CBSE Questions for Class 11 Commerce Applied Mathematics Relations Quiz 7 - MCQExams.com

Let $$X=\left\{ 1,2,3,4 \right\} $$ and $$Y=\left\{ 1,2,3,4 \right\} $$. Which of the following is a relation from $$X$$ to $$Y$$.
  • $${R}_{1}=\left\{ (x,y)| y=2+x, x\in X, y\in Y \right\} $$
  • $${R}_{2}=\left\{ (1,1),(2,1),(3,3),(4,3),(5,5) \right\} $$
  • $${R}_{3}=\left\{ (1,1),(1,3),(3,5),(3,7),(5,7) \right\} $$
  • $${R}_{4}=\left\{ (1,3),(2,5),(2,4),(7,9) \right\} $$
Let $$L$$ be the set of all straight lines in the Euclidean plane. Two lines $${l}_{1}$$ and $${l}_{2}$$ are said to be related by the relation $$R$$ if $${l}_{1}$$ is parallel to $${l}_{2}$$. Then the relation $$R$$ is-
  • Reflexive
  • Symmetric
  • Transitive
  • Equivalence
Let $$g\left( x \right)=1+x-\left[ x \right] $$ and $$f\left( x \right)=\begin{cases} \begin{matrix} -1 & x<0 \end{matrix} \\ \begin{matrix} 0 & x=0 \end{matrix} \\ \begin{matrix} 1 & x>0 \end{matrix} \end{cases}$$. Then for all $$x,f\left[ g\left( x \right) \right] $$ is equal to
  • $$x$$
  • $$1$$
  • $$f(x)$$
  • $$g(x)$$
If $$A = \left\{1,2,3\right\}$$, $$B = \left\{1,4,6,9\right\}$$ and $$R$$ is 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
 from the given statement $$N$$ denotes the natural number and $$W$$ denotes the whole number, so which statement in the following is correct
  • N=W
  • N $$\subset$$ W
  • W $$\subset$$ N
  • N $$\cong$$ W
Which one of the following relations on $$R$$ is equivalence relation
  • $$x \space R_1 \space y \Leftrightarrow |x| = |y|$$
  • $$x \space R_2 \space y \Leftrightarrow x \ge y$$
  • $$x \space R_3 \space y \Leftrightarrow x | y$$
  • $$x \space R_4 \space y \Leftrightarrow x < y$$
Given the relation $$R = \left\{(1,2), (2,3)\right\}$$ on the set $$A = \left\{1,2,3\right\}$$, the minimum number of ordered pairs which when added to $$R$$ make it an equivalence relation is
  • $$5$$
  • $$6$$
  • $$7$$
  • $$8$$
$$A$$ and $$B$$ are two sets having $$3$$ and $$4$$ elements respectively and having $$2$$ elements in common. The number of relations which can be defined from $$A$$ to $$B$$ is
  • $$2^5$$
  • $$2^{10} - 1$$
  • $$2^{12} - 1$$
  • $$none\ of\ these$$
If $$A = \left\{2,3\right\}$$ and $$B = \left\{1,2\right\}$$, then $$A \times B$$ is equal to 
  • $$\left\{(2,1), (2,2), (3,1), (3,2)\right\}$$
  • $$\left\{(1,2), (1,3), (2,2), (2,3)\right\}$$
  • $$\left\{(2,1), (3,2)\right\}$$
  • $$\left\{(1,2), (2,3)\right\}$$
Let $$X = \left\{1,2,3,4\right\}$$ and $$Y = \left\{1,3,5,7,9\right\}$$. Which of the following is relations from $$X$$ to $$Y$$
  • $$R_1 = \left\{(x,y) | y = 2x+1, x \in X, y \in Y\right\}$$
  • $$R_2 = \left\{(1,1),(2,1),(3,3),(4,3),(5,5)\right\}$$
  • $$R_3 = \left\{(1,1),(1,3),(3,5),(3,7),(5,7)\right\}$$
  • $$R_4 = \left\{(1,3),(2,5), (2,4), (7,9)\right\}$$
If $$R$$ is a relation from a finite set $$A$$ having $$m$$ elements to a finite set $$B$$ having $$n$$ elements, then the number of relations from $$A$$ to $$B$$ is:
  • $$2^{mn}$$
  • $$2^{mn} - 1$$
  • $$2mn$$
  • $$m^n$$
The relation $$R$$ is defined in $$A = \left\{1,2,3\right\}$$ by $$a\ R$$ $$b$$ if $$|a^2 - b^2| \le 5$$. Which of the following is false?
  • $$R = \left\{(1,1), (2,2), (3,3), (2,1), (1,2), (2,3), (3,2)\right\}$$
  • $$R^{-1} = R$$
  • Domain of $$R = \left\{1,2,3\right\}$$
  • Range of $$R = \left\{5\right\}$$
If $$R = \{(x, y):3x + 2y = 15 \text{ and }x\,, y\,\in \, N\}$$, the range of the relation R is .........
  • $$\{1, 2\}$$
  • $$\{1, 2,..., 5\}$$
  • $$\{1, 2,..., 7\}$$
  • $$\{3, 6\}$$
Let $$n(A) = n$$. Then the number of all relations on $$A$$ is
  • $$\displaystyle 2^{n}$$
  • $$\displaystyle 2^{\left ( n \right )!}$$
  • $$\displaystyle 2^{n^{2}}$$
  • none
If $$R$$ is an equivalence relation in a set $$A$$, then $$R^{-1}$$ is
  • Reflexive but not symmetric
  • Symmetric but not transitive
  • An equivalence relation
  • None of these
If $$\displaystyle A=\left\{ 2,4,5 \right\} ,B=\left\{ 7,8,9 \right\} $$ then $$\displaystyle n\left( A \times B \right) $$ is equal to
  • $$6$$
  • $$9$$
  • $$3$$
  • $$0$$
If $$(3p+q,p-q)=(p-q,3p+q)$$, then:
  • $$p=q=0$$
  • $$p=q$$
  • $$p=2q$$
  • $$p+q=0$$
Let $$A = \left\{p,q,r\right\}$$. Which of the following is an equivalence relation in $$A$$?
  • $$R_1 = \left\{(p,q), (q,r), (p,r), (p,p)\right\}$$
  • $$R_2 = \left\{(r,q), (r,p), (r,r), (q,q)\right\}$$
  • $$R_3 = \left\{(p,p), (q,q), (r,r), (p,q)\right\}$$
  • None of these
If $$A = \{1, 2 \}$$ and $$B = \{3, 4\}$$ then find $$A \times B$$
  • $$A \times B = \{(1,3),(1,2),(2,3),(2,4)\}$$
  • $$A \times B = \{(1,3),(1,4),(2,3),(2,4)\}$$
  • $$A \times B = \{(1,3),(1,4),(2,1),(2,4)\}$$
  • $$A \times B = \{(1,3),(1,4),(2,3),(2,1)\}$$
If $$\displaystyle R_{n}=\left \{ x:\frac{-1}{n}< x< \frac{1}{n} \right \}$$ then $$\displaystyle R_{5}\cup R_{15}=$$ ________
  • $$\displaystyle R_{5}$$
  • $$\displaystyle R_{15}$$
  • $$\displaystyle R_{3}$$
  • $$\displaystyle R_{20}$$
a R b if "a and b are animals in different zoological parks" then R is
  • only reflexive
  • only symmetric
  • only transitive
  • equivalence
R is a relation on set A then $$\displaystyle \left [ \left ( R^{-1} \right )^{-1} \right ]^{-1}$$ is_______
  • R
  • $$\displaystyle R^{-1}$$
  • $$\displaystyle A\times A$$
  • None of these
A relation which satisfies reflexive symmetric and transitive is ________ relation
  • an identity
  • a constant
  • an equivalence
  • None of these
The domain of the function f(x) = $$\displaystyle \frac{\left | x \right |-2}{\left | x \right |-3}$$ is ________
  • R
  • R - {2, 3}
  • R - {2, -2}
  • R - {-3, 3}
If $$\displaystyle R=R^{-1}$$ then the relation R is ________
  • reflexive
  • symmetric
  • anti-symmetric
  • transitive
Write the properties that the relation "is greter that" satisfies in the set of all positive integers
  • Reflexive
  • Symmetric
  • Antisymmetric
  • Transitive
If $$\displaystyle n\left ( A\times B \right )=36$$ then n(A) can possibly be____
  • $$7$$
  • $$8$$
  • $$9$$
  • $$10$$
The domain of the relation R = $$\displaystyle \left \{ \left ( x,y \right ):x,y\epsilon N \ and\ x+y\leq 3 \right \}$$ is____
  • {1,2,3}
  • {1,2}
  • {...-1,0,1,2,3}
  • None of these
The relation 'is a sister of' in the set of human beings is____
  • only transitive
  • only symmetric
  • equivalent
  • None of these
The relation 'is a factor of' on the set of natural numbers is not___________
  • reflective
  • symmetric
  • anti symmetric
  • transitive
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