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Recent questions tagged cbse
Questions
Discuss the continuity of the function $f$, where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} -2 ,& \quad\text{ if $ x $ \(\leq -1\)}\\ 2x,& \quad\text{ if $ -1 $ < x \(\leq1\)}\\ 2 ,& \quad\text{ if $ x $ > 1}\\ \end{array} \right. $
cbse
class12
bookproblem
ch5
sec1
q16
p160
sec-b
medium
math
asked
Nov 9, 2012
by
thanvigandhi_1
1
answer
Discuss the continuity of the function $f$, where $f$ is defined by $ f(x) = \left\{ \begin{array} {1 1} 2x ,& \quad\text{ if $ x $ < 0}\\ 0,& \quad\text{if $ 0 $ \(\leq x\) \(\leq1\)}\\ 4x ,& \quad\text{ if $ x $ > 1}\\ \end{array} \right. $
cbse
class12
bookproblem
ch5
sec1
q15
p160
medium
sec-b
math
asked
Nov 9, 2012
by
thanvigandhi_1
1
answer
Discuss the continuity of the function $f$, where $f$ is defined by \[ f(x) = \left\{ \begin{array} {1 1} 3 ,& \quad\text{ if $ 0 $ \(\leq x\) \(\leq1\)}\\ 4,& \quad\text{if $ 1 $ < \(x\) < 3 }\\ 5 ,& \quad\text{ if $ 3 $ \(\leq x\) \(\leq10\)}\\ \end{array} \right. \]
cbse
class12
bookproblem
ch5
sec1
q14
p160
sec-b
easy
math
asked
Nov 9, 2012
by
thanvigandhi_1
1
answer
Is the function defined by $ f(x) = \left\{ \begin{array} {1 1} x + 5 ,& \quad\text{ if $ x $ \(\leq 1\)}\\ x - 5,& \quad \text{if $x$ > 1}\\ \end{array} \right. $ a continuous function?
cbse
class12
bookproblem
ch5
sec1
q13
p159
math
sec-b
asked
Nov 9, 2012
by
thanvigandhi_1
1
answer
Find all points of discontinuity of $f$, where $f$fined by $ f(x) = \left\{ \begin{array} {1 1} x^{10} -1 ,& \quad\text{ if $ x $ \(\leq 1\)}\\ x^2,& \quad \text{if $x$ > 1}\\ \end{array} \right. $
cbse
class12
bookproblem
ch5
sec1
q12
p159
sec-b
medium
math
asked
Nov 9, 2012
by
thanvigandhi_1
1
answer
Find all points of discontinuity of $f$, where $f$ is defined by $ f(x) = \left\{ \begin{array} {1 1} x^3-3 ,& \quad\text{ if $ x $ \(\leq 2\)}\\ x^2+1,& \quad \text{if $x$ > 2}\\ \end{array} \right. $
cbse
class12
bookproblem
ch5
sec1
q11
p159
sec-b
easy
math
asked
Nov 9, 2012
by
thanvigandhi_1
1
answer
Find all points of discontinuity of $f$, where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} x + 1,& \quad\text{ if $ x $ \(\geq 1\)}\\ x^2+1,& \quad \text{if $x$ < 1}\\ \end{array} \right. $
cbse
class12
bookproblem
ch5
sec1
q10
p159
sec-b
easy
math
asked
Nov 9, 2012
by
thanvigandhi_1
1
answer
Find all points of discontinuity of $f$, where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} \large \frac x { |\;x\;| },& \quad\text{ if \(x\) < 0 }\\ -1 ,& \quad \text{if $x$ \( \geq 0\)}\\ \end{array} \right. $
cbse
class12
bookproblem
ch5
sec1
q9
p159
sec-b
medium
math
asked
Nov 9, 2012
by
thanvigandhi_1
1
answer
Find all points of discontinuity of $f$, where $f$ is defined by $ f(x) = \left\{ \begin{array} {1 1} \large \frac{ |\;x\;| }x,& \quad\text{ if x \(\neq\) 0 }\\ 0 ,& \quad \text{if $x$ =0}\\ \end{array} \right. $
cbse
class12
bookproblem
ch5
sec1
q8
p159
sec-b
easy
math
asked
Nov 9, 2012
by
thanvigandhi_1
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
Find all points of discontinuity of \(f\), where \(f\) is defined by $ f(x) = \left\{ \begin{array} {1 1} |\;x\;| + 3,& \quad\text{ if $ x $ \(\leq -3\)}\\ -2x ,& \quad \text{if $-3$ <x< 3}\\ 6x+2, & \quad\text{if $x$ \(\geq 3\)}\\ \end{array} \right. $
cbse
class12
bookproblem
ch5
sec1
q7
p159
sec-b
medium
math
asked
Nov 8, 2012
by
thanvigandhi_1
1
answer
Prove that the greatest integer function defined by $ f(x) = [x], 0<x<3$ is not differentiable at $x = 1 $ and $ x = 2 $
cbse
class12
bookproblem
ch5
sec2
q10
p166
exercise5-2
sec-b
easy
math
asked
Nov 8, 2012
by
thanvigandhi_1
1
answer
Prove that the function \( f \) given by $f(x) = | x - 1 |, x \in R\;$ is not differentiable at $\; x = 1$.
cbse
class12
bookproblem
ch5
sec2
q9
p166
exercise5-2
sec-b
medium
math
asked
Nov 8, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions with respect to x in $\;\cos(\sqrt {x} \;) $
cbse
class12
bookproblem
ch5
sec2
q8
p166
exercise5-2
sec-a
easy
math
asked
Nov 8, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions with respect to x: $\;2\sqrt {cot (x^2)}$
cbse
class12
bookproblem
ch5
sec2
exercise5-2
p166
q7
sec-b
easy
math
asked
Nov 8, 2012
by
thanvigandhi_1
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
Differentiate the functions with respect to x: $ cos \; x^3. sin^2 (x)^5 $
cbse
class12
bookproblem
ch5
sec2
exercise5-2
p166
q6
sec-b
medium
math
asked
Nov 8, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions with respect to $x: \large \frac{ sin\; (ax + b) } { cos \;( cx + d)} $
cbse
class12
bookproblem
ch5
sec2
exercise5-2
p166
sec-b
easy
q5
math
asked
Nov 8, 2012
by
thanvigandhi_1
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
Find all points of discontinuity of $f$, where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} 2x + 3,& \quad\text{ if $ x $ \(\leq 2\)}\\ 2x - 3,& \quad \text{if $x$ > 1}\\ \end{array} \right. $
cbse
class12
bookproblem
ch5
sec1
q6
p159
sec-b
medium
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Is the function f defined by $f(x) = \left\{\begin{array}{l l} x, & \quad \text{if $x$ \( \leq \) 1}\\ 5, & \quad \text{if $x$ > 1}\\ \end{array} \right.$ continuous at $(x = 0)$? At $(x = 1)$? At $(x = 2)$?
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q5
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Show that each of the relation $R$ in the set $A=\{x\in Z: 0 \leq x \leq 12\}$, given by $(i) R = \{(a,b) |a-b|$ is a multiple of 4 $\}$ is an equivalence relation. Find the set of all elements related to 1.
cbse
class12
bookproblem
ch1
ex1-1
q9
p6
easy
sec-a
modelpaper
2012
q13
math
asked
Nov 7, 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
Differentiate the functions with respect to $x$: $sec \;( tan (\sqrt x ) )$
cbse
class12
bookproblem
ch5
sec2
exercise5-2
p166
sec-a
easy
q4
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Differentiate the function with respect to x: $cos\;(sin x)$
cbse
class12
bookproblem
ch5
sec2
exercise5-2
p166
sec-a
easy
q2
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions with respect to x: $ \; sin ( x^2 + 5 ) $
cbse
class12
bookproblem
ch5
sec2
exercise5-2
p166
q-1
sec-a
easy
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Discuss the continuity of the following functions: \[ f ( x ) = sin\; x . cos\; x \]
cbse
class12
bookproblem
ch5
sec1
q21c
p160
math
sec-b
asked
Nov 7, 2012
by
thanvigandhi_1
0
answers
Discuss the continuity of the following functions: \[ f ( x ) = sin\; x - cos\; x \]
cbse
class12
bookproblem
ch5
sec1
q21b
p160
math
sec-b
asked
Nov 7, 2012
by
thanvigandhi_1
0
answers
Discuss the continuity of the following functions: \[ f ( x ) = sin\; x + cos\; x \]
cbse
class12
bookproblem
ch5
sec1
q21a
p160
math
sec-b
asked
Nov 7, 2012
by
thanvigandhi_1
0
answers
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
Examine the following functions for continuity. $f(x) = | \;x - 5\;|$
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q3
q3-4
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Examine the following functions for continuity $\; f(x) = \large \frac {x^2 - 25} {x + 5}$$, x\:\neq\: -5$
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q3
q3-3
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Examine the following functions for continuity. $f(x) = \frac {1} { x - 5}, x \: \neq \: 5 $
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q3
q3-2
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
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