CBSE Questions for Class 11 Commerce Applied Mathematics Relations Quiz 2 - MCQExams.com

Let the number of elements of the sets $$A$$ and $$B$$ be $$p$$ and $$q$$ respectively. Then, the number of relations from the set $$A$$ to the set $$B$$ is
  • $${ 2 }^{ p+q }$$
  • $${ 2 }^{ pq }$$
  • $$p+q$$
  • $$pq$$
Find the second component of an ordered pair $$(2, -3)$$
  • $$2$$
  • $$3$$
  • $$0$$
  • $$-3$$
A ______ maps elements of one set to another set.
  • order
  • set
  • relation
  • function
The ______ product of two sets is the set of all possible ordered pairs whose first component is a member of the first set and whose second component is a member of the second set.
  • cartesian
  • coordinate
  • simple
  • discrete
Identify the first component of an ordered pair $$(2, 1)$$.
  • $$1$$
  • $$2$$
  • $$-1$$
  • $$0$$
Cartesian product of sets $$A$$ and $$B$$ is denoted by _______.
  • $$A \times B$$
  • $$B \times A$$
  • $$A \times A$$
  • $$B \times B$$
What is the relation for the statement "A is taller than B"?
  • is taller than
  • A is taller
  • B is taller
  • is less than
Identify the first component of an ordered pair $$(0, -1) $$.
  • $$0$$
  • $$-1$$
  • $$2$$
  • $$1$$
If $$A = \{1, 2, 3\}, B = \{3, 4\}$$
find (A $$\times$$ B) $$\cup$$ (B $$\times$$ A)
  •  $$\{(1, 3), (2, 3), (3, 3), (1, 4), (2, 4), (3, 4), (3, 1), (4, 1), (3, 2), (4, 2), (4, 3)\}$$
  •  $$\{(2, 3), (3, 3), (1, 4), (2, 4), (3, 4), (3, 1), (4, 1), (3, 2), (4, 2), (4, 3)\}$$
  •  $$\{(1, 3), (2, 3), (3, 3), (1, 4), (2, 4), (3, 4), (3, 1), (4, 1), (4, 2), (4, 3)\}$$
  • None of these
If A= {0, 1} and B ={1, 0}, then what is A x B equal to ?
  • {(0, 1), (1, 0)}
  • {(0, 0), (1, 1)}
  • {(0, 1), (1, 0), (1, I)}
  • A X A
If $$A = \{a, b\}, B=\{1, 2, 3\}$$, find B $$\times$$ A
  • $$B$$ $$\times$$ $$A$$$$ = \{(1, a), (2, a), (3, a), (1, b) (2, b), (3, b)\}$$
  • $$B$$ $$\times$$ $$A$$$$ = \{ (2, a), (3, a), (1, b) (2, b), (3, b)\}$$
  • $$B$$ $$\times$$ $$A$$$$ = \{(1, a), (2, a), (3, a), (1, b) (2, b)\}$$
  • None of these
Let R be the set of real numbers and the mapping $$f:R\rightarrow R$$ and $$g:R\rightarrow R$$ be defined by $$f(x)=5-x^2$$ and $$g(x)=3\lambda-4$$, then the value of $$(fog)(-1)$$ is
  • $$-44$$
  • $$-54$$
  • $$-32$$
  • $$-64$$
Let $$A = \left \{x, y, z\right \}$$ and $$B = \left \{p, q, r, s\right \}$$. What is the number of distinct relations from $$B$$ to $$A$$?
  • $$4096$$
  • $$4094$$
  • $$128$$
  • $$126$$
Let R be the relation in the set N given by = {(a, b): a = b - 2, b > 6}. Choose the correct answer
  • $$(2, 4) \epsilon R$$
  • $$(3, 8) \epsilon R$$
  • $$(6, 8) \epsilon R$$
  • $$(8, 7) \epsilon R$$
Let $$A=\left\{ u,v,w,z \right\} ;B=\left\{ 3,5 \right\} $$, then the number of relations from $$A$$ to $$B$$ is
  • $$256$$
  • $$1024$$
  • $$512$$
  • $$64$$
Let A be a finite set containing n distinct elements. The number of relations that can be defined on A is.
  • $$2^n$$
  • $$n^2$$
  • $$2n^2$$
  • $$2n$$
On the set $$N$$ of all natural numbers define the relation $$R$$ by $$a R b$$ if and only if the G.C.D. of $$a$$ and $$b$$ is $$2$$. Then $$R$$ is:
  • Reflexive, but not symmetric
  • Symmetric only
  • Reflexive and transitive
  • Reflexive, symmetric and transitive
Consider two sets $$A=\{a, b, c\}, B=\{e, f\}$$. If maximum numbers of total relations from A to B; symmetric relation from A to A and from B to B are $$l, m, n$$ respectively, then the value of $$2l+m-n$$ is
  • $$212$$
  • $$184$$
  • $$240$$
  • $$64$$
The number of reflexive relation in set A = {a, b, c} is equal to
  • $$2^9$$
  • $$2^4$$
  • $$2^7$$
  • $$2^6$$
If the relation is defined on $$R-\left\{ 0 \right\} $$ by $$\left( x,y \right) \in S\Leftrightarrow xy>0$$, then $$S$$ is ________
  • an equivalence relation
  • symmetric only
  • reflexive only
  • transitive only
If $$A=\left\{2,4\right\}$$ and $$B=\left\{3,4,5\right\},$$ then
$$\left( A\cap B \right) \times \left( A\cup B \right)$$ is
  • $$\left\{(2,2),(3,4),(4,2),(5,4)\right\}$$
  • $$\left\{(2,3),(4,3),(4,5)\right\}$$
  • $$\left\{(2,4),(3,4),(4,4),(4,5)\right\}$$
  • $$\left\{(4,2),(4,3),(4,4),(4,5)\right\}$$
Let $$A=\left\{1,2,3,4,5\right\}, B=\left\{2,3,6,7\right\}.$$ Then the number of elements in $$\left( A\times B \right) \cap \left( B\times A \right)$$ is
  • $$18$$
  • $$6$$
  • $$4$$
  • $$0$$
Let A={ 1, 2, 3, 4} and R= {( 2, 2), (3, 3), (4, 4), (1, 2)} be a relation on A. Then R is
  • Reflexive
  • Symmetric
  • Transitive
  • None of these
If A = (a, b, c, d), B= (p, q, r, s). then which of the following are relations from A to B? Give reasons for your answer:
  • $$R_1$$ = {( a, p), (b, r), (c, s)}
  • $$R_2$$ = { ( q, b), (c, s), (d, r)}
  • $$R_3$$ = {(a, p), (a, q), (d, p), (c, r), (b, r)}
  • $$R_4$$ = {(a, p), (a, q), (b, s), (s, b)}
Given the relation R= {(1,2), (2,3) } on the set {1, 2, 3}, the minimum number of ordered pairs which when added to R make it an equivalence relation is 
  • 5
  • 6
  • 7
  • 8
The union of two equivalence relations is: 
  • always an equivalence relation
  • reflexive and symmetric but needn't be transitive
  • reflexive and transitive but need not be symmetric
  • None of these
Let R be a relation from a set A to a set B then 
  • $$R = A \cup B$$
  • $$ R = A \cap B$$
  • $$ R \subseteq A\times B$$
  • $$ R\subseteq B\times A$$
If $$n(A) = 2, n(B) = m$$ and the number of relation from $$A$$ to $$B$$ is $$64$$, then the value of $$m$$ is
  • $$6$$
  • $$3$$
  • $$16$$
  • $$8$$
If $$A$$ and $$B$$ are two sets containing four and two elements, respectively. Then the number of subsets of the set $$A\times B$$ each having at least three elements is
  • $$219$$
  • $$256$$
  • $$275$$
  • $$510$$
Find x and y, if $$(x+3,5)=(6,2x+y)$$.
  • x=3, y=-1
  • x=6, y=2
  • x=2,y=3
  • none of these
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