Email
Chat with tutors
Login
Ask Questions, Get Answers
Menu
X
home
ask
tuition
questions
practice
papers
mobile
tutors
pricing
X
Recent questions in Relations and Functions
Questions
>>
CBSE XII
>>
Math
>>
Relations and Functions
Find if the given operation has identity: $\;\; a \ast b = a^2 + b^2$
cbse
class12
bookproblem
ch1
sec4
p25
q10
q10-2
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
2
answers
Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $\;\; a \ast b = a-b$. Find which of the binary operations are commutative and which are associative.
cbse
class12
bookproblem
ch1
sec4
q9
q9-1
p25
easy
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Let $\ast$ be the binary operation on $N$ defined by $a \ast b=H.C.F. $ of a and b. Is $\ast$ commutative? Is $\ast$ associative? Does there exist identity for this binary operation on $N$?
cbse
class12
bookproblem
ch1
sec4
q8
p25
easy
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Is $\ast$ defined on the set $\{1,2,3,4,5\}$ by $a\ast b=L.C.M$.of $a$ and $b$ a binary operation?
cbse
class12
bookproblem
ch1
sec4
q7
p25
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Let \(\ast\) be the binary operation on \(N\) given by \(a\ast b=L.C.M\,.of\,a\,and\,b\). Find $\begin{array}{1 1}(i)\;\; 5 \ast7,\; 20 \ast 16 & (ii)\;\; Is\; \ast \;commutative?\\(iii)\;\; Is\; \ast \;associative? & (iv)\;\; Find\, the\,identity \, of \ast \, in N\\(v)\;\; Which \, elements\, of \, N\, are\, invertible\, for\, the\, operaation\,\ast ? & \;\end{array}$
cbse
class12
bookproblem
ch1
sec4
q6
p25
sec-b
math
asked
Nov 21, 2012
by
vaishali.a
2
answers
Let $\ast '$ be the binary operation on the set $\{1, 2, 3, 4, 5\}$ defined by $a \ast ' b = H.C.F$ of a and b. Is the operation same as the operation $\ast$ defined in the table below? $\begin{matrix} *&1&2&3&4&5 \\ 1&1&1&1&1&1 \\ 2&1&2&1&2&1 \\ 3&1&1&3&1&1 \\ 4&1&2&1&4&1 \\ 5&1&1&1&1&5 \end{matrix}$
cbse
class12
bookproblem
ch1
sec4
q5
p25
sec-a
easy
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Consider the binary operation \( \wedge\) on the set \(\{1, 2, 3, 4, 5\}\) defined by \(a \wedge b = min \{a, b\}\). Write the multiplication table of the operation \( \wedge\) .
cbse
class12
bookproblem
ch1
sec4
q3
p24
sec-a
easy
modelpaper
2012
q11
math
asked
Nov 20, 2012
by
vaishali.a
1
answer
For each operation $\ast$ defined below, determine whether $\ast$ is binary, commutative or associative. $\begin{array}{1 1}(i) \;\;\; On\, Z,\, define \,a*b\, = a-b & \;\\(ii) \;\;\; On\, Q,\, define \,a*b\, = ab+1 & \;\\(iii) \;\;\; On\, Q,\, define \,a*b\, = \frac {ab} {2} & \;\\(iv) \;\;\; On\, Z^+, \, define\, a*b= 2^{ab} & \;\\(v) \;\;\; On\, Z^+,\, define \,a*b\, = a^b & \;\\(vi) \;\;\; On R - \{ -1\},\, define\, a*b= \frac {a} {b+1} & \;\end{array}$
cbse
class12
bookproblem
ch1
sec4
q2
p24
sec-b
math
asked
Nov 20, 2012
by
vaishali.a
5
answers
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^+,\,$ defined $*\,$ by$\; a*b= a-b $
cbse
class12
bookproblem
ch1
sec4
q1
q1-1
p24
easy
sec-a
math
asked
Nov 19, 2012
by
vaishali.a
1
answer
Let \(f : R - \{ - \frac {4} {3} \} \to R \) be a function defined as \(f(x)= \frac {4x} {3x+4} \) .The inverse of \(f\) is the map \(g\): Range \(f \to R - \{ - \frac {4} {3} \} \) given by
cbse
class12
bookproblem
ch1
sec3
q14
p19
medium
sec-b
math
asked
Nov 19, 2012
by
vaishali.a
1
answer
If $f: R\to R$ be given by $f(x)=(3-x^3)^\frac {1}{3} $, then $fof(x)$ is
cbse
class12
bookproblem
ch1
sec3
q13
p19
sec-a
math
asked
Nov 19, 2012
by
vaishali.a
1
answer
Let \(f : X \to Y\) be an invertible function. Show that the inverse of $f^{-1}$ is $f$, i.e., $(f^{-1})^{-1} = f$.
cbse
class12
bookproblem
ch1
sec3
q12
p19
easy
sec-a
math
asked
Nov 16, 2012
by
vaishali.a
1
answer
Consider\(f:\{1,2,3\} \to\{a,b,c\}\) given by \(f(1)=a, \,f(2)=b\) and \(f(3)=c\). Find \(f^{-1} \) and show that \((f^{-1})^{-1} = f\).
cbse
class12
bookproblem
ch1
sec3
q11
p19
easy
sec-a
math
asked
Nov 15, 2012
by
vaishali.a
1
answer
Let \(f : X \to Y\) be an invertible function. Show that \(f\) has unique inverse.
cbse
class12
bookproblem
ch1
sec3
q10
p19
easy
sec-a
math
asked
Nov 15, 2012
by
vaishali.a
1
answer
Consider \(f:R_+ \to [\;\text{–5}, \infty )\)given by \(f(x)=9x^2 +6x\)-\(5\).Show that \(f\) is invertible with \( f^{-1} (y) = \bigg(\frac{(\sqrt{y+6}) -1} { 3}\bigg) \)
cbse
class12
bookproblem
ch1
sec3
q9
p19
medium
sec-b
math
asked
Nov 15, 2012
by
vaishali.a
1
answer
Consider \( f:R_+ \to [4,\infty)\)given by \(f(x)=x^2 +4\). Show that \(f\) is invertible with the inverse \(f^{-1}\)of \(f\) given by \(f^{-1}(y) = \sqrt {y-4}\),where $R_+$ is the set of all non-negative real numbers.
cbse
class12
bookproblem
ch1
sec3
q8
p18
medium
sec-b
math
asked
Nov 14, 2012
by
vaishali.a
1
answer
Consider $f:R \to R$ given by $f(x)=4x+3$. Show that $f$ is invertible. Find the inverse of $ f$
cbse
class12
bookproblem
ch1
sec3
q7
p18
medium
sec-b
math
asked
Nov 14, 2012
by
vaishali.a
1
answer
Show that $f : [-1,1]$ $ \rightarrow R$, given by $f(x) =\frac {x } { (x+2)}$ is one-one. Find the inverse of of the $f : [-1,1] \rightarrow $ Range $ f$.
cbse
class12
bookproblem
ch1
sec3
q6
p18
medium
sec-b
math
asked
Nov 14, 2012
by
vaishali.a
1
answer
State with reason whether following functions have inverse: (iii) \(h: \{2,3,4,5,\} \to \{7,9,11,13\}\) with \(h=\{(2,7),(3,9),(4,11),(5,13) \} \)
cbse
class12
bookproblem
ch1
sec3
q5
p18
q5-3
sec-a
easy
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
If $f(x) = \frac { (4x+3) } { (6x-4) }, x \neq \frac {2} {3}$, show that $ f(x) =x $, for all $ x \neq \frac {2} {3}$. What is the inverse of $f$
cbse
class12
bookproblem
ch1
sec3
q4
p18
medium
sec-b
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
Find \( gof\) and \(fog\), if (i) \( f(x) = |\;x\;| \, and \, g(x) = |\;5x-2\;| \)
cbse
class12
bookproblem
ch1
sec3
q3
q3-1
p18
easy
sec-a
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
Let \(f,\, g\, and\, h\) be functions from \(R\, to\, R.\) Show that \[ (f+g) oh = foh + goh\]
cbse
class12
bookproblem
ch1
sec3
q2
p18
easy
sec-a
q2-1
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
Let $f:\{1,3,4\} \to \{1,2,5\} $ and $g:\{1,2,5\}\to\{1,3\}$ be given by $f = \{(1, 2), (3, 5), (4, 1)\}$ and $ g = \{(1, 3), (2, 3), (5, 1)\}$. Write down $gof$.
cbse
class12
bookproblem
ch1
sec3
q1
p18
easy
sec-a
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
Let $f : R \to R$ be defined as $f (x) = 3x$. Choose the correct answer:
cbse
class12
bookproblem
ch1
sec2
q12
p11
easy
sec-a
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
Let $f: R \to R $, be defined as $f(x) = x^4$. Choose the correct answer.
cbse
class12
bookproblem
ch1
sec2
q11
p11
easy
sec-a
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
Let $A=R-\{3\}$ and $B=R-\{1\}$. Consider the function $ f:A \to B$ defined by $f(x)=\large\frac {x-2}{ x-3}$. Is $f$ one-one and onto?
cbse
class12
bookproblem
ch1
sec2
q10
p11
medium
sec-b
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
Let \(A\) and \(B\)be sets. Show that\(f : A × B \to\; B×A\)such that \( f(a,b)\,=\,(b,a)\) is bijective function
cbse
class12
bookproblem
ch1
sec2
q8
p11
medium
sec-b
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.(i) \(f : R\; \to R\; defined \; by \; f(x)\; =\; 3-4x\)
cbse
class12
bookproblem
ch1
sec2
q7
q7-1
p11
easy
sec-a
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
Let \(A=\{1,2,3\},\; B = \{4,5,6,7\}\) and let \(f = \{(1,4),(2,5),(3,6)\}\)be a function from \(A\) to \(B\). Show that \(f\) is one-one.
cbse
class12
bookproblem
ch1
sec2
q6
p11
easy
sec-a
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
Show that the Signum Function \(f : R \to R\), given by \[ f(x) = \left\{ \begin{array}{l l} 1, & if \; x \; > 0 \\ 0, & if\; x\;= 0 \text{ is neither one-one nor onto } \\ -1, & if\; x \;< 0 \end{array} \right. \]
cbse
class12
bookproblem
ch1
sec2
q5
p11
easy
sec-a
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
Show that the Modulus Function \(f : R \to R\), given by \( f(x) = |\;x\;|\), is neither one-one nor onto, where\( |\;x\;|\; is\; x\), if \(x\) is positive or \(0\) and \(|\;x\;|\; is\; \) \(-\)\(x\), if \( x\) is negative.
cbse
class12
bookproblem
ch1
sec2
q4
p11
sec-a
medium
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
Prove that the Greatest Integer Function \(f : R \to R\), given by \(f (x) = [x]\), is neither one-one nor onto, where \([x]\) denotes the greatest integer less than or equal to \(x\).
cbse
class12
bookproblem
ch1
sec2
q3
p10
easy
sec-b
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
Check the injectivity and surjectivity of the function: $f : N\to N\; given\; by\; f(x)\; = x^2 $
cbse
class12
bookproblem
ch1
sec2
q2
q2-1
p10
easy
sec-b
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
Show that the function \(f : R_* \rightarrow R_* \) defined by \( f(x) = (\frac{1} {x})\) is one-one and onto, where \(R_* \) is the set of all non-zero real numbers. Is the result true, if the domain \(R_* \) is replaced by \(N\) with co-domain being same as \(R_*\)?
cbse
class12
bookproblem
ch1
sec2
q1
p10
easy
sec-b
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
Let $R$ be the relation in the set $N$ given by $R=\{(a,b): a=b-2, b>6\}$. Choose the correct answer:
cbse
class12
bookproblem
ch1
sec1
q16
p7
sec-a
easy
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
Let $R$ be the relation in the set $\{1, 2, 3, 4\}$ given by $R = \{(1, 2), (2, 2), (1, 1), (4,4), (1, 3), (3, 3), (3, 2)\}$. Choose the correct answer.
cbse
class12
bookproblem
ch1
sec1
q15
p7
sec-a
math
easy
asked
Nov 8, 2012
by
vaishali.a
1
answer
Let \(L\) be the set of all lines in \(XY\) plane and \(R\) be the relation in \(L\) defined as \(R = \{(L1, L2) : L1\:\) is parallel to \(L2\}\). Show that \(R\) is an equivalence relation. Find the set of all lines related to the line \(y = 2x + 4.\)
cbse
class12
bookproblem
ch1
sec1
q14
p6
easy
sec-a
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
Show that the relation \(R\) defined in the set \(A\) of all polygons as \(R = \{(P_1, P_2) :\: P_1\ and \;P_2\) have same number of sides\(\}\), is an equivalence relation. What is the set of all elements in \(A\) related to the right angle triangle \(T\) with sides \(3, 4\) and \(5\)?
cbse
class12
bookproblem
ch1
sec1
q13
p6
easy
sec-a
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
Show that the relation \(R\) defined in the set \(A\) of all triangles as \(R = \{(T_1, T_2) : T_1\,is\, similar\, to\, T_2\}\), is equivalence relation. Consider three right angle triangles $(T_1 \;$ with sides $3, 4, 5, \; T_2$ with sides $5, 12, 13$, and $T_3$, with sides $6, 8, 10$) Which triangles among \(T_1\, T_2\, and\, T_3\) are related?
cbse
class12
bookproblem
ch1
sec1
q12
p6
medium
sec-b
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
The relation $R$ in the set $A$ of points in a plane given by $R = \{(P, Q)$ : distance of the point $P$ from the origin is same as the distance of the point $Q$ from the origin $\}$, is
cbse
class12
bookproblem
ch1
sec1
q11
p6
easy
sec-a
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
Show that the relation \(R\) in the set \(A= \{1,2,3,4,5\} \)given by \(R = \{(a, b) : |a – b| \,is\, even \} \), is an equivalence relation. Show that all the elements of \(\{1, 3, 5\} \) are related to each other and all the elements of \(\{2, 4\}\) are related to each other. But no element of \( \{1, 3, 5 \} \) is related to any element of \(\{2, 4\}\).
cbse
class12
bookproblem
sec1
ch1
q8
p9
easy
sec-b
math
asked
Nov 7, 2012
by
vaishali.a
1
answer
Show that 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 an equivalence relation.
cbse
class12
bookproblem
ch1
sec1
q7
p6
easy
sec-a
math
asked
Nov 7, 2012
by
vaishali.a
1
answer
Show that the relation \(R\) in the set {1,2,3} given by R={(1,2), (2,1)} is symmetric but neither reflexive nor transitive.
cbse
class12
bookproblem
ch1
sec1
q6
p6
sec-b
modelpaper
2012
q1
math
asked
Nov 7, 2012
by
vaishali.a
1
answer
Check whether the relation $R$ in $R$ defined by $R = {(a, b) : a \leq b^3}$ is reflexive, symmetric or transitive.
cbse
class12
bookproblem
ch1
sec1
q5
p6
easy
sec-a
math
asked
Nov 7, 2012
by
vaishali.a
1
answer
Show that the relation \(R\) in \(R\) defined as \(R = {(a, b) : a \leq b} \), is reflexive and transitive but not symmetric.
cbse
class12
bookproblem
ch1
sec1
q4
p5
sec-a
easy
math
asked
Nov 7, 2012
by
vaishali.a
1
answer
Check whether the relation R defined in the set ${1, 2, 3, 4, 5, 6}$ as $R= {(a,b) : b= a+1}$ is reflexive, symmetric or transitive.
cbse
class12
math
bookproblem
ch1
sec1
q3
p5
easy
sec-a
asked
Nov 7, 2012
by
vaishali.a
1
answer
Show that the relation \(R\) in the set \(R\) of real numbers, defined as $(R) =\{(a, b: (a \leq b^2 )\}$ is neither reflexive nor symmetric nor transitive.
cbse
class12
bookproblem
ch1
sec1
q2
p5
easy
sec-a
math
asked
Nov 7, 2012
by
vaishali.a
1
answer
Let \( A\ =\ R–\ {3}\)andB=R-{1}.Considerthefunctionoff:A
additionalproblem
cbse
class12
sec-a
easy
math
asked
Nov 2, 2012
by
vaishali.a
0
answers
Let \[ F :R->R: f(x) =2x+1 \] and \[ g:R->R:g(x)=x^2 –2 \] find (I) gof (II) fog
cbse
class12
additionalproblem
ch1
sec-a
easy
math
asked
Nov 2, 2012
by
vaishali.a
0
answers
Show that function \( f\: N\ ->N\), given by \( f(x)\ =\ 2x\), is one – one.
cbse
class12
additionalproblem
ch1
sec-a
easy
math
asked
Nov 2, 2012
by
vaishali.a
0
answers
Page:
« prev
1
...
4
5
6
7
Home
Ask
Tuition
Questions
Practice
Your payment for
is successful.
Continue
...