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CBSE Questions for Class 12 Commerce Maths Relations And Functions Quiz 11 - 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
 If A={x|x/2Z,0x10}B={x|x is one digit prime }C={x|x/3N,x12},
Then A(BC) is equal to-


  • {2,6}
  • {3,6,12}
  • {2,6,12}
  • {6,8}
The function f:NN defined by f(x)=x5[x5], 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
The inverse of the function f(x)=exexex+ex is 
  • 12ln1+x1x
  • 12ln2+x2x
  • 12ln1x1+x
  • 2 ln (1+x)
Let f:RR be defined as 
f(x)=x3+2x2+4x+sin(πx2) and  g(x)be the inverse function of f(x), then g(8)is equal to :
  • 12
  • 9
  • 111
  • 11
The function f:RR defined by f(x)=6x+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
Let f:RR be defined by f(x)=x|x|2+cosx+1 then f(x) is
  • One-one only
  • Onto only
  • Neither one-one nor onto
  • Bijection
Let f:R(1,1) be defined as f(x)=exexex+ex then f is
  • One-one onto
  • One-one into
  • Many-one onto
  • Many-one-into
If A2A+I=0 then A1
  • A2
  • A+I
  • IA
  • AI
A number of decimal system when represented in binary system then its first and last digits are same and the rest digits are also of another kind. Further this number appears to be palindrome of number. The number is
  • 57
  • 19
  • 8
  • 9
If f:ZZ,f(n)={n+1;nisevenn3;nisodd is f is ...........
  • only one one
  • only Onto
  • one one & Onto both
  • Neither one one nor Onto
Which one of the following functions is not invertible?
  • f:RR,f(x)=3x+1
  • f:R[0,),f(x)=x2
  • f:R+R+,f(x)=1x3
  • None of these
If f:RRdefinedbyf(x)=ex2ex2ex2+ex2,thenfis
  • one-one but not onto
  • not one-one but onto
  • one-one and onto
  • neither one-one noronto
If  27    3 =243 and  5     4 = 80 .Then what is the value of  3     7 = ?
  • 84
  • 147
  • 63
  • 23
If f(x)=αxx+1, where x1 and (fof) (x) = x, then α=
  • 2
  • 2
  • 1
  • 1
f(x) is
  • One-one and onto
  • One-one and into
  • Many-one and onto
  • Many-one and into
Let N be the set of natural numbers and two functions f and g be defined as
and g(n)=n(1)n then fog is:
  • one-one but not onto
  • onto but not one-one
  • neither one-one nor into
  • both one-one and onto
The inverse of 19 mod 141 is :
  • 50
  • 51
  • 52
  • 55
let f:RR be a function defined by f(x)=x23x+4x2+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
The function f:RR defined by f(x)=e|x|exex+ex is
  • One-One and onto
  • One-one but not onto
  • Not one-one but onto
  • Neither one-one nor onto
f:NNwheref(x)=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 limx0g(x)=aandlimx0G(x)=b, then f' (x) is equal to
  • 1+ab
  • ab
  • f(x)
  • ab f(x)
Consider the function f(x)=ex and g(x)=sin1x, then which of the following is/are necessarily true.
  • Domain of gof= Domain of f
  • Range of gof  Range of g
  • Domain of gof is (,0)
  • Range of gof is (π2,0)
f:AB will be an into function if

  • f(A)B
  • f(A)=B
  • Bf(A)
  • f(B)A
Suppose that g(x)=1+xandf(g(x))=3+2x+xthenf(x)is
  • 1+2x2
  • 2+x2
  • 1+x
  • 2+x
Which one of the following is one-one?
  • f:RR given by f(x)=|x1| for all xR
  • g:[π/2,π/2]givenby g(x)=|sinx|
  • h:[π/2,π/2]R given by h(x)=sinx for all x[π/2,π/2]
  • ϕ:RR given by f(x)=x24 for all xR
Let f:RR  defined by f(x)=ex2ex2ex2+ex2, 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
Consider the binary operation on Q defined by xy=1+12x+xy,x,yQ then 23 equals
  • 31
  • 41
  • 43
  • 51
The inverse of the function 
f(x)=exexex+ex+2 is given by
  • loge(x2x1)1/2
  • loge(x13x)1/2
  • loge(x2x)1/2
  • loge(x1x+1)2
Let f:RR, be defined as f(x)=ex2+cosx then f is
  • One-one and onto
  • One-one and into
  • Many-one and onto
  • many-one and into
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) = x2, Then the value of the integral 10f(x)g(x)dx,is
  • ee2252
  • e+e2232
  • ee2232
  • e+e22+52
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)=X2, the value of the integral 10f(x)g(x)dxis
  • 14(e7)
  • 14(e2)
  • 14(e3)
  • none of the above
the inverse of the function f(x)=10x10x10x+10xis
  • 12log10(1+x1x)
  • 12log10(1x1+x)
  • 14log10(2x2x)
  • none of these
f:RR  defined by  f(x)=xx2+1,xR  is
  • one-one
  • onto
  • bijective
  • neither one one nor onto
If f (x) = cosx and g (x) = x2 then (gof) (x) is ....
  • cos2 x
  • cosx2
  • both (a)&(b)
  • x2 cosx
If the function f:[1,)[1,) is defind by f(x)=2x(x1), then f1(x) is 
  • (12)x(x1)
  • 12(1+1+4log2x)
  • 12(11+4log2x)
  • None of these
If  f(x)=x2+1,g(x)=x+1x2+1  and  h(x)=2x3,  then  f(h(g(x))=
  • 0
  • 1x2+1
  • 25
  • xx2+1
f:RR  where  f(x)=x2+ax+1x2+x+1.  Complete set of values of  a  such that  f(x)  is onto to is :
  • (,)
  • (,0)
  • (0,)
  • None
Let f be a real -valued function defined on the interval (-1,1) such that 
{e^{ - x}}f(x) = 2 + \int\limits_{}^x {\sqrt {{t^2} + 1} } .dt,\forall x \in ( - 1,1)
and let {f^{ - 1}} be the inverse function of f . Then \left[ {{f^{ - 1}}(2)} \right] is equal to 
  • 1
  • 1/3\,
  • 1/2\,
  • 1/e\,
If the operation * is defined as \left( a\times b \right) ={ a }^{ 2 }+{ b }^{ 2 } then \left( 3\times 4 \right) =5 is
  • 650
  • 125
  • 625
  • 3125
Let f(x)= y=\begin{cases} { x }^{ 2 }-3x+4\quad \quad :\quad X<3 \\ \quad \quad \quad x+7\quad \quad :\quad X\ge 3 \end{cases}\quad and\quad g(x)=\begin{cases} \quad \quad x+6\quad \quad \quad :\quad X<4 \\ { x }^{ 2 }+x+2\quad \quad :\quad X\ge 4 \end{cases}
then which of the following is/ are true-
  • (f+g) (1)=9
  • (f-g)(3.5)= 1
  • (f+g) (0)=24
  • \left( \dfrac { f }{ g } \right) (5)=\dfrac { 8 }{ 3 }
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 a function  f : R \rightarrow R  be such that  f ( x + y ) = f ( x ) f ( y )  for all  x , y \in R  where  f ( x ) = 1 + x \phi ( x )  and  \lim _ { x \rightarrow 0 } \phi ( x ) = 1 ,  then :
  • f ^ { \prime } ( x ) does not exist
  • f ^ { \prime } ( x ) = 2 f ( x ) for all x
  • f ^ { \prime } ( x ) = f ( x ) for all x
  • 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
Find the inverse of f(x)=3x+2
  • {f^{ - 3}}\left( z \right) = \frac{{z - 2}}{3}
  • {f^{ - 3}}\left( z \right) = \frac{{z + 2}}{3}
  • {f^{ - 3}}\left( z \right) = \frac{{z - 5}}{2}
  • {f^{ 3}}\left( z \right) = \frac{{z - 2}}{3}
If f(x)=x+tanx and g(x) is inverse of f(x) then g'(x) is equal to 
  • \dfrac { 1 }{ 1+(g(x)-{ x) }^{ 2 } }
  • \dfrac { 1 }{ 1-(g(x)-{ x) }^{ 2 } }
  • \dfrac { 1 }{ 1+(g(x)-{ x) }^{ 2 } }
  • \dfrac { 1 }{ 2-(g(x)-{ x) }^{ 2 } }
If f : N\rightarrow N be defined by f(x) = 2x + 3 then f^{-1} (x) =
  • 2x - 3
  • \dfrac {x - 3}{2}
  • \dfrac {x + 3}{2}
  • Not defined
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
Let f(x)=x+\cos x+2 and g(x) be the  inverse function of f(x) then g^1(3)=
  • 1
  • 2
  • 3
  • 0
0:0:1


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Practice Class 12 Commerce Maths Quiz Questions and Answers