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CBSE Questions for Class 12 Commerce Maths Relations And Functions Quiz 1 - MCQExams.com

If f(x)=x+tanx and f is inverse of g, then g(x) is equal to
  • 11+[g(x)x]2
  • 12[g(x)+x]2
  • 12+(xg(x))2
  • None of these
f:RR is a function defined by f(x)=10x7.  If  g=f1  then  g(x)=  
  • 110x7
  • 110x+7
  • x+710
  • x710
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}}
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
If f:(0,\infty )\rightarrow (0,\infty ) is defined by f(x)=x^{2}, then f^{-1}(x)=
  • \sqrt{x}
  • \dfrac{1}{\sqrt{x}}
  • Not invertible
  • \dfrac{2}{\sqrt{x}}
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
The first component of all ordered pairs is called
  • Range
  • Domain
  • Function
  • None of these
The second component of all ordered pairs of a relation is
  • Range
  • Domain
  • mapping
  • none of these
A ______ maps elements of one set to another set.
  • order
  • set
  • relation
  • function
Suppose y is equal to the sum of two quantities of which one varies directly as x and the other inversely as x If y = 6 when x = 4 and \displaystyle y=\frac{10}{3} when x = 3 then what is the relation between x and y?
  • \displaystyle y=x+\frac{4}{x}
  • \displaystyle y+2x=\frac{4}{x}
  • \displaystyle y=2x+\frac{8}{x}
  • \displaystyle y=2x-\frac{8}{z}
If X is brother of the son of Y's son. How is X related to Y?
  • Son
  • Brother
  • Cousin
  • Grandson
  • Uncle
In the group G = \left \{1, 5, 7, 11\right \} under \otimes_{12} the value of 7\otimes_{12} 11^{-1} is equal to
(\otimes_{12}: under multiplication modulo 12)
  • 5
  • 7
  • 11
  • 1
What is the relation for the statement "A is taller than B"?
  • is taller than
  • A is taller
  • B is taller
  • is less than
x varies directly as y and inversely as the square of z. When y = 4 and z is 14 x =If y = 16 and z = 7 what is x?
  • 180
  • 160
  • 280
  • 200
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 a,b\in A, a*b\in A then
  • * is a unary operation in A
  • a * b = b * a
  • * is a binary operation in A
  • a * b \neq b * a
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
Squaring a given number is a
  • relation in some set
  • relation
  • unary operation
  • binary operation
If * is a binary operation in A then
  • A is closed under *
  • A is not closed under *
  • A is not closed under +
  • A is closed under -
+ is
  • binary operation on R
  • not a binary operation on R
  • a binary operation in Q^c
  • not a binary operation in E
* is said to be commutative in A for all a,b\in A
  • a + b = b + a
  • a * b = b * a
  • a - b = b - a
  • a * b \neq b * a
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}
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}
Find number of all such functions y = f(x) which are one-one?
  • 0
  • 3^{5}
  • ^{5}P_{3}
  • 5^{3}
The inverse of the function y=\cfrac { { 2 }^{ x } }{ 1+{ 2 }^{ x } } is
  • x=\log _{ 2 }{ \cfrac { 1 }{ 1-{ 2 }^{ y } } }
  • x=\log _{ 2 }{ \left( 1-\cfrac { 1 }{ y } \right) }
  • x=\log _{ 2 }{ \left( \cfrac { 1 }{ 1-y } \right) }
  • x=\log _{ 2 }{ \left( \cfrac { y }{ 1-y } \right) }
If f : R - \left \{\dfrac {3}{5}\right \}\rightarrow R - \left \{\dfrac {3}{5}\right \}; f(x) = \dfrac {3x + 1}{5x - 3}, then ___________.
  • f^{-1} (x) = 2f(x)
  • f^{-1} (x) = f(x)
  • f^{-1} (x) = -f(x)
  • f^{-1} (x) does not exists
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
The number of real linear functions f(x) satisfying f\left\{ f(x) \right\} =x+f(x)
  • 0
  • 4
  • 5
  • 2
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
If D be subset of the set of all rational numbers which can be expressed as terminating decimals, then D is closed under the binary operations of:
  • addition, subtraction and division
  • addition, multiplication and division
  • addition, subtraction and multiplication
  • subtraction, multiplication and division
If a\ast b={ a }^{ 3 }+{ b }^{ 3 } on z, then \left( 1\ast 2 \right) \ast 0=........
  • 0
  • 729
  • 81
  • 27
State True or False.
Let f : R \rightarrow R be defined by f (x) = cos (5x + 2). Then f is invertible. 
  • True
  • False
If a language of natural numbers has a binary regularly of 0 and 1, then which one of the following strings represents the natural number 7?
  • 1
  • 101
  • 110
  • 111
The number of binary operations on \left\{ 1,2,3,4 \right\} is ______.
  • { 4 }^{ 2 }
  • { 4 }^{ 8 }
  • { 4 }^{ 3 }
  • { 4 }^{ 16 }
If f: R->R is defined by f(x) = |x|, then
  • f^{-1}_{}(x) = -x
  • f^{-1}_{}(x) = \dfrac{1}{|x|}
  • The function f^{-1}_{}(x) does not exist
  • f^{-1}_{}(x) = \dfrac{1}{x}
If a \times b =2 a - 3b + ab, then 3 \times 5+5\times 3 is equal to
  • 22
  • 24
  • 26
  • 28
Let R be the relation on Z defined by R = \{(a, b): a, b \in z, a - b is an integer\}. Find the domain and Range of R.
  • z, z
  • z^+, z
  • z, z^-
  • None of these
If x \times y = x^{2}+y^{2}-xy then the value of 9 \times 11 is :
  • 93
  • 103
  • 113
  • 121
Let f(x)={x}^{3}-6{x}^{2}+15x+3. Then, 
  • f(x)> 0 for all x\in R
  • f(x)> f(x+1) for all x\in R
  • f(x) is invertible
  • f(x)< 0 for all x\in R
The number of binary operation on {1, 2, 3... n} is..
  • 2^n
  • n^2
  • n^3
  • n^{2n}
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
0:0:1


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Practice Class 12 Commerce Maths Quiz Questions and Answers