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

Let A=(5,6); how many binary operations can be defined on this set?
  • 8
  • 10
  • 16
  • 20
If $$f(x_{1})=f(x_{2})\Rightarrow x_{1}=x_{2}\forall x_{1},x_{2}\epsilon A$$, then what type of a function is $$f:A\rightarrow B?$$
  • One-one
  • Constant
  • Onto
  • Many one
If =$$f=\left\{ (-2,4),(0,6),(2,8) \right\} $$ and 
$$g=\left\{ (-2,-1),(0,3),(2,5) \right\} $$, then 
$$\left( \frac { 2f }{ 3g } +\frac { 3g }{ 2f }  \right) (0)=\quad $$
  • 1/12
  • 25/12
  • 5/12
  • 13/12
If $$g(x)-x^{2}-x+1 and f(x)=\sqrt{\frac{1}{x}-x}$$, then-
  • Domain of f(g(x)) ids[0,1]
  • Range of f(g(x)) is $$(0,\frac{7}{2\sqrt{3}})$$
  • f (g(x)) is many -one function
  • f(g(x)) is unbounded function
$$f: ( 0,\infty )\rightarrow [0,\infty )$$  defined by $$f(x)=x^{2}$$  is 
  • one - one but not onto
  • onto but not one - one
  • bijective
  • neither one - one nor onto
Number of solution of the equation  $$f ( x ) = g ( x )$$  are same as number of point of intersection of the curves $$y = f ( x )$$  and  $$y = g ( x )$$  hence answer the following question.
Number of the solution of the equation  $$x ^ { 2 } = | x - 2 | + | x + 2 | - 1$$  is
  • $$0$$
  • $$3$$
  • $$2$$
  • $$4$$
If $$f(x)=\frac{1}{x},g(x)=\frac{1}{x^{2}} $$ and h $$(x)= x^{2},$$ then
  • $$fog (x)= x^{2}, x\neq \bar{0}, h(g(x))= \frac{1}{x^{2}}$$
  • $$h(g(x))= \frac{1}{x^{2}}x\neq 0, fog(x)= x^{2}$$
  • $$fog(x)=x^{2},x\neq 0,h(g(x))= (g(x))^{2},x\neq 0$$
  • None of these
If $$f(x)= sin^{2}x$$ and the composite functions g{f(x)}=|sin x|, then the function g(x)=
  • $$\sqrt{x-1}$$
  • $$\sqrt{x}$$
  • $$\sqrt{x+1}$$
  • $$-\sqrt{x}$$
Number of solution of the equation  $$f ( x ) = g ( x )$$  are same as number of point of intersection of the curves $$y = f ( x )$$  and  $$y = g ( x )$$  hence answer the following question.
Number of the solution of the equation  $$2 ^ { x } = | x - 1 | + | x + 1 |$$  is
  • $$0$$
  • $$1$$
  • $$2$$
  • $$\infty$$
If $$f:A\rightarrow B$$ then for $$f^{-1}$$=
  • $$I_{A}$$
  • $$I_{B}$$
  • $$A\rightarrow B$$
  • none of these
If $$f:N\rightarrow N,f(x)=x+3$$, then $$\quad { f }^{ -1 }(x)=.....$$
  • $$x+3$$
  • does not exist
  • $$x-3$$
  • $$3-x$$
If $$f(x)=(x^2-1)$$ and $$g(x)=(2x+3)$$ then $$(g o f)(x)=?$$
  • $$(2x^2+3)$$
  • $$(3x^2+2)$$
  • $$(2x^2+1)$$
  • None of these
If $$f(x)=8x^3$$ and $$g(x)=x^{1/3}$$ then $$(g o f)(x)=?$$
  • $$x$$
  • $$2x$$
  • $$\dfrac{x}{2}$$
  • $$3x^2$$
If $$f(x)=\dfrac{1}{(1-x)}$$ then $$(f o f o f)(x)=?$$
  • $$\dfrac{1}{(1-3x)}$$
  • $$\dfrac{x}{(1+3x)}$$
  • $$x$$
  • None of these
If $$f(x)=x^2, g(x)=\tan x$$ and $$h(x)=log x$$ then $$\{h o (g o f)\}\left(\sqrt{\dfrac{\pi}{4}}\right)=?$$
  • $$0$$
  • $$1$$
  • $$\dfrac{1}{x}$$
  • $$\dfrac{1}{2} \log \dfrac{\pi}{4}$$
If $$f=\{(1, 2), (3, 5), (4, 1)\}$$ and $$g=\{(2, 3), (5, 1), (1, 3)\}$$ then $$(g o f)=?$$
  • $$\{(3, 1), (1, 3), (3, 4)\}$$
  • $$\{(1, 3), (3, 1), (4, 3)\}$$
  • $$\{(3, 4), (4, 3), (1, 3)\}$$
  • $$\{(2, 5), (5, 2), (1, 5)\}$$
If $$f(x)=x^2-3x+2$$ then $$(f o f)(x)=?$$
  • $$x^4$$
  • $$x^4-6x^3$$
  • $$x^4-6x^3+10x^2$$
  • None of these
Let $$f: R \rightarrow R$$ defined by $$f(x)= e\frac { { e }^{ { x }^{ 2 } }-{ e }^{ { -x }^{ 2 } } }{ { e }^{ { x }^{ 2 } }+{ e }^{ { -x }^{ 2 } } } $$ 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
If $$f(x) = -{ \frac { x\left| x \right|  }{ 1+x^{ 2 } }  }$$ then $$f^{-1} (x) $$ equals
  • $$\sqrt { \frac { x\left| x \right| }{ 1-\left| x \right| } } $$
  • $$(Sgn x) \sqrt { \frac { x\left| x \right| }{ 1-\left| x \right| } } $$
  • $$- \sqrt { \frac {x} {1-x}}$$
  • None of these
Which of the following is not true about $$h_2(x)$$
  • Domain R
  • It periodic function with period $$2\pi$$
  • Range is [0, 1]
  • None of these
Which of thefollowing functions are indentical?
  • f(x)= ln $$x^{2}$$ and g(x)= 2 In x
  • f(x)= $$log_x e$$ and $$g(x)= \dfrac{1}{log_e x}$$
  • f(x)= sin $$(cos^{-1}x)$$ and g(x)= $$cos({sin^{-1}x})$$
  • none of these
If $$ f(x)=\dfrac{2}{x-3}, g(x)=\dfrac{x-3}{x+4} $$ and $$ h(x)=-\dfrac{2(2 x+1)}{x^{2}+x-12} $$ then $$ \lim _{x \rightarrow 3}[f(x)+g(x)+h(x)] $$ is
  • $$ -2 $$
  • $$ -1 $$
  • $$ -\dfrac{2}{7} $$
  • 0
The number of roots of the equation g(x) = 1 is
  • 2
  • 1
  • 3
  • 0
0:0:1


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