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

$$x*y=\sqrt {\dfrac {(x+y)(y^{2}-12x)}{(x-2)(y-7)}}$$ then what will be the value of $$5*9$$?
  • $$7$$
  • $$8$$
  • $$10$$
  • $$9$$
Let $$R$$ be a reflexive relation in a finite set having $$n$$ elements and let there be $$m$$ ordered pairs in $$R$$. Then,
  • $$m \ge n$$
  • $$m \le n$$
  • $$m = n$$
  • None of these
Find the domain of the function defined as $$f(x)=\dfrac{1}{1-x^2}$$.
  • $$x\epsilon R -\{1,-1\}$$
  • $$x\epsilon R -\{0\}$$
  • $$x\epsilon R -\{-1\}$$
  • $$x\epsilon R -\{1\}$$
Let S be a non-empty set. Let R be a relation on P(S), defined as ARB$$\Leftrightarrow A\cap B\neq \phi$$. The relation R is?
  • Reflexive
  • Symmetric
  • Transitive
  • None of these
If $$f:\,R\, \to R\,$$ is an even function which is differentiable on R and $${f^N}\left( \pi  \right) = 1\,the\,{f^N}\left( { - \pi } \right)\,{\rm{is}}$$
  • -1
  • 0
  • 1
  • 2
Let $$A = \left\{ {a,\,b,\,c} \right\}$$ and $$B = \left\{ {4,\,5} \right\}$$. Consider a relation defined from set A to set B, then R is equal to
  • A
  • B
  • $$A \times B$$
  • $$B \times A$$
If $$A = \{2, 3, 5\}$$ and $$B = \{5, 7\}$$, find the set with highest number of elements:
  • $$A \times B$$
  • $$ B \times A$$
  • $$A \times A$$
  • $$B \times B$$
For two sets $$A$$ and $$B$$, $$A\times B=B\times A$$.
  • True
  • False
If $$f:R \to R$$ is defined by $$f\left( x \right) = {x^2} - 3x + 2$$ and $$f\left( {{x^2} - 3x - 2} \right) = a{x^4} + b{x^3} + c{x^2} + dx + e$$ then $$a + b + c + d + e = $$
  • $$1$$
  • $$2$$
  • $$30$$
  • $$20$$
Let $$A = \left\{ {x,\,y,\,z} \right\}$$ and $$B = \left\{ {1,\,2} \right\}$$. The number relations from A to B is 
  • 64
  • 32
  • 16
  • 28
Let R be a relation from N to N defined by 
$$R = \left\{ {\left( {a,\,b} \right):a,\,b\, \in \,N\,\,and\,\,a = {b^2}} \right\}$$
  • $$\left( {a,a} \right) \in R\,$$, for all $$\,a \in N$$
  • $$\left( {a,b} \right) \in R$$, implies $$\left( {b,a} \right) \in R$$
  • $$\left( {a,b} \right) \in R,\,\left( {b,c} \right) \in \,R$$ implies $$\left( {a,c} \right) \in R$$
  • None of these
If $$A = \left \{1, 2, 3, 4\right \}$$ and $$I_{A}$$ be the identify relation on $$A$$, then
  • $$(1, 2) \epsilon I_{A}$$
  • $$(2, 2) \epsilon I_{A}$$
  • $$(2, 1) \epsilon I_{A}$$
  • $$(3, 4) \epsilon I_{A}$$
Let $$R = \left \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 2)\right \}$$ be a relation on the set $$A = \left \{1, 2, 3, 4\right \}$$. The relation $$R$$ is
  • Reflexive
  • Transitive
  • Not symmetric
  • none of these
Let $$A$$ and $$B$$ be two sets containing four and two elements respectively.Then the number of subset of the  set $$A \times B$$, each having at least three elements is 
  • $$256$$
  • $$275$$
  • $$510$$
  • $$219$$
If x is real, then $$\dfrac{x^2+2x+c}{x^2+4x+3c}$$ can take all real values if?
  • $$0 < c < 2$$
  • $$0 < c < 1$$
  • $$-1 < c < 1$$
  • None of the above
If $$a\ne R$$ and the equation $$-3(x-[x])^2+2(x-[x])+a^2=0$$ ( where $$[x]$$ denotes the greatest integer $$\le x$$) has no integral solution, then all possible values of a lie in the interval : 
  • $$(-2,-1)$$
  • $$(-\infty ,-2)\cup(2,\infty)$$
  • $$(-1 ,0)\cup(0,1)$$
  • $$(1,2)$$
$${x\epsilon R:\frac{14x}{x+1}-\frac{9x-30}{x-4}<0}$$ is equal to 
  • (-1,4)
  • (1,4) $$\cup $$(5,7)
  • (1,7)
  • (-1,1) $$\cup $$ (4,6)
If $$\left| { z }_{ 1 }-a \right| <a,\left| { z }_{ 2 }-a \right| <b,\left| { z }_{ 3 }-a \right| <c$$, $$(a,b,c\in R)$$ then $$\left| { z }_{ 1 }+{ z }_{ 2 }+{ z }_{ 3 } \right| $$ is
  • less than $$(a+b+c)$$
  • more than $$(a+b+c)$$
  • less than $$2(a+b+c)$$
  • more than 2$$(a+b+c)$$
The area of the region $$R = \{(x, y) : |x| \le |y| \, \text{and} \, x^2 + y^2 \le 1 \}$$ is 
  • $$\dfrac{3 \pi}{8}$$ sq. units
  • $$\dfrac{5 \pi}{8} $$ sq. units
  • $$\dfrac{\pi}{2}$$ sq. units
  • $$\dfrac{\pi}{8} $$ sq. units
If  $$f:R\rightarrow R,g:R\rightarrow R$$ are defined by $$f(x)=5x-3,g(x)={ x }^{ 2 }+3,$$ then $$(go{ f }^{ -1 })(3)=\\ $$
  • $$\frac { 25 }{ 3 } $$
  • $$\frac { 111}{ 25 } $$
  • $$\frac { 9 }{ 25 } $$
  • $$\frac { 25 }{ 111 } $$
Let A and B be sets containing 2 and 4 elements respecetively. The number of subsets $$A \times B$$ having 3 or more elements is 
  • $$219$$
  • $$211$$
  • $$256$$
  • $$220$$
A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by :$$(x,y)\in\;R\; \rightarrow x$$ is relatively prime to y. Then, domain of R is
  • {2, 3, 5}
  • {3, 5}
  • {2, 3, 4}
  • {2, 3, 4,5}
If $$R$$ is the relation from set $$A$$ to a set $$B$$ and $$S$$ is the relation from $$B$$ to a set $$C$$, then the relation $$SoR$$
  • If from $$A$$ to $$C$$
  • If from $$C$$ to $$A$$
  • Does not exist
  • None of these
The domain of $$f(x)=\frac{1}{\sqrt{(x-1)(x-2)(x-3)}}$$ is 
  • $$(-\infty ,1)\cup (3,\infty )$$
  • $$(1,2)\cup (3,\infty )$$
  • $$(-\infty ,2)$$
  • R
Let $$A=\left\{ 2,4,6,8 \right\} $$. A relation $$R$$ on $$A$$ is defined by $$R={(2,4),(4,2),(4,6),(6,4)}$$. Then $$R$$ is:
  • $$anti-symmetric$$
  • $$reflexive$$
  • $$symmetric$$
  • $$transitive$$
For A= { 1, 2, 3} thel relation R = {(1,1), (2,2)}, (3,3)} is 
  • reflective only
  • symmetric only
  • transitive only
  • equivalence
The relation $$R$$ on the set $$Z$$ of all integer numbers defined by $$(x,y)\ \epsilon \ R\ \Leftrightarrow x-y$$ is divisible by $$n$$ is
  • Equivalence
  • Symmetric only
  • Reflexive only
  • Transitive only
The relation $$“$$is congruent to$$"$$ on the set of all triangles in a plane is
  • reflexive only
  • symmetric only
  • transitive only
  • equivalence
The domain of $$\dfrac { 10 ^ { x } + 10 ^ { - x } } { 10 ^ { x } - 10 ^ { - x } }$$ is
  • $$R$$
  • $$R - \{ 0 \}$$
  • $$R - \{ 1 \}$$
  • $$R ^ { + }$$
The number of equivalence relations on a five element set is
  • $$32$$
  • $$42$$
  • $$50$$
  • $$52$$
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