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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
Simplify the boolean expression
asked
Apr 16, 2015
by
hectordavid1995
1
answer
Evaluate : $\lim \int \limits _0^{\pi} \large\frac{x \tan x }{\sec x . \tan x}$$dx$
class12
cbse
boardexam
2015
set-1
sec-b
math
modelpaper
asked
Mar 22, 2015
by
meena.p
1
answer
If function $f(x) =|x-3| +|x-4| $, then show that $f(x)$ is not differentiable at $x=3$ and $x=4$
class12
cbse
boardexam
2015
set-1
sec-b
math
modelpaper
asked
Mar 20, 2015
by
meena.p
1
answer
Find the inverse of matrix $A=\begin{bmatrix} 3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2 \end{bmatrix}$ and hence show that $A^{-1} .A =I$
class12
cbse
2015
set-1
sec-b
math
boardexam
modelpaper
asked
Mar 19, 2015
by
meena.p
1
answer
If $ a \neq b \neq c$ and $\begin{vmatrix}a & b & c \\b & c & a \\c & a & b \end{vmatrix}$$=0$ , then using properties of determinants, prove that $a+b+c=0$
class12
cbse
2015
set-1
sec-b
math
boardexam
modelpaper
asked
Mar 19, 2015
by
meena.p
1
answer
If $\tan ^{-1} x+\tan ^{-1}y+\tan ^{-1} z= \large\frac{\pi}{2}$$,x,y,z>0$, then find the value of $xy+yz+zx$
class12
cbse
2015
set-1
sec-b
math
boardexam
modelpaper
asked
Mar 19, 2015
by
meena.p
1
answer
There are 3 families A,B and C. The number of men , women and children in these are as under : Dairy expense of men , women and children are $ Rs 200, Rs .150$ and $Rs 200$ respectively. Only men and women earn and children or not. using matrix multiplication , calculate the dairy expenses of each family. What impact does more children in the family create on the society ?
class12
cbse
2015
set-1
sec-b
math
boardexam
modelpaper
asked
Mar 19, 2015
by
meena.p
1
answer
Write the direction cosines of the normal to the plane $3x+4y+12z=52$
class12
cbse
2015
set-1
sec-a
math
boardexam
modelpaper
asked
Mar 19, 2015
by
meena.p
1
answer
Write the value of $\hat i. (\hat j \times \hat k) + \hat j .( \hat k \times \hat i) +\hat k.(\hat i \times \hat j)$.
class12
cbse
2015
set-1
sec-a
math
boardexam
modelpaper
asked
Mar 19, 2015
by
meena.p
1
answer
Write the projection of vector $2 \hat i +3 \hat j - \hat k$ along the vector $\hat i +\hat j$
class12
cbse
2015
set-1
sec-a
math
boardexam
modelpaper
asked
Mar 19, 2015
by
meena.p
1
answer
let A = (-1,0,1,2) B=(-4,-2,0,2) and f, g:A->B be functions defined by f(x)=X2-X and g(x)=2| x-1/2 |, -1 x belongs to A. Are f and g equal?
asked
Mar 17, 2015
by
krishvlk
1
answer
A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface of the remainer is $\large\frac{8}{9}$ of the curved surface of the whole cone, find the ratio of the line-segment into which the cone’s altitude is divided by the plane.
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-d
asked
Feb 19, 2015
by
meena.p
1
answer
The average of $11,12,13,14$ and x is $13$. The value of x is
olympiad
math
ch-2
linear-equations-in-one-variable
class8
asked
Feb 11, 2015
by
meena.p
1
answer
Draw a plot showing the variation of photo electric current against the intensity of incident validation on a given photo sensitive surface.
cbse
class12
physics
modelpaper
mock-test-series-2015
asked
Jan 28, 2015
by
meena.p
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 <br> a) Reflexive only<br> b) Symmetry<br> C) both reflexive and symmetry but not transitive<br> d) Is an equivalence relation.<br> Also show that the set of all points related to a point Pis not equal to (0,0) is the circle passing through P with origin as centre.
cl121
cbse
class12
bookproblem
ch1
sec1
q11
p6
easy
sec-a
math
asked
Jun 12, 2014
by
balaji.thirumalai
1
answer
Find the equation of the plane through the line of intersection of the planes $ x+y+z=1$ and $2x+3y+4z=5$ which is perpendicular to the plane $x-y+z=0$. Also find the distance of the plane obtained above, from the origin.
modelpaper-2014-chennai
cbse
class12
math
sec-c
q23a
asked
Mar 25, 2014
by
thanvigandhi_1
1
answer
Let $(f:R \to R)$ be defined as $(f(x)=2x+3.)$Find the function $(g(x):R \to R)$ such that $(g\;o\;f = f\;o\;g = I_R.)$
cbse
class12
additionalproblem
ch1
misc
sec-b
easy
math
jeemain
sets-relations-and-functions
relations-and-functions
asked
Jan 29, 2014
by
balaji
1
answer
If $\ast$ is a binary operation on the set $(\{0, 1, 2, 3, 4, 5\})$ defined as \[ a \ast b = \left\{ \begin{array} {1 1} a+b, & \quad \text{ if a$+$b $<$ 6} \\ a+b-6, & \quad \text{ if a+b $\geq$ 6} \\ \end{array} \right. \] then draw the composition table for the operation and find the identity element and inverse of $4$ if exists.
ch1
cbse
class12
sec-b
medium
additionalproblem
math
asked
Jan 27, 2014
by
rvidyagovindarajan_1
1
answer
let * be a binaray operation on N given by a*b = 1cm (a,b) ,a,b belong to N find 2*4 and is N,* associative?
asked
Oct 4, 2013
by
sharon.r.varghese_1
1
answer
If $f:R\rightarrow R$ is defined $f(x)=x^2-3$ then $f^{-1}x$ = ?
jeemain
math
class12
ch1
sets-relations-and-functions
sec-a
easy
asked
May 13, 2013
by
rvidyagovindarajan_1
1
answer
Let the function $f\;:\;R \rightarrow R$ be defined by$ f(x)=\cos x,\forall \;x\;\in R$. What kind of a function is f?
class12
cbse
ch1
easy
sec-a
additionalproblem
math
asked
Mar 30, 2013
by
balaji.thirumalai
1
answer
Let C be the set of complex numbers. What kind of a mapping defines $f\; :\;C \rightarrow R\;given\;by\;f(z)=|\;z\;|,\forall\; z \in C$?
class12
cbse
ch1
easy
sec-a
additionalproblem
math
asked
Mar 30, 2013
by
balaji.thirumalai
1
answer
A binary operation $\ast$ on the set $\{0, 1, 2, 3, 4, 5\}$ is defined as
$a * b= \left\{ \begin{array}{1 1} a+b & \quad if\;a+b < 6\\ a+b-6 & \quad if a+b \geq 6 \end{array} \right.$
ch1
cbse
class12
sec-a
medium
additionalproblem
math
asked
Mar 20, 2013
by
balaji.thirumalai
1
answer
Define a binary operation \(\ast\) on the set \(\{0, 1, 2, 3, 4, 5\}\) as \[ a \ast b = \left\{ \begin{array} {1 1} a+b, & \quad \text{ if a$+$b $<$ 6} \\ a+b-6, & \quad \text{ if a+b $\geq$ 6} \\ \end{array} \right. \] Zero is the identity for this operation. True or False?
ch1
cbse
class12
sec-a
easy
additionalproblem
math
asked
Mar 20, 2013
by
balaji.thirumalai
1
answer
Consider a binary operation $\ast$ on the set \(\{1, 2, 3, 4, 5\}\) given by the following multiplication table (Table 1.2). \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} (iii) Compute $(2 \ast 3) \ast (4 \ast 5)$
easy
p25
sec-a
cbse
q4
sec4
class12
bookproblem
ch1
q4-3
math
asked
Mar 20, 2013
by
balaji.thirumalai
1
answer
Consider a binary operation $\ast$ on the set \(\{1, 2, 3, 4, 5\}\) given by the following multiplication table (Table 1.2). \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} (ii) is $\ast$ commutative?
easy
p25
sec-a
q4
sec4
class12
bookproblem
cbse
q4-2
ch1
math
asked
Mar 20, 2013
by
balaji.thirumalai
1
answer
Consider a binary operation $\ast$ on the set \(\{1, 2, 3, 4, 5\}\) given by the following multiplication table (Table 1.2). \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} (i) Compute $(2*3)*4$ and $2*(3*4)$
cbse
class12
bookproblem
ch1
sec4
q4
easy
q4-1
p25
sec-a
math
asked
Mar 20, 2013
by
balaji.thirumalai
1
answer
State whether the following statement is true or false. Justify. ii) If $\ast$ is a commutative binary operation on N, then $a \ast (b \ast c) = (c \ast b) \ast a$.
class12
cbse
sec-a
ch1
sec4
q12
q12-2
easy
p25
math
asked
Mar 20, 2013
by
balaji.thirumalai
1
answer
State whether the following statements are true or false. Justify. (i) For an arbitrary binary operation $\ast$ on a set N, $a \ast a=a \forall a \in N$
cbse
class12
bookproblem
ch1
sec4
easy
p26
q12
q12-1
sec-a
math
asked
Mar 20, 2013
by
balaji.thirumalai
1
answer
Find which of the operations given below has identity:$(vi)\;\; a \ast b = ab^2$
cbse
class12
bookproblem
easy
ch1
sec4
p25
q10
q10-6
sec-a
math
asked
Mar 19, 2013
by
meena.p
1
answer
Find which of the operations given below has identity:$(v)\;\; a \ast b = \large\frac {ab} {4}$
cbse
class12
bookproblem
easy
ch1
sec4
p25
q10
q10-5
sec-a
math
asked
Mar 19, 2013
by
meena.p
1
answer
Find which of the operations given below has identity: $(iv)\;\; a \ast b = (a-b)^2$
cbse
class12
bookproblem
easy
ch1
sec4
p25
q10
q10-4
sec-a
math
asked
Mar 19, 2013
by
meena.p
1
answer
Find which of the operations given below has identity: $(iii)\;\; a \ast b = a+ab$
cbse
class12
bookproblem
easy
ch1
sec4
p25
q10
q10-3
sec-a
math
asked
Mar 19, 2013
by
meena.p
1
answer
Find which of the operations given below has identity: (i) $a \ast b = a - b$.
cbse
class12
bookproblem
easy
ch1
sec4
p25
q10
q10-1
sec-a
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
Let $\ast$ be the binary operation on $N$ given by $a \ast b =$ LCM of $a$ and $b$. $(v)$ Which elements of $N$ are invertible for the operation $\ast$ ?
cbse
class12
bookproblem
ch1
sec4
easy
p24
q6
q6-5
sec-a
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
Let $\ast$ be the binary operation on $N$ given by $a \ast b =$ LCM of $a$ and $b$. $(iv)$ Find the identity of $\ast$ in $N$.
cbse
class12
bookproblem
ch1
sec4
p24
q6
q6-4
easy
sec-a
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
Let $\ast$ be the binary operation on $N$ given by $a \ast b =$ LCM of $a$ and $b$. $(iii)$ Is $ \ast$ associative?
cbse
bookproblem
ch1
sec4
easy
p24
q6
q6-3
sec-a
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
Let $\ast$ be the binary operation on $N$ given by $a \ast b =$ LCM of $a$ and $b$. $(ii)$ Is $\ast$ commutative?
cbse
ch1
sec4
bookproblem
easy
sec-a
p24
q6
q6-2
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
Let $\ast$ be the binary operation on $N$ given by $a \ast b = $ LCM of $a$ and $b$. $(i)$ Find $5 \ast 7, \; 20 \ast 16$.
cbse
bookproblem
easy
ch1
sec4
p25
q6
q6-1
sec-a
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
Consider a binary operation * on the set ${1,2,3,4,5}$ given by the following multiplication table:
cbse
class12
ch1
sec2
q10
sec-a
easy
math
asked
Mar 19, 2013
by
balaji.thirumalai
0
answers
For each operation $\ast$ defined below, determine whether $\ast$ is binary, commutative or associative: On $Z$, define $a \ast b = a-b$
class12
cbse
bookproblem
ch1
sec4
p24
q2
q2-1
sec-a
easy
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
True or False: If a function $f: X \rightarrow Y$ is invertible, it has a unique inverse.
cbse
class12
ch1
toolbox
concepts
true-or-false
sec-a
easy
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
True or False: The function $f$ has an inverse: $ f:{1,2,3,4,}\to{10}$ with $f={(1,10),(2,10),(3,10),(4,10)}$
cbse
class12
additionalproblem
ch1
easy
sec-a
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
The function $g: \{ 5,6,7,8\} \to \{1,2,3,4\}$ is invertible. True or False?
class12
cbse
ch1
additionalproblem
easy
sec-a
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
The following function $h: \{2,3,4,5,\} \to \{7,9,11,13\}$ with $ h=\{(2,7),(3,9),(4,11),(5,13) \}$ is invertible. True or False?
cbse
class12
ch1
short-answer
additionalproblem
sec-a
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
State with reason whether following functions have inverse: (ii) \(g: \{ 5,6,7,8\} \to \{1,2,3,4\}\) with \(g= \{(5,4),(6,3),(7,4),(8,2)\}\)
cbse
class12
ch1
sec3
p18
sec-a
bookproblem
q5
q5-2
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
State with reason whether following functions have inverses: (i) \( f: \{ 1,2,3,4,\} \to \{10\}\) with \( f= \{(1,10),(2,10),(3,10), (4,10)\}\)
class12
cbse
ch1
sec3
q5
q5-1
easy
sec-a
p18
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
Let \(f,\, g\, and\, h\) be functions from \(R\, to\, R.\) True or False: \[ (f . g) oh = (foh) . (goh)\]
class12
cbse
ch1
toolbox
concepts
sec-a
easy
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
Let \(f,\, g\, and\, h\) be functions from \(R\, to\, R.\). True of False: \[ (f + g) oh = (foh) + (goh)\]
cbse
class12
ch1
concepts
toolbox
sec-a
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
Let \(f,\, g\, and\, h\) be functions from \(R\, to\, R.\) Show that \[ (f . g) oh = (foh) . (goh)\]
cbse
class12
ch1
sec3
bookproblem
easy
sec-a
q2
q2-2
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
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