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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
Let $f:R_+\rightarrow[-5,\infty) $ given by $f(x)=9x^2+6x-5.$ show that f is invertiable with $ f^{-1}(y)=\frac{\sqrt{y+6}-1}{3}.$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q16
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
1
answer
Show that the relation R on N x N defined by $(a,b)R(c,d)\;\Leftrightarrow \; a+d = b+c $is an equivalence relation.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q15
p3
math
sec-a
asked
Jan 23, 2013
by
meena.p
0
answers
If R is a relation on a set $A(A \neq \phi),$ prove that R is symmetric iff $R^{-1} = R$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q14
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
If $f(x)=log \big(\frac{1+x}{1-x}\big)$ show that $f(x)+f(y)=f \big(\frac{x+y}{1+xy}\big)$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q13
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Let $ f(x)=\frac{\alpha x}{x+1},x\;\neq\;-1,$ find the value of $\alpha$ such that $f(f(x))=x$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q12
p3
math
sec-a
asked
Jan 23, 2013
by
meena.p
0
answers
Let f, g be two functions defined by \[f(x)=\frac{x}{x+1},g(x)=\frac{x}{1-x},\;then\;find\;(fog)^{-1}(x)\]
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q11
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Show that $\frac{1}{\sin^3x}+\cot x+\frac{1}{x^5}+x^3 $ is an odd function.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q10
p3
math
sec-a
asked
Jan 23, 2013
by
meena.p
0
answers
If $f(x)=\frac{1+x}{1-x},$show that $f[f(\tan\theta)]= - cot\theta$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q9
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
If $f(x)=\frac{5x+3}{4x-5}\big(x\neq\frac{5}{4}\big),$find g(x) such that $gof(x) = x$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q8
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Let $f :R \rightarrow R $ defined by $f(x) = (ax^2+b)^3$ find the function $g :R \rightarrow R $ such that $f(g(x)) = g(f(x))$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q7
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Let $ \int : {R\; \rightarrow \;R}$ be a function defined by $ f(x) = x^2-3x+4,$ for all $x \in R ,$ find the value of $f^{-1}(2)$.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q6
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
0
answers
Let A = {4,5,0}. Find the number of binary operations that can be defined on A.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q5
p3
math
sec-a
asked
Jan 22, 2013
by
meena.p
0
answers
Find the number of One-One functions from a finite set A to A, where n(A) = P
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q4
math
sec-a
asked
Jan 22, 2013
by
meena.p
0
answers
Let * be a binary operation on the set of real numbers. If a * b = a+b-ab, 2 * ( 3 * x ) = -7, find the value of x.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q3
p3
math
sec-b
asked
Jan 22, 2013
by
meena.p
1
answer
If $f(x)=\sin^2x+\sin^2\big(x+\frac{\pi}{3}\big)+\cos x.cos\big(x+\frac{\pi}{3}\big)\;and\;g\big(\frac{5}{4}\big)=1$, then find the value of gof(x)=x.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q2
p3
math
sec-b
asked
Jan 22, 2013
by
meena.p
0
answers
If $f(x)=\frac{x-1}{x+1},(x \neq 1,-1),$ show that $fof^{-1}$ is an identity function.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q1
p3
math
sec-b
asked
Jan 22, 2013
by
meena.p
0
answers
Let n be a fixed positive integer.Define a relation R in Z as follows: a,b E\inE Z, aRb if and only if a-b is divisible by n. Show that R is an equivalence relation.
cbse
class12
ch1
q15
p12
short-answer
exemplar
sec-a
easy
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
True or False: A binary operation on a set has always the identity element.
cbse
class12
ch1
q62
p17
true-or-false
exemplar
concepts
toolbox
math
sec-a
asked
Dec 20, 2012
by
sreemathi.v
1
answer
True or False: Every function is invertible.
cbse
class12
ch1
q61
p17
true-or-false
exemplar
concepts
toolbox
math
sec-a
asked
Dec 20, 2012
by
sreemathi.v
1
answer
True or False: The composition of functions is associative
cbse
class12
ch1
q60
p17
true-or-false
exemplar
concepts
toolbox
math
sec-a
asked
Dec 20, 2012
by
sreemathi.v
1
answer
True or False: The composition of functions is commutative.
cbse
class12
ch1
q59
p17
true-or-false
exemplar
concepts
toolbox
math
sec-a
asked
Dec 20, 2012
by
sreemathi.v
1
answer
True or False: The relation R on the set A={1,2,3} defined as R={(1,1),(1,2),(2,1),(3,3)} is reflexive,symmetric and transitive.
cbse
class12
ch1
q58
p17
true-or-false
exemplar
math
sec-a
asked
Dec 20, 2012
by
sreemathi.v
1
answer
True or False: Let A={0,1} and N be the set of natural numbers.Then the mapping $f:N \rightarrow A$ defined by f(2n-1)=0,f(2n)=1,$\quad n\in N$,is onto.
cbse
class12
ch1
q57
p17
true-or-false
exemplar
math
sec-a
asked
Dec 20, 2012
by
sreemathi.v
1
answer
True or False: An integer m is said to be related to another integer n if m is a integral multiple of n.This relation in Z is reflexive,symmetric and transitive.
cbse
class12
ch1
q56
p17
true-or-false
exemplar
concepts
toolbox
math
sec-a
asked
Dec 20, 2012
by
sreemathi.v
1
answer
True or False: Every relation which is symmetric and transitive is also reflexive.
cbse
class12
ch1
q55
p17
true-or-false
exemplar
concepts
toolbox
math
sec-a
asked
Dec 20, 2012
by
sreemathi.v
1
answer
True or False: Let $f:R \rightarrow R$ be the function defined by f(x)=sin (3x+2)$\quad x\in R$.Then f is invertible.
cbse
class12
ch1
q54
p17
true-or-false
exemplar
math
sec-a
asked
Dec 20, 2012
by
sreemathi.v
1
answer
True or False: Let R={(3,1),(1,3),(3,3)} be a relation defined on the set A={1,2,3}.Then R is symmetric,transitive but not reflexive.
cbse
class12
ch1
q53
p17
true-or-false
exemplar
math
sec-a
asked
Dec 20, 2012
by
sreemathi.v
1
answer
If $f(x)=(4-(x-7)^3\},then\;f^{-1}(x)$=____________.
cbse
class12
ch1
q52
p17
fitb
exemplar
math
sec-a
asked
Dec 20, 2012
by
sreemathi.v
1
answer
Let $f:R \rightarrow R$ be defined by $f(x)=\Large {\frac{x}{\sqrt{1+x^2}}}$.Then ( f o f o f )(x)=____________.
cbse
class12
ch1
q51
p17
fitb
exemplar
math
sec-a
asked
Dec 20, 2012
by
sreemathi.v
1
answer
Let f={(1,2)(3,5),(4,1)} and g={(2,3),(5,1),(1,3)}.Then g o f =_____________ and f o g=____________.
cbse
class12
ch1
q50
p16
fitb
exemplar
math
sec-a
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Let the relation R be defined on the set A={1,2,3,4,5}by R={$(a,b):\mid a^2-b^2 \mid <\;8.Then\;R\;is\;given\;by$______________.
cbse
class12
ch1
q49
p16
fitb
exemplar
math
sec-a
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Let the relation R be defined in N by aRb if 2a+3b=30.Then R=___________________
cbse
class12
ch1
q48
p16
fitb
exemplar
math
sec-a
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Let $\; f:R \rightarrow R$ be given as $\;f(x)=\tan x $. Then $\;f^{-1}(1)$ is
cbse
class12
ch1
q47
p16
objective
exemplar
math
sec-a
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Let $f:R \rightarrow R$ be defined by $ f(x)=\left \{ \begin{array}{1 1} 2x:x>3\\x^2:1<1x\leq 3\\ 3x:x\leq1\end{array} \right.$ $Then\;f(-1)+f(2)+f(4)\;is$
cbse
class12
ch1
q46
p16
objective
exemplar
math
sec-a
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Let $ f:N\rightarrow R$ be the function defined by $f(x)=\frac{2x-1}{2}\;and\;g:\;Q \rightarrow R $ be another function defined by g(x)=x+2. Then $(g\;o\;f)\frac{3}{2}$ is
cbse
class12
ch1
q45
p16
objective
exemplar
math
sec-a
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Let $f:[2,\infty)\rightarrow R $ be the function defined by $f(x)=x^2-4x+5,$ then the range of f is
cbse
class12
ch1
q44
p16
objective
exemplar
math
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Let $f :[0,1]\rightarrow[0,1]$ be defined by$$ f(x)= \left \{ \begin{array}{1 1}\;x,if\;x\;is\;rational & \;\\1-x,if\;x\;is\;irrational & \;\end{array} \right.$$ Then $(f o f)x$ is $$\begin{array}{1 1}(A)\;constant & (B)\;1+x\\(C)\;x & (D)\;none\;of\;these\end{array}$$
cbse
class12
ch1
q43
p15
objective
exemplar
math
sec-a
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Let $f:R-\{\frac{3}{5}\}\rightarrow R$ be defined by $f(x)=\Large {\frac{3x+2}{5x-3}}$ .Then
cbse
class12
ch1
q42
p15
objective
exemplar
math
sec-a
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Let $f:A\rightarrow B\;and\;g:B\rightarrow C$ be the bijective functions.Then $(g\;o\;f)^{-1}$ is
cbse
class12
ch1
q41
p15
objective
exemplar
math
sec-a
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Let f:$R\rightarrow R$ be the functions defined by $f(x)=x^3+5.$ Then $f^{-1}(x)$ is
cbse
class12
ch1
q40
p15
objective
exemplar
math
sec-a
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Which of the following functions from Z into Z are bijections?\begin{array}{1 1}(A)\;f(x)=x^3 & (B)\;f(x)=x+2\\(C)\;f(x)=2x+1 & (D)\;f(x)=x^2+1\end{array}
cbse
class12
ch1
q39
p15
objective
exemplar
math
sec-a
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Let $f:R\rightarrow R $ be defined by $f(x)=3x^2-5\; and \;g:R\rightarrow R \;by \;g(x)=\Large {\frac{x}{x^2+1}}$.Then g o f is
cbse
class12
ch1
q38
p15
objective
exemplar
sec-a
math
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Let $f\;:\;R\rightarrow R$ be defined by $f(x)\;=\;\frac{1}{x}\quad x\;\in\; R.$Then f is
cbse
class12
ch1
q37
p15
objective
exemplar
sec-a
math
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Let A={1,2,3,....n} and B={a,b}. Then the number of surjection from A into B is \begin{array}{1 1}(A)\quad"p_2 \qquad & (B)\quad 2"-2\\ (C)\quad 2^n-1 \qquad & (D)\quad none\;of\;these\end{array}
cbse
class12
ch1
q36
p14
objective
exemplar
sec-a
math
asked
Dec 19, 2012
by
sreemathi.v
1
answer
If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is
cbse
class12
ch1
q35
p14
objective
exemplar
sec-a
math
asked
Dec 19, 2012
by
sreemathi.v
1
answer
The identity element for the binary operation $\ast$ defined on $Q\sim \{0\}$ as $a\ast b=\large{\frac{ab}{2}} \normalsize \;a,b\in Q\sim\{0\}$ is
cbse
class12
ch1
q34
p14
objective
exemplar
sec-a
math
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Let A={1,2,3} and consider the relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}.Then R is:
cbse
class12
ch1
q33
p14
objective
exemplar
sec-a
math
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Let us define a relation R in R as aRb if $a \geq b$.Then R is
cbse
class12
ch1
q32
p14
objective
exemplar
sec-b
math
asked
Dec 19, 2012
by
sreemathi.v
1
answer
If a relation R on the set (1,2,3) be defined by R={(1,2)}, then R is
cbse
class12
ch1
q31
p14
objective
exemplar
sec-b
math
asked
Dec 19, 2012
by
sreemathi.v
1
answer
The maximum number of equivalence relations on the set A={1,2,3} are
cbse
class12
ch1
q30
p14
objective
exemplar
sec-b
math
asked
Dec 19, 2012
by
sreemathi.v
1
answer
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