CBSE Questions for Class 11 Commerce Applied Mathematics Functions Quiz 1 - MCQExams.com

The domain of $$f(x)=\frac{1}{\sqrt{|x|-x}}$$ is
  • $$(-\infty ,0)$$
  • $$(0,\infty ,)$$
  • $$(1, \infty )$$
  • $$(-\infty ,\infty )$$
A constant function $$f:A\rightarrow B $$ will be onto if
  • $$n(A) = n(B)$$
  • $$n (A) =1$$
  • $$n (B) = 1$$
  • $$n(A) > n(B)$$
The number of non-bijective mappings possible from $$A= \{1,2,3\}$$ to $$B=\{4, 5\}$$ is
  • $$9$$
  • $$8$$
  • $$12$$
  • $$6$$
A constant function $$f:A\rightarrow B$$ will be one-one if
  • $$n (A) = n(B)$$
  • $$n(A) = 1$$
  • $$n (B) = 1$$
  • $$n (A) < n (B)$$
If $$f:\mathbb{N} \rightarrow \mathbb{N}$$ and $$f(x) = x^{2}$$ then the function is
  • not one to one function
  • one to one function
  • into function
  • none of these
$$f(x)=1$$, if $$x$$ is rational and $$f(x)=0$$, if $$x$$ is irrational
then  $$(fof)  (\sqrt{5})=$$
  • $$0$$
  • $$1$$
  • $$\sqrt{5}$$
  • $$\dfrac{1}{\sqrt{5}}$$
The domain of the function,  f(x) = $$\sqrt {x-1}+\sqrt {5-x}$$  is
  • $$[1, \infty ) $$
  • $$(\infty , 5)$$
  • (1, 5)
  • [1, 5]
If $$f(x) = 3x + 2, g(x) = x^2 + 1$$, then the value of $$(fog) (x^2 +1)$$ is
  • $$3x^4 + 6x^2 + 8$$
  • $$3x^4 + 3x + 4$$
  • $$6x^4 + 3x^2 + 2$$
  • $$3x^2 + 6x + 2$$
If $$f:A\rightarrow B $$ is surjective then
  • no two elements of $$A$$ have the same image in $$B$$
  • every element of $$A$$ has an image in $$B$$
  • every element of $$B$$ has at least one pre-image in $$A$$
  • $$A$$ and $$B$$ are finite non empty sets
$$f:R\rightarrow R , g:R\rightarrow R$$ and  $$f(x)= \sin x$$, $$g(x)=x^{2}$$ then $$fog(x)=$$
  • $$x^{2}+\sin x$$
  • $$x^{2}\sin x$$
  • $$\sin^{2}x$$
  • $$\sin x^{2}$$
Find the value of $$\displaystyle \left( g\circ f \right) \left( 6 \right) $$ if $$\displaystyle g\left( x \right) ={ x }^{ 2 }+\frac { 5 }{ 2 } $$ and $$\displaystyle f\left( x \right) =\frac { x }{ 4 } -1$$.
  • 2.75
  • 3
  • 3.5
  • 8.625
If $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ are defined by $$f(x) =3x -4$$, and  $$g(x)=2 + 3x$$, find $$(g^{-1}\, of^{-1})(5)$$.
  • $$1$$
  • $$\dfrac {1}{2}$$
  • $$\dfrac {1}{3}$$
  • $$\dfrac {1}{5}$$
If $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ are defined by $$f(x) =2x +3, g(x)=x^2 + 7$$, what are the values of $$x$$ such that $$g(f(x))=8$$?
  • $$1, 2$$
  • $$-1, 2$$
  • $$-1, -2$$
  • $$1, -2$$
Find the correct expression for $$\displaystyle f\left( g\left( x \right)  \right) $$ given that $$\displaystyle f\left( x \right) =4x+1$$ and $$\displaystyle g\left( x \right) ={ x }^{ 2 }-2$$
  • $$\displaystyle -{ x }^{ 2 }+4x+1$$
  • $$\displaystyle { x }^{ 2 }+4x-1$$
  • $$\displaystyle 4{ x }^{ 2 }-7$$
  • $$\displaystyle 4{ x }^{ 2 }-1$$
  • $$\displaystyle 16{ x }^{ 2 }+8x-1$$
If $$f(x) = \sqrt {x^{2} - 3x + 6}$$ and $$g(x) = \dfrac {156}{x +17}$$, find the value of the composite function $$g(f(4))$$.
  • $$5.8$$
  • $$7.4$$
  • $$7.7$$
  • $$8.2$$
  • $$10.3$$
Find the domain of following function:
$$\sqrt { { x }^{ 2 }-9 } $$
  • $$(-\infty,-3]\cup[3,\infty)$$
  • $$(-\infty,-5)\cup(3,\infty)$$
  • $$(-\infty,-3)\cup(6,\infty)$$
  • None of these
For what value of x is $$fog = gof$$ if $$f(x)=x - 2$$ and $$g(x)=x^3+3$$?
  • $$\dfrac{-2}{3}$$
  • $$-1$$
  • $$\dfrac{3}{2}$$
  • $$\dfrac{-3}{2}$$
Which of the following functions is/are constant ?
  • $$f(x)=x^{2}+2$$
  • $$f(x)=x+\dfrac{1}{x}$$
  • $$f(x)=7$$
  • $$f(x)=6+x$$
Let $$f:\mathbb{R}\rightarrow \mathbb{R}$$ be a function such that for any irrational number $$r,$$ and any real number $$x$$ we have $$f(x)=f(x+r)$$. Then, $$f$$ is
  • an identity function
  • a constant function
  • a zero function
  • onto function
Let $$f$$ be a function from the set of natural numbers to the set of even natural numbers given by $$f\left( x \right)=2x$$. Then $$f$$ is
  • One to one but not onto
  • Onto but not one-one
  • Both one-one and onto
  • Neither one-one nor onto
If $$\{ (x, 2), (4, y) \}$$ represents an identity function, then $$( x, y)$$ is :
  • (2, 4)
  • (4, 2)
  • (2, 2)
  • (4, 4)
Find number of all such functions $$y = f(x)$$ which are one-one?
  • $$0$$
  • $$3^{5}$$
  • $$^{5}P_{3}$$
  • $$5^{3}$$
The number of real linear functions $$f(x)$$ satisfying $$f\left\{ f(x) \right\} =x+f(x)$$
  • $$0$$
  • $$4$$
  • $$5$$
  • $$2$$
Let $$f:N\times N\rightarrow N-\left\{ 1 \right\} $$ be defined as $$f(m,n)=m+n$$, then function $$f$$ is ______.
  • One-One and onto
  • Many- One and not onto
  • One- One and not onto
  • Many- One and onto
Let E = {1, 2, 3, 4} and F {1, 2}. Then the number of onto functions from E to F is
  • 14
  • 16
  • 6
  • 4
Find the domain for which the functions $$f(x)=2x^2-1$$ and $$g(x)=1-3x$$ are equal.
  • {-2,2}
  • {2, 1/2}
  • {-2,1/2}
  • None of these
Suppose that $$g\left( x \right) =1+\sqrt { x }$$ and $$f\left( g\left( x \right)  \right) =3+2\sqrt { x } +x$$, then $$f\left( x \right)$$ is
  • $$1+2{ x }^{ 2 }$$
  • $$2+{ x }^{ 2 }$$
  • $$1+x$$
  • $$2+x$$
Find the domain of $$\sqrt{\dfrac{\sqrt{x-2}}{x-3}}$$.
  • $$(2,\infty)$$
  • $$(3,\infty)$$
  • $$(-\infty, 2)$$
  • $$(-\infty, 3)$$
If domain of $$f(x)=\sqrt{{x}^{2}+bx+4}$$ is $$R$$, then maximum possible integral value of $$b$$ is
  • $$2$$
  • $$3$$
  • $$4$$
  • $$5$$
Let A = {0, 1} and N the set of all natural numbers. Then the mapping $$f : N \rightarrow A$$ defined by
$$f(2n - 1) = 0, f (2n) = 1 \forall n \epsilon N$$
is many-one onto.
  • True
  • False
$$f:R \to R,f\left( x \right) = \dfrac {{x^2} + 2x + c}{{x^2} + 4x + c}$$ is onto only if
  • $$c < 2$$
  • $$c \ge 0$$
  • $$c < 0$$
  • $$|c| \le 1$$
Let $$f(x) = \sqrt{log_2 \dfrac{10x - 4}{4 - x^2}-1}$$. Then sum of all integers in domain of $$f(x)$$ is
  • $$-15$$
  • $$-16$$
  • $$-17$$
  • $$-20$$
Domain of function as $$f\left( x \right) = \dfrac{{^3\sqrt {{x^2} - 5x + 6} }}{{{x^2} - x - 6}}$$ is 
  • $$\left[ {2,3} \right]$$
  • $$R - \left\{ { - 3,2} \right\}$$
  • $$R - \left\{ { - 2,3} \right\}$$
  • $$R$$
The domain of the fuction $$f(x)=\sqrt{\log_{16}x^2}$$ is ?
  • $$x=0$$
  • $$|x|\ge4$$
  • $$|x|\ge 1$$
  • $$|x|\ge 2$$
Domain of $$f(x)=\dfrac {4x}{\sqrt{x^2-16}}$$ 
  • $$|x|>4$$
  • $$|x|<4$$
  • $$|x|=4$$
  • $$ x\in R$$
If the domain of the function $$f(x)= \dfrac{x^2-5x+66}{x-4}$$is $$R-\{a\}$$, then the value of a -
  • 4
  • 6
  • 8
  • 12
Read the following information and answer the three items that follow :
Let $$f(x) = x^2 + 2x - 5 $$ and $$g(x) = 5x + 30$$
Consider the following statements:
$$f[g(x)]$$ is a polynomial of degree 3.
$$g[g(x)]$$ is a polynomial of degree 2.
Which of the above statements is/are correct ?
  • 1 only
  • 2 only
  • Both 1 and 2
  • Neither 1 nor 2
Let $$f(x)=\cfrac { 1 }{ 1-x } $$. Then $$\left\{ f\circ \left( f\circ f \right)  \right\} (x)$$
  • $$x$$ for all $$x\in R$$
  • $$x$$ for all $$x\in R-\left\{ 1 \right\} $$
  • $$x$$ for all $$x\in R-\left\{ 0,1 \right\} $$
  • none of these
Read the following information and answer the three items that follow :
Let $$f(x) = x^2 + 2x - 5 $$ and $$g(x) = 5x + 30$$
What are the roots of the equation $$g[f(x)] = 0$$ ?
  • $$1, -1$$
  • $$-1, -1$$
  • $$1, 1$$
  • $$0, 1$$
Read the following information and answer the three items that follow :
Let $$f(x) = x^2 + 2x - 5 $$ and $$g(x) = 5x + 30$$
If $$h(x) = 5f(x) - xg (x)$$, then what is the derivative of $$h(x)$$ ?
  • $$-40$$
  • $$-20$$
  • $$-10$$
  • $$0$$
The number of one-one functions that can be defined from $$A=\{4,8,12,16\}$$ to $$B$$ is $$5040,$$ then $$n(B)=$$
  • $$7$$
  • $$8$$
  • $$9$$
  • $$10$$
The number of injections that are possible from $$A$$ to itself is $$720,$$ then $$n (A) =$$
  • $$5$$
  • $$6$$
  • $$7$$
  • $$8$$
The number of one-one functions that can be defined from $$A = \left \{ 1,2,3 \right \} $$ to $$  B = \left \{ a,e,i,o,u \right \}$$ is 
  • $$3^{5}$$
  • $$5^{3}$$
  • $${_{}}^{5}P_{3}$$
  • $$5!$$
The number of non-surjective mappings that can be defined from $$A = \left \{ 1,4,9,16 \right \}  $$ to$$  B=\left \{ 2,8,16,32,64 \right \}$$ is
  • $$1024$$
  • $$20$$
  • $$505$$
  • $$625$$
If $$A = \left \{ 11, 12, 13, 14 \right \} $$ and $$  B = \left \{ 6,8,9,10 \right \} $$ then the number of bijections defined from $$A$$ to $$B$$ is
  • $$256$$
  • $$24$$
  • $$16$$
  • $$64$$
If function $$f$$ has an inverse, then which of the following conditions is necessary and sufficient
  • $$f$$ is a one-one function.
  • $$f$$ is an onto function.
  • $$f$$ is a one-one and onto function.
  • $$f$$ is an identity function.
If $$ f:A\rightarrow B $$ is a constant function which is onto then $$B$$ is
  • a singleton set
  • a null set
  • an infinite set
  • a finite set
If $$ f:A\rightarrow B $$ is a bijection then $$ f^{-1} of = $$
  • $$fof^{-1}$$
  • $$f$$
  • $$f^{-1}$$
  • an identity
The number of bijection that can be defined from $$A = \left \{ 1,2,8,9 \right \}  $$ to $$  B = \left \{ 3,4,5,10 \right \}$$ is
  • $$4^{4}$$
  • $$4^{2}$$
  • $$24$$
  • $$18$$
Assertion (A) : $$ f(x)=\dfrac{x^{2}-4}{x-2} $$ and $$ g(x) = x+2$$ are equal.

Reason (R): Two functions $$f$$ and $$g$$ are said to be equal if their domains and ranges are equal and $$f(x)=g(x) \forall x \in $$ domain.
  • Both $$A$$ and $$R$$ are true and $$R$$ is the correct explanation of $$A$$
  • Both $$A$$ and $$R$$ are true and $$R $$ is not correct explanation of $$A$$
  • $$A$$ is true but $$R$$ is false
  • $$A$$ is false but $$R$$ is true
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