CBSE Questions for Class 11 Commerce Applied Mathematics Relations Quiz 15 - MCQExams.com

If $$R$$ is relation is "greater then or equal" from $$A=\left\{1,2,3,4\right\}$$ to $$B=\left\{4,5,6\right\}$$, then $$R^{-1}=$$
  • $$\left\{(4,4)\right\}$$
  • $$\phi$$
  • $$A\ x\ B$$
  • $$R$$
Which of the following is always true
  • $$(p\Longrightarrow q)\equiv \sim q\Longrightarrow \sim p$$
  • $$\sim (p\Longrightarrow q)\equiv p\ \wedge \sim q$$
  • $$\sim (p\ \vee q)\equiv \vee\ p\ \vee \sim q$$
  • $$\sim (p\ \vee q)\equiv \sim\ p\ \wedge \sim q$$
If $$A={a,b,c,d,e}$$, then the number of equivalence relations on $$A$$ is 
  • $$26$$
  • $$52$$
  • $$54$$
  • $$63$$
The relation $$R=\left\{(1, 1), (2, 2), (3, 3)\right\}$$ on the set $$\left\{1, 2, 3\right\}$$ is 
  • symmetric only
  • reflexive only
  • an equivalence relation
  • transistive only
The number of ordered pairs (x, y) of natural numbers satisfy the equation $$x^2+y^2+2xy-2018x-2018y-2019^o=0$$ is?
  • $$0$$
  • $$1009$$
  • $$2018$$
  • $$2019$$
Let xyz =105 where x,y,z,then number of ordered triplets (x,y,z) satisfying the given equation
  • 15
  • 27
  • 6
  • 33
Let $$f:R\rightarrow R$$ be defined as 
$$f(x)={ x }^{ 3 }+{ 2x }^{ 2 }+4x+sin\left( \dfrac { \pi x }{ 2 }  \right) $$ and  $$g(x)$$be the inverse function of f(x), then $${ g }^{ ' }(8)$$is equal to :
  • $$\dfrac { 1 }{ 2 } $$
  • 9
  • $$\dfrac { 1 }{ 11 } $$
  • 11
Let $$N$$ be the set of all positive integers and $$\phi$$ be a relation on $$N\times \ N$$ defined by $$(a,b)\times (c,d)$$. If $$ad(b+c)=bc(a+d)$$ then $$\phi$$ is
  • symmetric only
  • reflexive only
  • transitive only
  • an equivalence relation
The total number of equivalence relations defined in the set $$S={a,b,c}$$ is 
  • $$5$$
  • $$3!$$
  • $$2^{3}$$
  • $$3^{3}$$
  • $$3^{2}$$
Let R be a relation over set N$$\times N$$defined by (a,b)R (c,d) if a + d = b + c then R is ...... ( Here N is the set of all natural numbers)
  • Reflexive only
  • Symmetric only
  • Transitive only
  • Equivalence relation
The minimum number of elements that must be added to the relation $$R=\{(1, 2), (2, 3)\}$$ on the set $$\{1, 2, 3\}$$ so that it is an equivalence relation.
  • $$3$$
  • $$4$$
  • $$7$$
  • $$6$$
The relation $$\bot $$ is
  • Reflective
  • Symmetric
  • Transitive
  • Equivalence
A relation $$R_1$$ is defined set $$A={1,2,3}$$ such that $$R_1\equiv {(1,1),(2,2),(2,3),(3,2)}$$, then minimum number of elements required in $$R_1$$ so that $$R_1$$ becomes R which in an equivalence relation is
  • $$5$$
  • $$3$$
  • $$1$$
  • $$0$$
$$\sim  ( p \leftrightarrow \sim  q )$$  is a tautology.
  • True
  • False
 $$R={(1, 2), (2,3),(3 4)}$$ be a relation on the set of natural numbers. Then the last number of elements that must be included inn R to get a new relation S where S is an equivalence relation, is 
  • 5
  • 7
  • 9
  • 11
If $$k\ \epsilon\ R^+$$ and the middle term of $$(\dfrac{k}{2} + 2)^8$$ is $$1120$$, then value of k is
  • $$3$$
  • $$2$$
  • $$1$$
  • $$4$$
If a relation R is defined on the set Z of integers as follows : (a,b) $$\epsilon \quad R\Leftrightarrow { a }^{ 2 }+{ b }^{ 2 }=25,$$ , Then domain (R)= 
  • {3,4,5}
  • {0,3,4,5}
  • {0,$$\pm $$3, $$\pm $$4, $$\pm $$5}
  • {3,4}
Let A={1,2,3} and R={(1,1),(2,2),(1,2),(2,1),(1,3)}, then R is
  • Reflexive
  • Symmetric
  • Transitive
  • None of these
Let $$R_1$$ and $$R_2$$ be equivalence relations on a set A, the $$R_1 \cup R_2$$ may or may not be
  • Reflexive
  • Symmetric
  • Transitive
  • Cannot say anything
Let $$A=\left\{ 1,2,3 \right\} ,\quad B=\left\{ 1,3,5 \right\} .$$ If relation R from A to B is given by $$R=\left\{ \left( 1,3 \right) ,\left( 2,5 \right) ,\left( 3,3 \right)  \right\} .\quad Then\quad { R }^{ 1 }\quad is$$
  • $$\left\{ \left( 3,3 \right) ,\left( 3,1 \right) ,\left( 5,2 \right) \right\} $$
  • $$\left\{ \left( 1,2 \right) ,\left( 2,5 \right) ,\left( 3,3 \right) \right\} $$
  • $$\left\{ \left( 1,3 \right) ,\left( 5,2 \right) \right\} $$
  • None of these
If n(A)=5 then number of relation on 'A' is:
  • $${ 2 }^{ 5 }$$
  • $${ 2 }^{ 25 }$$
  • $${ 5 }^{ 2 }$$
  • none
Consider the set $$A = \{ ( 1,2,3 ) \}$$ and the relation $$R = \{ ( 1,2 ) , ( 1,3 ) \}$$ then $$R$$ is
  • Reflexive
  • Transitive
  • Symmetric
  • Equivalence
If $$A=\{ a,b,c\}$$ then relation $$R=\left\{ \left( b,c \right)  \right\}$$ on A  is 
  • reflexive only
  • symmetric only
  • transitive only
  • reflexive and transitive only
For real numbers x and y, we write $$xRy\Leftrightarrow { x }^{ 2 }-{ y }^{ 2 }+\sqrt { 3 } $$ is an irrational number, then the relation R is
  • Reflexive
  • Symmetric
  • Transitive
  • Equivalence
The number of equivalence relations that can be defined on a set {a,b,c}, is
  • 3
  • 5
  • 7
  • 8
Consider the set $$A=(1, 2, 3)$$ and the R be the smallest equivalence relation on R then R is
  • $${(1, 1), (2, 2), (3,3)}$$
  • $${(1,1), (2 ,2), (3, 3), (1, 2), (2, 1)}$$
  • $${(1, 1,(2 ,2), (3, 3), (1, 2), (2, 1), (1, 3), (3, 1), (2, 3), (3, 2)}$$
  • None of these
The relation $$R=\left\{ \left( 1,1 \right) ,\left( 2,2 \right) ,\left( 3,3 \right)  \right\} $$ on the set $$\left\{ 1,2,3 \right\} $$ is
  • symmetric only
  • reflexive only
  • transitive only
  • an equivalence relation
If $  A  $ is a finite set containing n distinct elements, then the number of relations on A is equal to
  • $$ 2^{n} $$
  • $$ 2^{n^{2}} $$
  • $$ 2^{2} $$
  • none of these
If R is an equivalence relation on a set A, then $$R^1$$ is 
  • reflexive only
  • symmetric but not transitive
  • equivalence
  • transitive
Let  $$N$$  denotes the set of all natural numbers and  $$R$$  be the relation on  $$N \times N$$  defined by  $$( a , b ) R ( c , d )$$ iff  $$a d ( b + c ) = b c ( a + d ) ,$$  then  $$R$$  is
  • symmetric only
  • reflexive only
  • transitive only
  • an equivalence relation
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers