CBSE Questions for Class 11 Commerce Applied Mathematics Relations Quiz 16 - MCQExams.com

Let $$R:N \to N$$ be defined by $$R = \{ (a,b):a,b \in N$$ and $$a = {b^2}\}$$ then, which of the following is true? 
  • $$(a,a) \in R,\forall a \in N$$
  • $$(a,b) \in R, \Rightarrow (b,a) \in R$$
  • $$(a,b) \in R,(b,c) \in R \Rightarrow (a,c) \in R$$
  • None of the above
Let $$A$$ be set of first ten natural numbers and $$R$$ be a relation on $$A$$ defined by (x , y) $$\in$$ $$R$$ $$\Rightarrow$$ x + 2y = 10 , then domain of $$R$$ is
  • $$\left \{ 1 , 2 , 3 ,............, 10 \right \}$$
  • $$\left \{ 2 , 4 , 6 , 8 \right \}$$
  • $$\left \{ 1 , 2 , 3 , 4 \right \}$$
  • $$\left \{ 2 , 4 , 6 , 8 , 10 \right \}$$
If $$h=\left\{ ((x,y),(x-y, x+y))/ x,y \epsilon  N \right\}  $$ is a relation on NxN, then domain of h
  • $$\left\{ (x,y):\quad x
  • $$\left\{ (x,y):\quad x\le y,x,y\epsilon N \right\} $$
  • $$\left\{ (x,y):\quad x>y,x,y\epsilon N \right\} $$
  • $$\left\{ (x,y):\quad x \ge y,x,y\epsilon N \right\} $$
If $$A=\left\{ x:{ x }^{ 2 }-3x+2=0 \right\} $$, and R is a universal relation on A, then R is 
  • $${(1, 1), (2, 2)}$$
  • $${(1, 1)}$$
  • $$\{ \phi \} $$
  • None of these.
Let $$R_1, R_2$$ are relation defined on $$Z$$ such that $$aR_1b \Longleftrightarrow (a - b)$$ is divisible by $$3$$ and $$a \,R_2 b \Longleftrightarrow (a - b)$$ is divisible by $$4$$. Then which of the two relation $$(R_1 \cup R_2), (R_1 \cap R_2)$$ is an equivalence relation?
  • $$(R_1 \cup R_2)$$ Only
  • $$(R_1 \cap R_2)$$ Only
  • Both $$(R_1 \cup R_2), (R_1 \cap R_2)$$
  • Neither $$(R_1 \cup R_2)$$ nor $$(R_1 \cap R_2)$$
Let $$R_1$$ be a relation defined by 
$$R_1 =$${ $$(a, b)| a >b , a, b \epsilon R$$}. Then $$R_1$$ is
  • an equivalence relation on R
  • reflexive, transitive but not symmetric
  • symmetric, transitive but nor reflective
  • neither transitive nor reflective but symmetric
If a relation { R } on the set { 1,2,3 } be definedby R = { ( 1,2 ) } then { R } is
  • reflexive
  • transitive
  • Symmetric
  • None of these
The relation R defined in N as $$aRb \Leftrightarrow b$$ is divisible by a is
  • Reflexive but not symmetric
  • Symmetric but not transitive
  • Symmetric and transitive
  • Equivalence relation
If $$(x^{2}-2)+(y+3)i=7+4i$$  then x and y are 
  • $$\pm 3 and 4 $$
  • $$\pm \sqrt{5} and 4 $$
  • $$\pm 3 and 1 $$
  • None of these
Let T be the set of all triangles in the Euclidean plane, and let a relation R' on T be defined as aRb if a is congruent to b for all a, b $$\in$$ T. Then, R is?
  • Reflexive but not symmetric
  • Transitive but not symmetric
  • Equivalence
  • None of these
Let $$R = \left \{(2, 3), (3, 3), (2, 2), (5, 5), (2, 4), (4, 4), (4, 3)\right \}$$ be a relation on the set $$\left \{2, 3, 4, 5\right \}$$, then
  • $$R$$ is reflexive and symmetric but not transitive
  • $$R$$ is reflexive and transitive but not symmetric
  • $$R$$ is symmetric and transitive but not reflexive
  • $$R$$ is an equivalence relation
If $$A = \left \{1, 2, 3, 4, 5\right \}$$ then
  • The number of relation on $$A$$ is $$2^{25}$$
  • The number of relation on $$A$$ is $$2^{20}$$
  • The number of reflexive relation on $$A$$ is $$20^{20}$$
  • The number of reflexive relation on $$A$$ is $$2^{15}$$
If $$A=\left\{1,2,4  \right\}$$, $$B=\left\{1,4,6,9  \right\}$$ and $$R$$ is a relation from $$A$$ to $$B$$ defined by $$x$$ is greater than $$y$$. The rangle of $$R$$ is :
  • $$\left\{1,4,6,9 \right\} $$
  • $$\left\{4,6,9 \right\} $$
  • $$\left\{ 1 \right\} $$
  • none of these
If  $$g(f(x))= |sinx|$$  and  $$g(f(x))= sin^2 \sqrt{x},$$  then
  • $$f(x)= \sqrt{x}, \ g(x)= sin^2x$$
  • $$f(x) = sin \sqrt{x}, \ g(x)= x^2$$
  • $$f(x)= \sqrt{sinx}, \ g(x)= x^2$$
  • $$f(x)= |x|, \ g(x)= sin^2 x$$
If $$A=\{ 1,2,3\} $$ then the number of equivalance relation containing the element {1,2} is :
  • 1
  • 2
  • 3
  • 14
Let S be the set of all straight lines in a plane. Let R be a relation on S defined by $$a$$ R $$b\Leftrightarrow a||b$$. Then, R is?
  • Reflexive and symmetric but not transitive
  • Reflexive and transitive but not symmetric
  • Symmetric and transitive but not reflexive
  • An equivalence relation
If $$f(x) = -{ \frac { x\left| x \right|  }{ 1+x^{ 2 } }  }$$ then $$f^{-1} (x) $$ equals
  • $$\sqrt { \frac { x\left| x \right| }{ 1-\left| x \right| } } $$
  • $$(Sgn x) \sqrt { \frac { x\left| x \right| }{ 1-\left| x \right| } } $$
  • $$- \sqrt { \frac {x} {1-x}}$$
  • None of these
From the following relations defined on set Z of integers, which of the relation is not equivalence relation
  • $$ aR_{1} b \Leftrightarrow ( a + b) $$ is an even integer
  • $$ aR_{1} b \Leftrightarrow ( a - b) $$ is an even integer
  • $$ aR_{3} b \Leftrightarrow ( a + b) a < b $$
  • $$ aR_{4} b \Leftrightarrow ( a + b) a = b $$
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