CBSE Questions for Class 11 Commerce Applied Mathematics Relations Quiz 10 - MCQExams.com

Let $$n$$ be a fixed positive integer. Define a relation $$R$$ in the set $$Z$$ of integers by $$aRb$$ if and only if $$\dfrac {n}{a - b}$$. The relation $$R$$ is
  • Reflexive
  • Symmetric
  • Transitive
  • An equivalence relation
If two sets $$A$$ and $$B$$ are having $$39$$ elements in common, then the number of elements common to each of the sets $$A\times B$$ and $$B\times A$$ are
  • $${ 2 }^{ 39 }$$
  • $${ 39 }^{ 2 }$$
  • $$78$$
  • $$351$$
If $$f:R\rightarrow R,g\quad :R\rightarrow R$$ are defined by $$f\left( x \right) =5x-3,g(x)={ x }^{ 2 }+3,$$ then $$\left( { gof }^{ -1 } \right) \left( 3 \right) =$$
  • $$\frac { 25 }{ 3 }$$
  • $$\frac { 111 }{ 25 } $$
  • $$\frac { 9 }{ 25 } $$
  • $$\frac { 25 }{ 111 } $$
If $$\int\dfrac{2\cos x-\sin x+\lambda}{\cos x-\sin x-2}dx=A In\left|\cos x+\sin x-2\right|+Bx+C$$. Then the ordered triplet $$\left(A,B,\lambda\right)$$, is 
  • $$\left(\dfrac{1}{2},\dfrac{3}{2},-1\right)$$
  • $$\left(\dfrac{3}{2},\dfrac{1}{2},-1\right)$$
  • $$\left(\dfrac{1}{2},-1, \dfrac{3}{2}\right)$$
  • $$\left(\dfrac{3}{2},-1, \dfrac{1}{2}\right)$$
Let X be the set of all citizens of India. Elements x, y in X are said to be related if the difference of their age is 5 years. Which one of the following is correct ?
  • The relation is an equivalence relation on X.
  • The relation is symmetric but neither reflexive nor transitive.
  • The relation is reflexive but neither symmetric nor transitive.
  • None of the above
Find the correct co-related number.
$$5:36::6:?$$ 
  • $$48$$
  • $$50$$
  • $$49$$
  • $$56$$
Let $$S$$ be a relation on $$\mathbb{R}^{+}$$ defined by $$xSy\Leftrightarrow { x }^{ 2 }-{ y }^{ 2 }=2\left( y-x \right)$$, then $$S$$ is
  • Only reflecxive
  • Only symmetric
  • Only Trasitive
  • Equivalence
If $${C}_{r}$$ stands for $${ _{  }^{ n }{ C } }_{ r }$$ then $$\left( { C }_{ 0 }+{ C }_{ 1 } \right) +\left( { C }_{ 1 }+{ C }_{ 2 } \right) +....\left( { C }_{ n-1 }+{ C }_{ n } \right) \quad $$ is equal to
  • $${ 2 }^{ n }-1$$
  • $${ 2 }^{ n+1 }+1$$
  • $${ 2 }^{ n+1 }-1$$
  • $${ 2 }^{ n+1 }-2$$
For real values of x ,the range of $$\frac {x^2+2x+1}{X^2+2x-1}$$ is
  • $$(-\infty,0) \cup (1,\infty)$$
  • $$\begin{bmatrix}\frac{1}{2},2\end{bmatrix}$$
  • $$\begin{bmatrix} -\infty,\frac {-2}{9} \end{bmatrix}\cup (1,\infty)$$
  • $$(-\infty,-6)\cup(-2,\infty)$$
Let $$R$$ be a relation defined as $$aRb$$ if $$1 + ab > 0$$, then the relation $$R$$ is
  • reflexive and symmetric
  • symmetric but not reflexive
  • transitive
  • equivalence
Let N denote the set of all natural numbers. Define two binary relations on N as $$R_1=\{(x, y)\epsilon N\times N : 2x+y=10\}$$ and $$R_2=\{(x, y)\epsilon N\times N:x+2y=10\}$$. Then.
  • Both $$R_1$$ and $$R_2$$ are transitive relations
  • Both $$R_1$$ and $$R_2$$ are symmetric relations
  • Range of $$R_2$$ is $$\{1, 2, 3, 4\}$$
  • Range of $$R_1$$ is $$\{2, 4, 8\}$$
Let $$A=\left\{ a,b,c \right\} $$ and $$B=\left\{ 1,2 \right\} $$. Consider a relation $$R$$ defined from set $$A$$ to set $$B$$. Then $$R$$ is equal to set
  • $$A$$
  • $$B$$
  • $$A\times B$$
  • $$B\times A$$
The maximum number of equivalence relation on the set $$A=\{1,2,3,4\}$$ are
  • $$15$$
  • $$13$$
  • $$20$$
  • $$5$$
The number of reflexive relations of a set with three elements is equal to 
  • $$2^{12}$$
  • $$2^9$$
  • $$2^6$$
  • $$2^3$$
The relation P defined from R to R as a P b $$\Leftrightarrow$$ 1 + ab > 0, for all a, b $$\epsilon$$ R is
  • reflexive only
  • reflexive and symmetric only
  • transitive only
  • equivalence
If R is a relation on a finite set having n elements, then the number of relations on A is :
  • $$2^n$$
  • $$2^{n^2}$$
  • $$n^2$$
  • $$n^n$$
Let $$\rho$$ be a relation defined on$$N$$, the set of natural numbers, as
$$\rho =\left\{ \left( x,y \right) \in N\times N:2x+y=41 \right\} $$ then
  • $$\rho$$ is an equivalence relation
  • $$\rho$$ is only reflexive relation
  • $$\rho$$ is only symmetric relation
  • $$\rho$$ is not transitive
If $$A=\left\{2,3,5\right\}, B=\left\{2,5,6\right\}$$, then $$\left( A-B \right) \times \left( A\cap B \right)$$ is
  • $$\left\{(3,2),(3,3),(3,5)\right\}$$
  • $$\left\{(3,2),(3,5),(3,6)\right\}$$
  • $$\left\{(3,2),(3,5)\right\}$$
  • $$none\ of\ these$$
If $$A=\left\{1,2,3\right\}$$ and $$B=\left\{3,8\right\},$$ then
$$\left( A\cup B \right) \times \left( A\cap B \right)$$ is
  • $$\left\{(3,1),(3,2),(3,3),(3,8)\right\}$$
  • $$\left\{(1,3),(2,3),(3,3),(8,3)\right\}$$
  • $$\left\{(1,2),(2,2),(3,3),(8,8)\right\}$$
  • $$\left\{(8,3),(8,2),(8,1),(8,8)\right\}$$
Let $$R = gS - 4$$. When $$S = 8, R = 16$$. When $$S = 10, R$$ is equal to
  • $$11$$
  • $$14$$
  • $$20$$
  • $$21$$
  • None of these
Let n be a fixed positive integer. Define a relation R on I (the set of all integers) as follows:
aRB iff n/ (a -b), that is iff a - b is divisible by n. Then R is an equivalence relation on I.
  • True
  • False
If $$\alpha$$, $$\beta$$ be a straight lines in a plane, then  $$R_1$$ and $$R_2$$ is reflexive, symmetric and transitive $$\alpha , R_1, \beta$$ if $$\alpha \perp \beta $$ and $$\alpha  R_2 \beta $$ if $$\alpha || \beta$$.
  • True
  • False
If the line $$x=\alpha$$ divides the area of the region $$R=\left\{(x,y)\in \mathbb{R}^2:x^3\le y\le x,0\le x\le 1\right\}$$ into two equal parts, then 
  • $$0\lt \alpha\le \dfrac{1}{2}$$
  • $$\dfrac{1}{2}\lt \alpha\lt 1$$
  • $$2\alpha^4-4\alpha^2+1=0$$
  • $$\alpha^4+4\alpha^2-1=0$$
If $$aN = (ax/x \ \epsilon \ N)$$ and $$bN \cap cN = dN,$$, where $$b, c \ \epsilon N$$ are relatively prime, then 
  • d = bc
  • c = bd
  • b = cd
  • none
Let $$f\left( x \right) :\begin{cases} x,\quad x\quad is\quad rational \\ 0,\quad x\quad is\quad irrational \end{cases}$$
and 
$$g\left( x \right) :\begin{cases} 0,\quad x\quad is\quad rational \\ x,\quad x\quad is\quad irrational \end{cases}$$

If $$f:R\rightarrow R$$ and $$g:R\rightarrow R$$, then $$(f-g)$$ is

  • one-one and into
  • neither one-one nor onto
  • many-one and onto
  • one-one and onto
If $$f:R \to R$$ is a function satisfying $$f(x + y) = f(xy)$$ for all $$x, y \in R$$ and $$f\left(\dfrac{3}{4}\right) = \left( \dfrac{3}{4} \right)$$ , then $$f\left( \dfrac{9}{16} \right)$$ =
  • $$\dfrac{3}{4}$$
  • $$\dfrac{9}{16}$$
  • $$\dfrac{\sqrt{3}}{2}$$
  • $$0$$
If $$R$$ is the largest equivalence relation on a set $$A$$ and $$S$$ is any relation on $$A$$, then
  • $$R\subset S$$
  • $$S\subset R$$
  • $$R=S$$
  • none of these
Let $$s = \{(x, y)| \sin y = \sin x; x, y \in R \}$$, then $$s$$ is
  • Not transitive
  • equivalence
  • transitive but not reflexive
  • partial order relation
Find the domain of the function defined as $$f(x)=\dfrac{x+1}{2x+3}$$.
  • $$x\epsilon$$ R$$-$${$$\dfrac{3}{2}$$}
  • $$x\epsilon$$ R$$-$${$$\dfrac{-3}{2}$$}
  • $$x\epsilon$$ R
    • $$x\epsilon$$ R$$-$${$$\dfrac{2}{3}$$}
Let R be a relation from$$ A=\left\{ 1,2,3,4 \right\}  to B=\left\{ 1,3,5 \right\}$$  such that $$R=[(a,b):a<b,where\ a\epsilon A\ and\ b\epsilon B]$$. What is $$R$$ equal to?
  • $$(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)$$
  • $$(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)$$
  • $$(3,3),(3,5),(5,3),(5,5)$$
  • $$(3,3),(3,4),(4,5)$$
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