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Recent questions tagged sec-a
Questions
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
Find $ \frac {dy}{dx} $ in the following: $ \sin^2x +\cos^2y = 1 $
cbse
class12
bookproblem
ch5
sec3
q8
p169
exercise5-3
sec-a
easy
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find $ \frac {dy}{dx} $ in the following: $ x^3 +x^2y + xy^2 +y^3 = 81 $
cbse
class12
bookproblem
ch5
sec3
q6
p169
exercise5-1
easy
sec-a
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find $ \frac {dy}{dx} $ in the following: $ x^2 +xy + y^2 = 100 $
cbse
class12
bookproblem
ch5
sec3
q5
p169
exercise5-3
sec-a
easy
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find $ \frac {dy}{dx} $ in the following: $ xy +y^2 = tan \: x + y $
cbse
class12
bookproblem
ch5
sec3
q4
p169
exercise5-3
sec-a
easy
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find $\frac {dy}{dx}$ in the following: $ax +by^2 = cos \: y$
cbse
class12
bookproblem
ch5
sec3
q3
p169
sec-a
easy
exercise5-3
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find $\frac {dy}{dx}$ in the following: $2x +3y = sin \: y$
cbse
class12
bookproblem
ch5
sec3
q2
p169
exercise5-3
sec-a
easy
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find $\frac {dy}{dx}$ in the following: $2x +3y = sin \: x$
cbse
class12
bookproblem
ch5
sec3
exercise5-3
169
q-1
sec-a
easy
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find the values of $k$ so that the function $f$ is continuous at the indicated point in $f(x) = \left\{ \begin{array} {1 1} kx+1 ,& \quad\text{ if $ x $ \(\leq \pi\)}\\ \cos x,& \quad \text{if $x$ > \(\pi\)}\\ \end{array} \right.$ at $x = \pi$
cbse
class12
bookproblem
ch5
sec1
q28
p161
sec-a
easy
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Determine if $f$ defined by $f(x) = \left\{ \begin{array} {1 1} x^2sin \large\frac{ 1 }{x},\normalsize & \quad\text{ if x \(\neq\) 0 }\\ 0 ,& \quad \text{if $x$ =0}\\ \end{array} \right. $ is a continuous function?
cbse
class12
bookproblem
ch5
sec1
q24
p160
sec-a
easy
math
asked
Nov 10, 2012
by
thanvigandhi_1
1
answer
For what value of \( \lambda \) is the function defined by \(f\) defined by $ f(x) = \left\{ \begin{array} {1 1} \lambda(x^2 - 2x) ,& \quad\text{ if $ x $ \(\leq 0\)}\\ 4x + 1,& \quad \text{if $x$ > 0}\\ \end{array} \right. $ Continuous at \(x = 0\)?
cbse
class12
bookproblem
ch5
sec1
q18
q18-1
p160
sec-a
easy
math
asked
Nov 10, 2012
by
thanvigandhi_1
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
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
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
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
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
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
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 \(A\) 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
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
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
Examine the following functions for continuity. $f(x) = x-5$
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q3
q3-1
math
asked
Nov 6, 2012
by
thanvigandhi_1
1
answer
Prove that the function \( f (x) = x^n \) is continuous at \( x = n \), where n is a positive integer.
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q4
math
asked
Nov 5, 2012
by
thanvigandhi_1
1
answer
Examine the continuity of the function $f (x) = 2x^2 - 1$ at $x = 3$
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
q2
sec-a
easy
math
asked
Nov 5, 2012
by
thanvigandhi_1
1
answer
Prove that the function $f (x) = 5x-3$ is continuous at $x=0$, $x=-3$ and $x=5$.
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
q1
sec-a
easy
math
asked
Nov 5, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer. The planes: 2x – y + 4z = 5 and 5x – 2.5y + 10z = 6 are:
cbse
class12
additionalproblem
easy
sec-a
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Find the vector equation of the line passing through $(1, 2, 3)$ and perpendicular to the plane $\hat{r} . (\hat{i} +2\hat{j} -5\hat{k}) +9 = 0$
cbse
class12
bookproblem
ch11
misc
p498
q7
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
If the lines $\large\frac{x-1} {-3} = \frac{y-2}{2k} = \frac{z-3}{2}$ and $\large\frac{x-1}{3k} = \frac{y-1}{1} = \frac{z-6}{-5}$ are perpendicular, find the value of $k$.
cbse
class12
bookproblem
ch11
misc
p498
q6
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
If the coordinates of the points $A, B, C, D$ be (1, 2, 3), (4, 5, 7), (-4, 3, -6) and (2, 9, 2) respectively, then find the angle between the lines $AB$ and $CD$.
cbse
class12
bookproblem
ch11
misc
p498
q5
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Find the equation of a line parallel to x-axis and passing through the origin.
cbse
class12
bookproblem
ch11
misc
p498
q4
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
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