CBSE Questions for Class 11 Commerce Applied Mathematics Functions Quiz 8 - MCQExams.com

If $$f(x) = \sqrt {4 - {x^2}}  + \dfrac{1}{{\sqrt {\left| {\sin x} \right| - \sin x} }}$$, then the domain of f(x) is 
  • [-2,0]
  • (0,2]
  • [-2,2}
  • [$$\dfrac{\pi}{2} $$, 2]
If $$f(x)= sin^{2}x$$ and the composite functions g{f(x)}=|sin x|, then the function g(x)=
  • $$\sqrt{x-1}$$
  • $$\sqrt{x}$$
  • $$\sqrt{x+1}$$
  • $$-\sqrt{x}$$
the equation $$|x+1$^{log}(x+1)^{3+2x-x^{2}}= (x-3)|x|$$  has 
  • Uniques solution
  • Two solution
  • No solutions
  • more thatn two solution
if f(x)=$$\sqrt {4 - {x^2}}  + \dfrac{1}{{\sqrt {|\sin x| - \sin x} }}$$, then the domain of f(x) is 
  • $$[-2,0)$$
  • $$[0,2]$$
  • $$[-2,2]$$
  • $$None\ of\ these$$
The domain of the function
$$f ( x ) = \log _ { 1 / 2 } \left( - \log _ { 2 } \left( 1 + \dfrac { 1 } { \sqrt [ 4 ] { x } } \right) - 1 \right)$$ is
  • $$0 < x < 1$$
  • $$0 < x \leq 1$$
  • $$x \geq 1$$
  • null set
Find the domain of function $$\sin^{-1}\left[\dfrac {1+x^{2}}{2x}\right].$$
  • $$[-1,1]$$
  • $$(-1,1)$$
  • $$\left\{-1,1\right\}$$
  • $$\left\{0\right\}$$
The domain of $$ f(x)= e^{sin (x-|x|)}+|x|cos (\dfrac{x}{|x+1|})$$ , where [.] represents greatest integer function , is 
  • R
  • R-[-1, 0]
  • R-[0,1]
  • R-[-1)
The equation $$|x-1|+|a|=4$$ can have real solution for $$x$$ if a belongs to the interval
  • $$(-\infty,4]$$
  • $$(4,\infty)$$
  • $$(-4,4)$$
  • $$(\infty,-4)\cup (4,\infty)$$
If $$f ( x ) = \sin ^ { - 1 } ( \sin x ) + \cos ^ { - 1 } ( \sin x ) \text { and } \phi ( x ) = f ( f ( f ( x ) ) )$$ then $$\phi ^ { \prime } ( x )$$
  • 1
  • $$\sin x$$
  • 0
  • none of these
if $$f\left( x \right) = 3x + 2$$ , $$g\left( x \right) = {x^2} + 1$$,then the values of $$\left( {f_og} \right)\left( {{x^2} - 1} \right)$$
  • $$3{x^4} - 6{x^2} + 8$$
  • $$3{x^4} + 3x + 4$$
  • $$6{x^4} + 3{x^2} - 2$$
  • $$6{x^4} + 3{x^2} + 2$$
Let A = {1,2,3,4,5} and B={1,2,3,4,5}. If $$f:A\rightarrow B$$ is an one-one function and $$f(x)=x$$ holds only for one value of  $$x\epsilon \{ 1,2,3,4,5\} ,$$ then the number of such possible function is  
  • $$120$$
  • $$36$$
  • $$45$$
  • $$44$$
Number of positive integers in the domain of the function $$f(x)=\sqrt {\log_{0.5}\log_{6}\left(\dfrac {x^{2}+x}{x+4}\right)}$$ is
  • $$5$$
  • $$6$$
  • $$7$$
  • $$8$$
Difference between the greatest and the least values of the function
$$f(x) = x(ln x - 2)$$ on $$[1, e^{2}]$$ is
  • $$2$$
  • $$e$$
  • $$e^{2}$$
  • $$1$$
The function $$f :\left[-\dfrac{1}{2}, \dfrac{1}{2}\right]\rightarrow \left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right]$$ defined by $$f(x)=\sin^{-1}(3x-4x^{3})$$ is 
  • both one-one and onto
  • onto but not one-one
  • one-one but not onto
  • neither one-one nor onto
The domain of the function $$f\left(x\right)=\sin^{-1}{\left(1+{e}^{x}\right)^{-1}}$$ is 
  • $$R$$
  • $$[-1,0]$$
  • $$[0,1]$$
  • $$[-1,1]$$
The interval on which the function $$f(x)=2x^3+9x^2+12x-1$$ is decreasing is?
  • $$[-1, \infty)$$
  • $$[-2, -1]$$
  • $$(-\infty, -2]$$
  • $$[-1, 1]$$
Let g be the inverse function of differentiable function f and $$G\left( x \right) =\frac { 1 }{ g\left( x \right)  } if\quad f\left( 4=2 \right) $$ and $$f'\left( 4 \right) =\frac { 1 }{ 16 } $$, then the value of $${ \left( G'\left( 2 \right)  \right)  }^{ 2 }$$ equals to:
  • 1
  • 4
  • 16
  • 64
The domain of the function $$f(x) = \frac {1} {\sqrt {^{10}C_{x - 1} - 3 \times ^{10} C_x}}$$ contains the points
  • 9, 10, 11
  • 9, 10, 12
  • all natural numbers
  • None of these
If $$f:( - 1,1) \to B$$ , is a function defined by $$f(x) = {\tan ^{ - 1}}\dfrac{{2x}}{{1 - {x^2}}}$$, then find $$B$$ when $$f(x)$$ is both one-one and onto function. 
  • $$\left[ { - \frac{\pi }{2},\frac{\pi }{2}} \right]$$
  • $$\left( { - \frac{\pi }{2},\frac{\pi }{2}} \right)$$
  • $$\left( {0,\frac{\pi }{2}} \right)$$
  • $$\left[ {0,\frac{\pi }{2}} \right)$$
The sum of all real values of $$x$$ satisfying the equation
$${\left( {{{\rm{x}}^{{\rm{2 - }}}}{\rm{5x + 5}}} \right)^{{{\rm{x}}{{\rm{^2 + 4x - 60}}}}}}{\rm{ = 1}}$$ is
  • $$-4$$
  • $$6$$
  • $$5$$
  • $$3$$
If  $$f \left( \dfrac { x + y } { 2 } \right) = \dfrac { f ( x ) + f ( y ) } { 2 }$$  for all  $$x , y \in R$$  and  $$f ^ { \prime } ( o ) = - 1 , f ( o ) = 1$$  then  $$f(2)=$$
  • $$\dfrac { 1 } { 2 }$$
  • $$1$$
  • $$-1$$
  • $$\dfrac { -1 } { 2 }$$
The domain of $$f(x) = \sqrt{2 - log_3 (x - 1)}$$ is
  • $$(2, 12]$$
  • $$(\infty, 10]$$
  • $$(3, 12]$$
  • $$(1, 10]$$
If $$f(x)=x^{3}+x^{2}f'(1)+xf''(2)+f'''(3)\ \forall x\ \epsilon \ R$$, then $$f(x)$$ is
  • one-one and onto
  • one-one and into
  • many-one and onto
  • non-invertible
Let $$E=\left\{1,2,3,4\right\}$$ and $$F=\left\{1,2\right\}$$. Then the number of onto functions from $$E$$ to $$F$$ is
  • $$14$$
  • $$16$$
  • $$12$$
  • $$8$$
The domain of the function, $$f(x)=\dfrac{|x|-2}{|x|-3}$$ is
  • $$R$$
  • $$R-\{2,3\}$$
  • $$R-\{2,-2\}$$
  • $$R-\{-3,3\}$$
If $$f\left( x \right) =\sqrt { { x }^{ 2 }-4 } $$ and $$g\left( x \right) =\dfrac { x-1 }{ x-3 } $$ then number of integer elements, which are not in the domain of the function $$(f.g)(x)$$ equals 
  • 3
  • 4
  • 5
  • None of these
Let $$N$$ be the set of natural numbers and two functions $$f$$ and $$g$$ be defined as $$f,g : N\to N$$ such that :
$$f (n)= \begin{cases}\dfrac{n+1}{2}& \text{if n is odd}\\ \dfrac{n}{2} & \text{in n is even} \end{cases}$$
and $$g(n) = n - (-1)^n$$. The fog is:
  • Both one-one and onto
  • One-one but not onto
  • Neither one-one nor onto
  • onto but not one-one
If $$f(x)=\dfrac {4^{x}}{4^{x}+2}$$, then the value of $$f(x)+f(1-x)$$ is
  • $$0$$
  • $$-1$$
  • $$1$$
  • $$can't\ be\ determined$$
Domain of the function $$f\left( x \right) =\sqrt { 2-2x-{ x }^{ 2 } } $$ is 
  • $$-\sqrt { 3 } \le x\le \sqrt { 3 } $$
  • $$-1-\sqrt { 3 } \le x\le -1+\sqrt { 3 } $$
  • $$-2\le x\le 2$$
  • $$-2+\sqrt { 3 } \le x\le -2-\sqrt { 3 } $$
Let $$f(x)=x^ {135}+x^ {125}-x^ {115}+x^ {5}+1$$. If $$f(x)$$ divided by $$x^ {3}-x$$, then the remainder is some function of $$x$$ say $$g(x)$$. Then $$g(x)$$ is an:-
  • one-one function
  • many one function
  • into function
  • onto function
The domain of the function $$\sin^{-1} (log_2(\frac{x}{3}))$$ is-  
  • [$$\frac{1}{2},3$$]
  • [$$\frac{1}{2},3$$]
  • [$$\frac{3}{2},6$$]
  • [$$\frac{1}{2},2$$]
Domain of function $$f(x)=\dfrac{|x|-x}{2x}$$ is
  • $$\mathbb{R}$$
  • $$\mathbb{R}-\{0\}$$
  • $$\mathbb{Z}$$
  • $$\mathbb{N}$$
The domain of $$f(x)= e^{\sqrt{x}}+cos x $$ is 
  • $$(-\infty ,\infty )$$
  • $$[0,\infty )$$
  • (0,1)
  • $$(1,\infty )$$
The domain of function $$f ( x ) = \dfrac { x ^ { 2 } - 10 x + 26 } { x ^ { 4 } \left( x ^ { 2 } - 9 \right)  \left( 1 + 27 x ^ { 2 } \right) }$$ 
  • $$\mathbf { x } \in \mathbf { R } - \{ 0,\pm3 \}$$ 
  • $$\mathbf { x } \in \mathrm { R } - \{ 0,3 \}$$ 
  • $$x \in R$$
  • none
The domain of the function $$f(x)=\sqrt {\dfrac{x^{2}-1}{x-2}}$$ is 
  • $$(2,\infty )$$
  • $$(1,\infty )$$
  • $$[-1,1] \cup (2,\infty)$$
  • none of these
The domain of the function $$f ( x ) = \log _ { 2 }  x^2$$  is
  • $$\mathbf { x } \in \mathbf { R }$$
  • $$x \in [ 0 , \infty )$$
  • $$x \in (- \infty ,0)\cup( 0 , \infty )$$
  • $$x \in R - \{ x | x \in 1 \}$$
Domain of the function $$f(x) = \dfrac{x^2-3x+2}{x^2+x-6}$$ is
  • {$$x:x \epsilon R, x \neq -3$$}
  • {$$x:x \epsilon R, x \neq 2$$}
  • {$$x:x \epsilon R$$}
  • {$$x:x \epsilon R, x \neq 2, x \neq -3$$}
The function $$y=\dfrac { x }{ 1+{ x }^{ 2 } } $$ has its domain as
  • $$x \in R$$
  • $$x\in R-(-1,1)$$
  • $$x \in \left( 0,\infty \right) $$
  • $$x \in \left( -\infty ,-1 \right) $$
The domain of the function, $$f(x)=\sqrt{2-x}$$$$-\dfrac{1}{\sqrt{9-x^{2}}}$$  is 
  • (-3,1)
  • [-3,1]
  • (-3,2)
  • (-3,2]
 $$f : R \rightarrow R , f ( x ) = e ^ { | x | } - e ^ { - x }$$  is many-one into function.
  • True
  • False
Number of one-one functions from A to B where $$n(A)=4, n(B)=5$$.
  • $$4$$
  • $$5$$
  • $$120$$
  • $$90$$
Consider $$f(x) = \dfrac{x^2}{1 + x^3}$$ ; $$g(t) = \displaystyle \int f(t) dt$$ . If $$g(1) = 0$$ then $$g(x)$$ equals 
  • $$\dfrac{1}{3} ln(1 + x^3)$$
  • $$\dfrac{1}{3} ln\left ( \dfrac{1 + x^3}{2} \right )$$
  • $$\dfrac{1}{2} ln\left ( \dfrac{1 + x^3}{3} \right )$$
  • $$\dfrac{1}{3}l n\left ( \dfrac{1 + x^3}{3} \right )$$
Domain of the function $$f(x)=$$ $$\dfrac { x-3 }{ (x-1)\sqrt { { x }^{ 2 }-4 }  } $$
  • $$(1,2)$$
  • $$(-\infty,-2)\cup(2,\infty)$$
  • $$(-\infty,-2)\cup(1,\infty)$$
  • $$(-x,x)-{(t\pm2)}$$
In a set $$A=\left\{1,2,3,4\right\}$$, the relation R is defined as $$x\quad R\quad y\quad \Longleftrightarrow \quad x\le y$$, then the domain of the inverse relation is
  • $$\left\{1,2,3\right\}$$
  • $$\left\{3,4,5,6\right\}$$
  • $$\left\{1,2,3,4\right\}$$
  • $$\left\{4,5,6\right\}$$
$$f : R \rightarrow R , f ( x ) = 2 x + | \sin x |$$  is one-one onto.
  • True
  • False
If $$f:R\rightarrow R,f\left( x \right) =\dfrac { { ax }^{ 2 }+6x-8 }{ a+6x-{ 8x }^{ 2 } } $$ is onto, then $$\alpha \in $$
  • $$\left( 1,\infty \right) $$
  • $$\left( 0,\infty \right) $$
  • $$\left( 2,12 \right) $$
  • $$\left[ 2,14 \right] $$
If f : $$R\rightarrow S$$, defined by f(x) =sin x -$$\sqrt{3}$$ cos x +1, is onto, then the interval of S is 
  • [0, 3]
  • [-1, 1]
  • [0, 1]
  • [-1, 3]
If $$  f : R \rightarrow R  $$ be given by $$  f(x)=\left(3-x^{3}\right)^{\dfrac{1}{3}},  $$ then $$fof(x)$$ is
  • $$
    x^{\dfrac{1}{3}}
    $$
  • $$
    1^{3}
    $$
  • x
  • $$
    \left(3-x^{3}\right)
    $$
Let : $$R\rightarrow R$$ defined as $$f\left( x \right) =\dfrac { x\left( x+1 \right) \left( { x }^{ 4 }+1 \right) +{ 2x }^{ 4 }+{ x }^{ 2 }+2 }{ { x }^{ 2 }+x+1 } $$
  • odd and one-one
  • even and one-one
  • many to one and even
  • many to one and neither even nor odd
The domain of the function $$f(x) =$$$$\dfrac{\sin^{-1}(x-3)}{\sqrt{9-x^2}}$$ is 
  • $$[1, 2]$$
  • $$[2, 3)$$
  • $$[2, 3]$$
  • $$[1, 2)$$
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers