CBSE Questions for Class 11 Commerce Applied Mathematics Relations Quiz 5 - MCQExams.com

If $$ABC\sim PQR$$, then AB:PQ =
  • $$AC:PB$$
  • $$AC:PR$$
  • $$AB:PR$$
  • $$AC:RQ$$
Let $$A=\left \{ 1, 2, 3 \right \}$$. Then number of equivalence relations containing (1, 2) is:
  • 1
  • 2
  • 3
  • 4
Let A and B be finite sets containing m and n elements respectively. The number of relations that can be defined from A and B is:
  • mn
  • $$2^{mn}$$
  • $$2^{m+n}$$
  • $$n^{m}$$
Which of the following are not equivalence relations on I?
  • a R b if $$a+b$$ is an even integer
  • a R b if $$a-b$$ is an even integer
  • a R b if $$a< b$$
  • a R b if $$a= b$$
If $$X=\left \{ 1, 2, 3, 4, 5 \right \}$$ and $$Y=\left \{ 1, 3, 5, 7, 9 \right \}$$, determine which of the following sets represent a relation and also a mapping.
  • $$R_{1}=\left \{ (x, y):y=x+2, x\in X, y\in Y \right \}$$
  • $$R_{2}=\left \{ (1, 1),(2, 1),(3, 3),(4, 3),(5, 5) \right \}$$
  • $$R_{3}=\left \{ (1, 1),(1, 3),(3, 5),(3, 7),(5, 7) \right \}$$
  • $$R_{4}=\left \{ (1, 3),(2, 5),(4, 7),(5, 9),(3, 1) \right \}$$
Let R be a reflexive relation on a finite set A having n elements, and let there be m ordered pairs in R. Then:
  • $$m\geq n$$
  • $$m\leq n$$
  • $$m=n$$
  • $$m=-n$$
Let A be a finite set containing n distinct elements. The number of relations that can be defined on A is:
  • $$2^{n}$$
  • $$n^{2}$$
  • $$2^{n^{2}}$$
  • 2n
Let $$A=\left \{ 1, 2, 3 \right \}$$. Which of the following is not an equivalence relation on A?
  • $$\left \{ (1, 1),(2, 2),(3, 3) \right \}$$
  • $$\left \{ (1, 1),(2, 2),(3, 3),(1, 2),(2, 1) \right \}$$
  • $$\left \{ (1, 1),(2, 2),(3, 3),(2, 3),(3, 2) \right \}$$
  • $$\left \{ (1, 1),(2, 1) \right \}$$
"Every reflexive relation is an anti-symmetric relation", Is it true?
  • True
  • False
The relation "congruence modulo $$m$$" is:
  • reflexive only
  • symmetric only
  • transitive only
  • an equivalence relation
Let R be the relation in the set N given by $$=\left \{ (a, b):a=b-2, b >6 \right \}$$. Choose the correct answer.
  • $$(2, 4)\in R$$
  • $$(3, 8)\in R$$
  • $$(6, 8)\in R$$
  • $$(8, 7)\in R$$
Find the number of relations from $$\left \{ m, o, t, h, e, r \right \}$$ to $$\left \{ c, h, i, l, d \right \}$$
  • $$30$$
  • $$30^{2}$$
  • $$2^{30}$$
  • $$60$$
Which of the following statements is true?
  • The x-axis is a vertical line
  • The y-axis is a horizontal line
  • The scale on both axes must be the same in a Cartesian plane
  • The point of intersection between the x-axis and the y-axis is called the origin
If $$R$$ is a relation from a set $$A$$ to a set $$B$$ and $$S$$ is a relation from $$B$$ to a set $$C$$, then the relation $$SOR$$
  • is from $$A$$ to $$C$$
  • is from $$C$$ to $$A$$
  • does not exist
  • none of these
Let $$A=\left \{ 1,2,3 \right \}$$. The total number of distinct relations that can be defined over $$A$$ is:
  • $$2^{9}$$
  • $$6$$
  • $$8$$
  • None of the above
Let $$X=\{1, 2, 3, 4, 5 \} $$ and $$Y=\{1, 3, 5, 7, 9\}$$ . Which of the following is/are relations from $$X$$ to $$Y$$?
  • $$R_1=\{(x, y):y=2+x, x\in X,y\in Y\}$$
  • $$R_2=\{(1, 1), (2, 1), (3, 3), (4, 3), (5, 5)\}$$
  • $$R_3=\{(1, 1), (1, 3), (3, 5), (3, 7), (5, 7)\}$$
  • $$R_4=\{(1, 3), (2, 5), (2, 4), (7, 9)\}$$
Let $$R=\{(1, 3), (2, 2), (3, 2)\}$$ and $$S=\{(2, 1), (3, 2), (2, 3)\}$$ be two relations on set $$A=\{1, 2, 3\}$$.Then $$R$$o$$S$$ is equal
  • $$\{(2, 3), (3, 2), (2, 2)\}$$
  • $$\{(1, 3), (2, 2), (3, 2), (2 ,1), (2, 3)\}$$
  • $$\{(3, 2), (1, 3)\}$$
  • $$\{(2, 3), (3, 2)\}$$
Give a relation R={(1,2), (2,3)} on the set of natural numbers, add a minimum number of ordered pairs.  
  • enlarged relation is symmetric
  • enlarged relation is transitive
  • enlarged relation is reflexive.
  • enlarged relation is equivalence relation
If $$A=\{1, 2, 3\}$$ and $$B=\{3, 8\}$$, then $$(A\cup B)\times (A\cap B)$$ is
  • $$\{(3, 1), (3, 2), (3, 3), (3, 8)\}$$
  • $$\{(1, 3), (2, 3), (3, 3), (8, 3)\}$$
  • $$\{(1, 2), (2, 2), (3, 3), (8, 8)\}$$
  • $$\{(8, 3), (8, 2), (8, 1), (8, 8)\}$$
If $$\displaystyle :n(A)= m, $$ then number of relations in $$A$$ are
  • $$\displaystyle 2^{m}$$
  • $$\displaystyle 2^{m}-2 $$
  • $$\displaystyle 2^{m^{2}} $$
  • None of these
If $$\displaystyle X= \left \{ 1,2,3,4,5 \right \}$$ and $$\displaystyle Y= \left \{ 1,3,5,7,9 \right \}$$ then which of the following sets are relation from $$X$$ to $$Y$$
  • $$\displaystyle R_{1}= \left \{ (x,a):a= x+2,x\in X,a\in Y \right \} $$
  • $$\displaystyle R_{2}= \left \{ (1,1),(2,1),(3,3),(4,3),(5,5) \right \} $$
  • $$\displaystyle R_{3}= \left \{ (1,1),(1,3),(3,5),(3,7),(5,7) \right \} $$
  • $$\displaystyle R_{4}= \left \{ (1,3),(2,5),(4,7),(5,9),(3,1) \right \} $$
In order that a relation $$R$$ defined on a non-empty set $$A$$ is an equivalence relation.
It is sufficient, if $$R$$
  • is reflexive
  • is symmetric
  • is transitive
  • possesses all the above three properties.
Let $$ A= \{ 1,2,3,.......50\} $$ and $$B=\{2,4,6.......100\}$$ .The number of elements $$\left ( x, y \right )\in A\times B$$ such that $$x+y=50$$
  • $$24$$
  • $$25$$
  • $$50$$
  • $$75$$
Let $$\displaystyle A=  \left \{ a,b,c \right \} $$ and $$\displaystyle B=  \left \{ 4,5 \right \} $$ Consider a relation $$R$$ defined from set $$A$$ to set $$B$$ then $$R$$ is subset of
  • $$A$$
  • $$B$$
  • $$\displaystyle A\times B $$
  • $$\displaystyle B\times A $$
If $$A = \{5, 7\}, B= \{7, 9\}$$ and $$C = \{7, 9, 11\},$$ find $$(A \times B) \cup (A \times C)$$
  • $$\{(5, 7), (9, 9), (5, 11), (7, 7), (7, 9), (7,11)\}$$
  • $$\{(5, 7), (5, 9), (5, 11), (7, 7), (7, 9), (7,11)\}$$
  • $$\{(5, 5), (5, 9), (5, 11), (7, 7), (7, 9), (7,11)\}$$
  • none of these
Let $$A=\left \{ 1,2,3 \right \}$$ and $$B=\left \{ a,b \right \}$$.Which of the following subsets of $$A\times B$$ is a mapping from $$A$$ to $$B$$
  • $$\left \{ \left ( 1,a \right ),\left ( 3,b \right ),\left ( 2,a \right ),\left ( 2,b \right ) \right \}$$
  • $$\left \{ \left ( 1,b \right ),\left ( 2,a \right ),\left ( 3,a \right ) \right \}$$
  • $$\left \{ \left ( 1,a \right ),\left ( 2,b \right ) \right \}$$
  • none of these
If $$A=\{2, 4\}$$ and $$B=\{3, 4, 5\}$$ then $$(A\cap B)\times (A\cup B)$$ is
  • $$\{(2, 2), (3, 4), (4, 2), (5, 4)\}$$
  • $$\{(2, 3), (4, 3), (4, 5)\}$$
  • $$\{(2, 4), (3, 4), (4, 4), (4, 5)\}$$
  • $$\{(4, 2), (4, 3), (4, 4), (4, 5)\}$$
If $$R$$ is an anti symmetric relation in $$\displaystyle A$$ such that $$(a,b),(b,a)\:\in\: R$$ then
  • $$\displaystyle a\leq b$$
  • $$\displaystyle a= b$$
  • $$\displaystyle a\geq b$$
  • None of these
$$R$$ is a relation from $$\displaystyle \left \{ 11,12,13 \right \}$$ to $$\displaystyle \left \{ 8,10,12 \right \}$$ defined by $$y=x-3$$ then the $$R^{-1}$$ .
  • $$\displaystyle \left \{ (11,8),(13,10) \right \}$$
  • $$\displaystyle \left \{ (8,11),(10,13) \right \}$$
  • $$\displaystyle \left \{ (8,11),(9,12),(10,13) \right \}$$
  • $$None\ of\ these$$
Let $$A$$ and $$B$$ be two finite sets having $$m$$ and $$n$$ elements respectively. Then the total number of mapping from $$A$$ to $$B$$ is
  • $$mn$$
  • $$\displaystyle 2^{mn}$$
  • $$\displaystyle m^{n}$$
  • $$\displaystyle n^{m}$$
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