f(x)g(x)\quad dx\quad is } $$
  • $$\frac { 1 }{ 4 } (e-7)$$
  • $$\frac { 1 }{ 4 } (e-2)$$
  • $$\frac { 1 }{ 4 } (e-3)$$
  • none of the above
$$f:A\rightarrow B$$ will be an into function if
  • $$f\left(A\right) \subset B$$
  • $$f\left(A\right)=B$$
  • $$B\subset f\left(A\right)$$
  • $$f\left(B\right) \subset A$$
If f (x) = cosx and g (x) = x$$^2$$ then (gof) (x) is ....
  • cos$$^2$$ x
  • cosx$$^2$$
  • both (a)&(b)
  • x$$^2$$ cosx
Suppose that $$g(x)=1+\sqrt { x } and\quad f(g(x))=3+2\sqrt { x } +x\quad then\quad f(x)\quad is$$
  • $$\quad 1+2{ x }^{ 2 }$$
  • $$\quad 2+{ x }^{ 2 }$$
  • $$1+x$$
  • $$2+x$$
Which one of the following is one-one?
  • $$f:R\rightarrow R$$ given by $$f(x) =\left| x-1 \right| $$ for all $$x\in R$$
  • $$g:\left[ -\pi /2,\pi /2 \right] \rightarrow given by$$ $$g(x)=\left| sinx \right| $$
  • $$h:\left[ -\pi /2,\pi /2 \right] \in R$$ given by $$h(x) =sin x $$ for all $$x\in \left[ -\pi /2,\pi /2 \right] $$
  • $$\phi :R\rightarrow R$$ given by $$f(x)={ x }^{ 2 }-4$$ for all $$x\in R$$
Let $$f:R\rightarrow R$$, be defined as $$f(x)={ e }^{ x^{ 2 } }+cosx$$ then f is
  • One-one and onto
  • One-one and into
  • Many-one and onto
  • many-one and into
$$f : R \rightarrow R$$  defined by  $$f ( x ) = \dfrac { x } { x ^ { 2 } + 1 } , \forall x \in R$$  is
  • one-one
  • onto
  • bijective
  • neither one one nor onto
State which of the following defines a mapping from A to B, if $$A={a,b,c,}$$ and $$B={x,y,z}.$$
  • None of these.
Choose correct answer (s) from given choice
If f(x) = x + 4, g (x) = 5x and h(x) = 12/x. Find the value of $${ f }^{ -1 }(g(h(6)))$$ 
  • 10
  • 14
  • 6
  • 0
If  $$f ( x ) = \sqrt { x ^ { 2 } + 1 } , g ( x ) = \dfrac { x + 1 } { x ^ { 2 } + 1 }$$  and  $$h ( x ) = 2 x - 3 ,$$  then  $$f ^ { \prime } \left( h ^ { \prime } \left( g ^ { \prime } ( x ) \right) =\right.$$
  • $$0$$
  • $$\dfrac { 1 } { \sqrt { x ^ { 2 } + 1 } }$$
  • $$\dfrac { 2 } { \sqrt { 5 } }$$
  • $$\dfrac { x } { \sqrt { x ^ { 2 } + 1 } }$$
$${ f }:{ R }\rightarrow { R }$$  where  $$f ( x ) = \dfrac { x ^ { 2 } + a x + 1 } { x ^ { 2 } + x + 1 }.$$  Complete set of values of  $$'a'$$  such that  $$f ( x )$$  is onto to is :
  • $$( - \infty , \infty )$$
  • $$( - \infty , 0 )$$
  • $$( 0 , \infty )$$
  • None
The domain of $$f(x) = \sin^{-1} log_2 (x^2/2)$$ is
  • $$(0, \infty)$$
  • $$(0, \surd{2})$$
  • $$(-1, 0) \cup (0, 1)$$
  • $$[-2, -1] \cup [1, 2]$$
The domain of real valued function $$f(x)$$ for which $$4^ {f(x)}+4^ {1-f(x)}=4^ {x}$$ is
  • $$(-1,1)$$
  • $$(1,\infty)$$
  • $$(\infty ,1)$$
  • $$(-\infty ,-1)$$
Which of the following function(s) have the same domain and range?
  • $$f\left( x \right) =\sqrt { 1-{ x }^{ 2 } } $$
  • $$g\left( x \right) =\dfrac { 1 }{ x } $$
  • $$h\left( x \right) =\sqrt { x } $$
  • $$l\left( x \right) =\sqrt { 4-x } $$
Domain of the function $$y=\sqrt{\dfrac{x-2}{x+2}}+\sqrt{\dfrac{1-x}{1+x}}$$ is 
  • $$(-\infty, 0)$$
  • $$R$$
  • $$(-\infty, 0]$$
  • $$\phi$$
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