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Recent questions in Relations and Functions
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CBSE XII
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Math
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Relations and Functions
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.(ii) \(f : R\; \to R\; defined \; by \; f(x)\; =\; 1+x^2\)
cbse
class12
bookproblem
ch1
sec2
q7
q7-2
p11
easy
sec-a
math
asked
Mar 18, 2013
by
meena.p
1
answer
Check the injectivity and surjectivity of the following functions: (i) \(f : N\to N\; given\; by\; f(x)\; = x^2 \)
cbse
class12
bookproblem
ch1
sec2
q2
q2-1
p10
easy
sec-a
math
asked
Mar 14, 2013
by
meena.p
1
answer
Let X={1,2,3} and Y={4,5}.Find whether the following subsets of X x Y are functions from X to Y or not.$(iv)\quad k=\{(1,4),(2,5)\} $
cbse
class12
ch1
q12
q12-4
p11
exemplar
sec-a
easy
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Let X={1,2,3} and Y={4,5}.Find whether the following subsets of X x Y are functions from X to Y or not.$(iii)\quad h=\{(1,4),(2,5),(3,5)\} $
cbse
class12
ch1
q12
q12-3
p11
exemplar
sec-a
easy
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Let X={1,2,3} and Y={4,5}.Find whether the following subsets of X x Y are functions from X to Y or not.$(ii)\quad g=\{(1,4),(2,4),(3,4)\} $
cbse
class12
ch1
q12
q12-2
p11
exemplar
easy
sec-a
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Given the Modulus Function \(f : R \to R\), given by \( f(x) = |\;x\;|\), where\( |\;x\;|\; is\; x\), if \(x\) is positive or \(0\) and \(|\;x\;|\; is\; \) \(-\)\(x\), if \( x\) is negative. Is $f$ one-one or onto?
cbse
class12
ch1
sec2
sec-a
additionalproblem
easy
math
asked
Mar 13, 2013
by
balaji.thirumalai
1
answer
Given the Function $f:R\rightarrow R$, given by $f(x)=[x]$, where $[x]$ denotes the greatest integer less than or equal to $x$ which of the following is true?
cbse
class12
ch1
sec2
additionalproblem
easy
sec-a
math
asked
Mar 13, 2013
by
balaji.thirumalai
1
answer
Given a function $f:R_* \rightarrow R_*$ defined by $f(x)=\frac{1}{x}$, where $R_*$ is the set of all non-zero real numbers. Which of the following is true?
cbse
class12
ch1
sec2
additionalproblem
easy
sec-a
math
asked
Mar 13, 2013
by
balaji.thirumalai
1
answer
Let $S=\{a,b,c\}\;$ and$ \;T = \{1,2,3\}$. Find $F^{-1}$ of the following functions \(F\) from \(S\) to \(T\), if it exists - - $(ii)\;\; F=\{(a,2), (b,1), (c,1)\}$
cbse
class12
bookproblem
ch1
misc
q11
q11-2
p30
sec-a
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Let \(\ast\) be a binary operation on the set \(Q\) of rational numbers as follows: $(vi)\;\; a \ast b = {ab}^2$ Find which of the binary operations are commutative and which are associative.
cbse
class12
bookproblem
ch1
sec4
q9
q9-6
p25
easy
sec-b
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Let \(\ast\) be a binary operation on the set \(Q\) of rational numbers as follows: $(v)\;\; a \ast b = \frac{ab}{4}$ Find which of the binary operations are commutative and which are associative.
cbse
class12
bookproblem
ch1
sec4
q9
q9-5
p25
easy
sec-b
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Let \(\ast\) be a binary operation on the set \(Q\) of rational numbers as follows: $(iv)\;\; a \ast b = (a-b)^2$ Find which of the binary operations are commutative and which are associative.
cbse
class12
bookproblem
ch1
sec4
q9
q9-4
p25
easy
sec-b
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Let \(\ast\) be a binary operation on the set \(Q\) of rational numbers as follows: $(iii)\;\; a \ast b = a+ab$ Find which of the binary operations are commutative and which are associative.
cbse
class12
bookproblem
ch1
sec4
q9
q9-3
p25
easy
sec-b
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Let \(\ast\) be a binary operation on the set \(Q\) of rational numbers as follows: $(ii)\;\; a \ast b = a^2+b^2 $ Find which of the binary operations are commutative and which are associative.
cbse
class12
bookproblem
ch1
sec4
q9
q9-2
p25
easy
sec-b
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Determine whether or not each of the definition of $\ast$ given below gives a binary operation. In the event that $\ast$ is not a binary operation, give justification for this: (v)On $Z^+,define \;\ast\;by\;a\;\ast\;b=a.$
cbse
class12
bookproblem
ch1
sec4
q1
q1-5
p24
easy
sec-a
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
In the event that $\ast$ is not a binary operation, give justification for this: On $Z^+,$ defined $\;\ast\;by\;a\;\ast\;b=|a-b|.$
cbse
class12
bookproblem
ch1
sec4
q1
q1-4
p24
sec-a
easy
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Determine whether or not each of the definition of $\ast$ given below gives a binary operation. In the event that $\ast$ is not a binary operation, give justification for this: On $R$,defined $\ast\;by\;a\;\ast \;b=ab^2$
cbse
class12
bookproblem
ch1
sec4
q1
q1-3
p24
sec-a
easy
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Determine whether or not each of the definition of $\ast$ given below gives a binary operation. In the event that $\ast$ is not a binary operation, give justification for this $on\; z^+,define\; \ast by \;a\;\ast\; b=ab.$
cbse
class12
bookproblem
ch1
sec4
q1
q1-2
p24
easy
sec-a
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Find $ gof$ and $fog$, if $f(x) = 8x^3$ and $g(x)=x^\frac{1}{3}$
cbse
class12
bookproblem
ch1
sec3
q3
q3-2
p18
sec-a
easy
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
True or False? Let $f : X \rightarrow Y$ and $g : Y \rightarrow Z$ be two invertible functions. Then $g\;o\; f$ is also invertible with $(g \;o\; f)^{-1} = g^{-1} \; o f^{-1}$.
class12
cbse
concepts
toolbox
ch1
sec-a
easy
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
Which of the following is true? A function f : X → Y is invertible if and only if:
cbse
class12
ch1
concepts
toolbox
sec-a
easy
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
A relation $R$ in $X$ given by $R = X \times X$ is called what?
class12
cbse
ch1
toolbox
concepts
sec-a
easy
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
Fill in the blank: Given a binary operation ∗ : A × A → A, an element e ∈ A, if it exists, is called ____ for the operation ∗, if a ∗ e = a = e ∗ a, ∀ a ∈ A.?
cbse
concepts
toolbox
ch1
class12
sec-a
easy
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
Given two functions f(x) and g(x), (g o f) implies which of the following?
cbse
class12
ch1
concepts
toolbox
sec-a
easy
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
If a * b = b* a ∀ a, b, ∈ A, then the binary operation * on A is said to be what?
class12
toolbox
cbse
concepts
ch1
sec-a
easy
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
If (a ∗ b) ∗ c = a ∗ (b ∗ c), ∀ a, b, c, ∈ A, then the binary operation * on A is said to be what?
cbse
class12
concepts
toolbox
ch1
sec-a
easy
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
Which of the following is true?
class12
cbse
ch1
concepts
toolbox
sec-a
easy
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
True or False: A Function can be both one-one and onto.
cbse
class12
ch1
concepts
toolbox
sec-a
easy
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
Fill in the blank: A function f : X → Y is said to be ______, if every element of Y is the image of some element of X under f, i.e., for every y ∈ Y, there exists an element x in X such that f (x) = y.
cbse
class12
ch1
concepts
toolbox
sec-a
easy
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
Fill in the blank: A function $f: A \rightarrow B$ is called _____ if there are two or more elements in A that have the same image in B.
cbse
class12
ch1
concepts
toolbox
sec-a
easy
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
Fill in the blank: A function $f: A \rightarrow B$ where for every $x1, x2 \in X, f (x1) = f (x2) \Rightarrow x1 = x2$, is called a ______ function?
cbse
class12
ch1
concepts
toolbox
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
Fill in the blank: A relation R in a set A is called ______ relation, if each element of A is related to every element of A, i.e., R = A × A.
toolbox
concepts
ch1
class12
cbse
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
Fill in the Blank: A relation $R$ in a set $A$ is called ______ relation, if no element of $A$ is related to any element of $A$, i.e., $R = \phi \subset A \times A.$
cbse
class12
ch1
concepts
toolbox
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
For a relation R in a set A to be called $\mathbf{symmetric}$, if $(a_1,a_2) \in R$, which of the following must also be true
cbse
class12
ch1
toolbox
concepts
math
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
A relation R in a set A is called $\mathbf{transitive},$ if $(a_1,a_2) \in R$ and $(a_2,a_3) \in R$ and which of the following conditions must also hold true?
toolbox
ch1
class12
concepts
cbse
math
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
Given $(a_1,a_2) \in R$ and $(a_2,a_3) \in R \; \Rightarrow \;(a_1,a_3)\in R$ for all$\; a_1,a_2,a_3 \in A$. Then the relation $R$ is called what?
ch1
cbse
concepts
class12
toolbox
math
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
In a set $A$, if $(a_1,a_2) \in R\;\Rightarrow\; (a_2,a_1)\in R \; for \;a_1,a_2 \in A$, then what is the relation $R$ called?
cbse
concepts
toolbox
ch1
class12
math
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
If $(a,a) \in R\;$ for every $\; a\in\;A$, then what is the relation $R$ in the set $A$ is called?
cbse
ch1
class12
concepts
toolbox
math
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
A relation R is an equivalance relation if it satisifes which of the following properties?
cbse
class12
ch1
concepts
toolbox
math
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
Give an example of a relation which is (v) Symmetric and transitive but not reflexive.
cbse
class12
bookproblem
ch1
sec1
p6
easy
sec-a
q10
q10-5
math
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
Give an example of a relation which is (iv) Reflexive and transitive but not symmetric.
cbse
class12
bookproblem
ch1
sec1
p6
easy
sec-a
q10
q10-4
math
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
Give an example of a relation which is (iii) Reflexive and symmetric but not transitive.
cbse
class12
bookproblem
ch1
sec1
p6
easy
sec-a
q10
q10-3
math
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
Give an example of a relation which is (ii) Transitive but neither reflexive nor symmetric.
cbse
class12
bookproblem
ch1
sec1
p6
easy
sec-a
q10-2
q10
math
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
In a set of integers, is the Relation $R = \{(1,2), (2,1)\}$ symmetrical, transitive or reflexive?
class12
sec-a
cbse
sec1
ch1
additionalproblem
easy
math
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
The relation $R$ in the set $A=\{x\in Z: 0 \leq x \leq 12\}$, given by $ R = \{(a,b) |a-b|$ is a multiple of 4$\}$. Is the relation reflexive, symmetrical or transitive?
cbse
class12
additionalproblem
ch1
sec1
sec-a
easy
math
jeemain
medium
sets-relations-and-functions
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
Is the relation $R$ in the set $A=\{x\in Z: 0 \leq x \leq 12\}$, given by $ R = \{(a,b): a=b\}$ symmetrical, transitive or reflexive?
cbse
class12
ch1
sec1
easy
sec-a
additionalproblem
math
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
Show that the relation $R$ in the set $A=\{x\in Z: 0 \leq x \leq 12\}$, given by $(ii) R = \{(a,b): a=b\}$ is an equivalence relation. Find the set of all elements related to 1.
cbse
class12
bookproblem
ch1
sec1
p6
easy
sec-a
q9
math
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
Is the relation R in the set A={1,2,3,4,5} given by $R=${$(a,b):|a-b| $is even} symmetrical, reflexive or transitive?
cbse
class12
ch1
sec1
easy
sec-a
additionalproblem
math
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
Given the relation $R$ in the set $A$ of all the books in a library of a college, given by ( $R = \{ (x, y) : x\;$ and $\; y\;$ have same number of pages$\}$ ). Is $R$ reflexive, symmetric or transitive.
cbse
class12
ch1
sec1
easy
sec-a
additionalproblem
math
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
Is the relation $R$ in the set ${1,2,3}$ given by $R={(1,2), (2,1)}$ symmetric, reflexive or transitive.
cbse
class12
ch1
sec1
easy
sec-a
additionalproblem
math
asked
Mar 8, 2013
by
balaji.thirumalai
1
answer
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