CBSE Questions for Class 11 Commerce Applied Mathematics Relations Quiz 12 - MCQExams.com

Let $$A = \left\{ {1,2,3} \right\}$$ and $$R = \left\{ {\left( {1,1} \right),\left( {1,3} \right),\left( {3,1} \right),\left( {2,2} \right),\left( {2,1} \right),\left( {3,3} \right)} \right\}$$, then the relation $$R$$ and $$A$$ is
  • reflexive
  • symmetric
  • transitive
  • equivalence
If $$A$$ and $$B$$ are independent event such that $$P(A \cap B')=\dfrac {3}{25}$$ and $$P(A' \cap B)=\dfrac {8}{25}$$, then $$P(A)=$$
  • $$1/5$$
  • $$3/8$$
  • $$2/5$$
  • $$4/5$$
Let $$S=\{x \in R : x\geq 0$$ and $$2|\sqrt{x}-3|+\sqrt{x}(\sqrt{x}-6)+6=0\}$$. Then S?
  • Contains exactly one element
  • Contains exactly two elements
  • Contains exactly four elements
  • Is an empty set
The domain of $$\dfrac{1}{\sqrt{x-x^{2}}}+\sqrt{3x-1-2x^{2}}$$ is 
  • $$(\dfrac{1}{2},11)$$
  • $$(\dfrac{1}{2},31)$$
  • $$(\dfrac{1}{2},17)$$
  • $$(\dfrac{1}{2},41)$$
The set of values of '$$b$$' for which the origin and the point $$(1,1)$$ lie on the same side of the straight line $${ a }^{ 2 } x + ab y + 1 = 0 \;\;\forall \;\; a\in R,\; b > 0$$ are:
  • $$b\in (2,4)$$
  • $$b\in (0,2)\quad $$
  • $$b\in (0,4)\quad $$
  • $$b\in (2,6)$$
Total number of equivalence relation defined in the set $$s=\{a, b, c\}$$ is
  • $$5$$
  • $$31$$
  • $$2^3$$
  • $$3^3$$
Let A be a finite set and n(A) = 5, then the number of relations which are not symmetric is _____________________.
  • $$2^{25}$$
  • $$2^{15}$$
  • $$2^{25} - 2^{10}$$
  • $$2^{25} - 2^{15}$$
If $$x\ \epsilon \ R$$, the number of solutions of $$\sqrt{2x+1}-\sqrt{2x-1}-1$$ is
  • $$1$$
  • $$2$$
  • $$4$$
  • $$infinite$$
If $$\sqrt { \log _ { 4 } \left( \log _ { 2 } \left( \log _ { 2 } \left( x ^ { 2 } - 2 x + a \right) \right) \right. } )$$ is defined $$\forall x \in R$$, then

  • $$[ 10 , \infty )$$
  • $$[ 9 , \infty )$$
  • $$[ 2 , \infty )$$
  • $$[ 5 , \infty )$$
The domain of log $$\left( { tan }^{ -1 }x \right) $$ is :-
  • R
  • $${ R }^{ + }$$
  • $$\left( 0,\infty \right) $$
  • $$\left( -\frac { \pi }{ 2 } ,\frac { \pi }{ 2 } \right) $$
Let $$T$$ be the set of all triangle in the Euclidean plane, and let a relation $$R$$ on $$T$$ be defined as $$aRb$$ if a is congruent to $$b\ \forall \ a, b\ \epsilon \ T$$. Then $$R$$ is
  • reflective but not transitive
  • transitive but not symmetric
  • equivalence
  • none of these
Let S be the set of all real nos, then the relation $$R = \{ ( a , b ) : | a - b |$$ is a multiple of 4$$\}$$ then the relation.
  • Reflexive but not symmetric
  • Symmetric but not reflexive
  • Reflexive only
  • Equivalence
Which of the following is true for a relation :$$A\longrightarrow A$$
  • If R is reflexive then domain of R is A
  • If R is symmetric then domain of R is A
  • If R be an increasing function, then R is transitive
  • If R is one one function then R is symmetric
Let $$A\equiv \left\{1,2,3,4\right\},\ B\equiv \left\{a,b,c\right\}$$, then number of function from $$A\rightarrow B$$, which are not onto is
  • $$9$$
  • $$24$$
  • $$45$$
  • $$6$$
If domain of $$y = f\left( x \right)$$ is $$ \left[ { - 3,\,\,2} \right]$$ then domain of $$y = f\left( {\left| {\left[ x \right]} \right|} \right)$$ is
  • $$[-3, 2]$$
  • $$[-2, 3)$$
  • $$[-3, 3]$$
  • $$[-2, 3]$$
Let  $$R = \{ ( 3,3 ) , ( 6,6 ) , ( 9,9 ) , ( 6,12 ) , ( 3,9 ) , ( 3,12 ) , ( 3,6 ) \}$$  be a relation on the set  $$A=\{ 3,6,9,12\} .$$  Then the relation  $$R ^ { - 1 }$$  is
  •  reflexive and transitive.
  • not symmetric
  • transitive
  • all the above
Consider the following relations :-
$$R=\{ (x,y):x,y$$  are real numbers and  $$x =w y$$  for some rational number  $$w \}$$ :
$$S = \{ \left( \dfrac { m } { n } , \dfrac { p } { q } \right) : m , n , p$$  and  $$q$$  are integers such that   $${ n },{ q } \neq 0$$  and  $${ qm }={ pn }\}.$$   Then :
  • $$R$$ is an equivalence relation but $$S$$ is not an equivalence relation
  • Neither $$R$$ nor $$S$$ is an equivalence relation
  • $$S$$ is an equivalence relation but $$R$$ is not an equivalence relation
  • $$R$$ and $$S$$ both are equivalence relations
If $$A=\left\{1,2,3\right\}$$, the number of symmetric relation in $$A$$ is
  • $$64$$
  • $$8$$
  • $$324$$
  • $$328$$
Let  $$S = \{ 1,2,3 , \ldots , 100 \} .$$  The number of non-empty subsets  $$A$$  of  $$S$$  such that the product of elements in  $$A$$  is even is :-
  • $$2 ^ { 50 } \left( 2 ^ { 50 } - 1 \right)$$
  • $$2 ^ { 100 } - 1$$
  • $$2 ^ { 50 } - 1$$
  • $$2 ^ { 50 } + 1$$
If $$A=\left\{ 2,3,5 \right\} ,B=\left\{ 4,6,8 \right\} $$, then the relation from $$A$$ into $$B$$ is 
  • $$\left\{(2,4),(3,5),(5,6)\right\}$$
  • $$\left\{(2,4),(5,8),(6,5)\right\}$$
  • $$\left\{(2,4),(3,6),(5,6)\right\}$$
  • $$\left\{(2,5),(3,6)\right\}$$
If A= {a, b} then possible number of relation on the set A.
  • $$2$$
  • $$4$$
  • $$16$$
  • none of these
If n(A)=4, n(B)=3, $$n(A\times B\times C)=24,then\quad n(C)$$ is equal to 
  • 288
  • 1
  • 2
  • 12
If a set $$A$$ has $$n$$ elements then the number of relations defined on $$A$$ is 
  • $$2^{ \left( { n }^{ 2 } \right) }$$
  • $$2^{ \left( { n }^{ 2 } \right) }-1$$
  • $$2^{ n }$$
  • None of these.
If $$R$$ is a relation on the set $$A=\left\{ 1,2,3,4,5,6,7,8,9 \right\} $$ given by $$xRy\Leftrightarrow y=3x$$, then $$R=$$
  • $$\left\{ \left( 3,1 \right) ,\left( 6,2 \right) ,\left( 8,2 \right) ,\left( 9,3 \right) \right\} $$
  • $$\left\{ \left( 3,1 \right) ,\left( 6,2 \right) ,\left( 9,3 \right) \right\} $$
  • $$\left\{ \left( 3,1 \right) ,\left( 2,6 \right) ,\left( 3,9 \right) \right\} $$
  • none of these
Let A and B be two sets such that $$A\times B=\left\{ \left( a,1 \right) ,\left( b,3 \right) ,\left( a,3 \right) ,\left( b,1 \right) ,\left( a,2 \right) ,\left( b,2 \right)  \right\} ,$$ then 
  • $$A=\left\{ 1,2,3 \right\} $$ and $$B=\left\{ a,b \right\} $$
  • $$A=\left\{ a,b \right\} $$ and$$ B=\left\{ 1,2,3 \right\} $$
  • $$A=\left\{ 1,2,3 \right\} $$ and $$B\subset \left\{ a,b \right\} $$
  • $$A\subset \left\{ a,b \right\} $$ and $$B\subset \left\{ 1,2,3 \right\} $$
A relation R is defined from {2,3,4,5} to {3,6,7,10} by XRY $$\Leftrightarrow $$ X is relatively prime to Y, then domain of R is 
  • {2,3,5}
  • {3,5}
  • {2,5}
  • {2,3,4,5}
If the cardinality of a set $$A$$ is $$4$$ and that of a set $$B$$ is $$3$$, then what is the cardinality of the set $$A\Delta B$$.
  • $$1$$
  • $$5$$
  • $$7$$
  • $$Cannot\ be\ determined$$
Let $$A$$ be set of first ten natural numbers and $$R$$ be a relation on A, defined by $$(x,y)\in R\Rightarrow x+2y=10$$, then domain of $$R$$ is 
  • {1, 2, 3, ......,10}
  • {2, 4, 6, 8}
  • {1, 2, 3, 4}
  • {2, 4, 6, 8, 10}
What type of a relation is "Less than" in the set of real numbers?
  • only symmertric
  • only transitive
  • only reflexive
  • equivalence relation
For real numbers x and y, define xRy if $$x-y+\sqrt{2}$$ is an irrational number. Then the relation R is?
  • Not Reflexive
  • Not Symmetric
  • Not Transitive
  • None of these
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