CBSE Questions for Class 11 Commerce Applied Mathematics Relations Quiz 4 - MCQExams.com

The number of relations from $$ A=\left \{ 1,2,3 \right \} $$ to $$B = \left \{ 4,6,8,10 \right \}$$ is
  • $$4^{3}$$
  • $$2^{7}$$
  • $$ 2^{12}$$
  • $$3^{4}$$
The range of the function $$f(x)=\dfrac{\sin(\pi [x])}{x^{2}+1}$$ (where $$[.]$$ denotes greatest integer function) is
  • $$\{0\}$$
  • $$R$$
  • $$(0,1)$$
  • $$(0,\infty )$$
Which of the following are not equivalence relations on $$I$$?
  • $$aRb$$ if $$a + b$$ is an even integer
  • $$aRb$$ if $$a - b$$ is an even integer
  • $$aRb$$ if $$a < b$$
  • $$aRb$$ if $$a = b$$
Which one of the following is an elementary symmetric function of  $$x_{1},x_{2},x_{3},x_{4}$$.
  • $$x_{1}x_{2}x_{3}+x_{2}x_{3}x_{4}$$
  • $$x_{1}x_{2}+x_{2}x_{3}+x_{3}x_{1}$$
  • $$x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}$$
  • $$x_{1}x_{2}+x_{1}x_{3}+x_{1}x_{4}+x_{2}x_{3}+x_{2}x_{4}+x_{3}x_{4}$$
The solution of $$8x\equiv 6(mod \  14) $$ is
  • $$\{8, 6\}$$
  • $$\{6,14\}$$
  • $$\{6,13\}$$
  • $$\{8,14,6\}$$
If relation R$$=\left \{ (x,  x+2)  :  x  \in  N, 1 \leq  x <4 \right \}$$ then R is
  • $$\{(1, 3), (2, 4), (3, 5)\}$$
  • $$\{(2, 3), (4,2), (5, 3)\}$$
  • $$\{(1, 3), (2, 4), (3, 5), (4, 6)\}$$
  • none of these
The minimum number of elements that must be added to the relation $$R=\{(1,2,),(2,3)\} $$ on the set of natural numbers so that it is an equivalence is
  • $$4$$
  • $$7$$
  • $$6$$
  • $$5$$
If $$R$$ is the relation 'less than' from $$A=\{1, 2, 3, 4, 5\}$$ to $$B=\{1, 4\}$$, the set of ordered pairs corresponding to $$R$$, then the inverse of $$R$$ is
  • $$\{(3, 1), (3, 2), (3, 3)\}$$
  • $$\{(4, 1), (4, 2), (4, 3)\}$$
  • $$\{(4, 3), (4, 4), (4, 5)\}$$
  • $$\{(1, 3), (2, 4), (3, 5)\}$$
If $$A =\{1,2,3\}$$, $$B=\{1,4,6,9\}$$ and $$R$$ is a relation from $$A$$ to $$B$$ defined by '$$x$$ is greater than $$y$$'. The range of $$R$$ is
  • $$\{1, 4, 6, 9\}$$
  • $$\{4, 6, 9\}$$
  • $$\{1\}$$
  • $$\{4, 6\}$$
Let $$R = \{(2,3),(3, 4)\}$$ be relation defined on the set of natural numbers. The minimum number of ordered pairs required to be added in $$R$$ so that enlarged relation becomes an equivalence relation is
  • $$3$$
  • $$5$$
  • $$7$$
  • $$9$$
If $$A$$ is the set of even natural numbers less than $$8$$ and $$B$$ is the set of prime numbers less than $$7$$, then the number of relations from $$A$$ to $$B$$ is
  • $$2^{9}$$
  • $$9^{2}$$
  • $$3^{2}$$
  • $$2^{9}-1$$
If $$A=\left\{ 1,2,3 \right\} , B=\left\{ 1,4,6,9 \right\} $$ and $$R$$ is a relation from $$A$$ to $$B$$ defined by '$$x$$ is greater than $$y$$'. Then range of $$R$$ is
  • $$\left\{ 1,4,6,9 \right\} $$
  • $$\left\{ 4,6,9 \right\} $$
  • $$\left\{ 1 \right\} $$
  • None of these
If $$ X =\{1, 2,3,4,5\} $$ and $$Y =\{1,3,5,7,9\}$$, determine which of the following sets represent a relation and also a mapping?
  • $$R_{1}= \{(x,y)$$:$$ y=x+2, x \in Y,y \in Y\}$$
  • $$R_{2}=\{(1,1), (1,3), (3,5), (4,7), (5,9)\}$$
  • $$R_{3}=\{(1,1), (2,3), (3,5), (3,7), (5,7)\}$$
  • $$R_{4}=\{(1,3), (2,5), (4,7), (5,9), (3,1)\}$$
If A $$=$${$$x : x^{2}-3x+2= 0$$}, and $$R$$ is a universal relation on $$A$$, then $$R$$ is
  • $$\{(1,1),(2, 2)\}$$
  • $$\{(1,1)\}$$
  • $$\phi $$
  • $$\{(1,1),(1, 2)(2,1),(2,2)\}$$
If $$A=\{b,c,d\}$$ and $$B=\{x,y\}$$. Find which of the following are elements of $$A \times A$$.
  • $$\{b,b\}$$
  • $$\{b,c\}$$
  • $$\{b,d\}$$
  • All of the above
n(A)=m and n(B)=n ; then

  • n(A)+n(B)=n(A+B)
  • n(A)-n(B)=n(A+B)
  • A$$\times$$B=mn
  • n(A) $$\times$$n(B =n(A $$\times$$B)
Suppose $$S=\{1,2\}$$  and $$T=\{a,b\}$$  then $$T \times S$$
  • $$(a,1),(a,2),(b,1),(b,2)$$
    B×A={(a,1),(a,2),(b,1),(b,2)}
  • $$(1,a),(2,b),(b,1),(b,2)$$
  • $$(a,1),(a,2),(1,b),(2,b)$$
  • None of the above
Given $$A=\{b,c,d\}$$ and  $$B=\{x,y\}$$ : find element of  $$A\times B$$ .
  • $$\{b,x\}$$
  • $$\{b,y\}$$
  • $$\{c,x\}$$
  • All of the above
Given M={0,1,2} and N={1,2,3}, then (M $$\cup$$ N) $$\times$$(M-N) contains
  • $$\{0,0\}$$
  • $$\{1,0\}$$
  • $$\{2,0\}$$
  • $$\{3,0\}$$
$$\left (A \cap B  \right ) \times C$$

  • $$\left (A \times B \right ) \cap \left (B \times C \right )$$
  • $$\left (A \times C \right ) \cap \left (B \times C \right )$$
  • $$\left (A \times B \right ) \cup \left (B \times C \right )$$
  • $$\left (A \times B \right ) \cup \left (A \times C \right )$$
$$M={0,1,2}$$ and $$N={1,2,3}$$: find (N-M) $$\times$$(N $$\cap$$M)
  • $$\{3,1\}$$
  • $$\{3,2\}$$
  • $$\{3,3\}$$
  • None of the above
Given $$M=\{5,6,7\}$$ and $$N=\{6,8,10\}$$ find element of $$(M\cup N)\times N$$
  • $$\{5,6\}$$
  • $$\{5,8\}$$
  • $$\{5,10\}$$
  • All of the above
$$n(A)=4 $$ and  $$n(B) =5$$: $$n(A \times B)=$$
  • $$20$$
  • $$10$$
  • $$30$$
  • None of the above
n (A $$\times$$ B) =
  • n(A) x n(B)
  • n(A $$\bigcap$$ B)
  • n(A $$\bigcup$$ B)
  • all of these
Which one of the statement is false ?
  • $$\phi \times A = \phi$$
  • A $$\times$$ B = B $$\times$$ A
  • A $$\times$$ B = {(x $$\times$$ y) : x A and y B}
  • $$R^{-1}$$ = {(y, x) : (x, y) R}
A $$\times$$ (B - C) =
  • $$(A \times B) - (A \times C)$$
  • $$(A \times C) - (A \times B)$$
  • $$(A \times B) \bigcup (A \times C)$$
  • $$(A \times B) \bigcap (A \times C)$$
R is a relation in A and (a, b) $$\notin$$ r, implies (b, a) $$\notin$$ R then R is said to be ____ relation
  • symmetric
  • contradictory
  • skew symmetric
  • none of these
The minimum number of elements that must be added to the relation $$R=\left \{ (1, 2),(2, 3) \right \}$$ on the set of natural numbers, so that it is an equivalence is:
  • $$4$$
  • $$7$$
  • $$6$$
  • $$5$$
Let $$A=R-\left\{3\right\},B=R-\left\{1\right\} $$ and $$f:A \rightarrow B $$ defined by $$ f(x)\displaystyle =\frac{x-2}{x-3}$$ Is $$f$$ bijective ? 
If yes enter 1 else enter 0
  • True
  • False
If A $$=$$ {1, 2}, B $$=$$ {3, 4}, then A$$\times$$B $$=$$
  • {(1, 3), (1, 4), (2, 3), (2, 4)}
  • {(1, 1), (2, 2), (3, 3), (4, 4)}
  • {(4, 1), (3, 1), (4, 2), (3, 2)}
  • All the above
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