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Recent questions tagged exemplar
Questions
Two curves $x^3-3xy^2+2=0$ and $3x^2-y^3-2=0$ intersect at an angle of
cbse
class12
ch6
q45
p140
objective
exemplar
sec-a
difficult
math
asked
Aug 12, 2013
by
sreemathi.v
1
answer
If $x^my^n=(x+y)^{m+n}$,Prove that $(ii)\;\large\frac{d^2y}{dx^2}=$$0$
cbse
class12
ch5
q80
q80-2
p113
exemplar
sec-b
medium
math
asked
Jul 3, 2013
by
sreemathi.v
1
answer
If $\overrightarrow{a}=\hat i+\hat j+2\hat k\;and\;\overrightarrow{b}=2\hat i+\hat j-2\hat k,$then find the unit vector in the direction of $\;2\overrightarrow{ a}- \overrightarrow{b}$
cbse
class12
ch10
q2ii
p215
exemplar
easy
sec-a
math
asked
May 24, 2013
by
meena.p
1
answer
If A and B are square matrices of the same order,then $(iii)\quad [k(A-B)']=\text{________}.$
cbse
class12
ch3
q76
q76-3
p63
fitb
exemplar
sec-a
easy
math
asked
Apr 3, 2013
by
sreemathi.v
1
answer
If A and B are square matrices of the same order,then $(ii)\quad (kA)'=\text{________}.$(k is any scalar)
cbse
class12
ch3
q76
q76-2
p63
fitb
exemplar
sec-a
easy
math
asked
Apr 3, 2013
by
sreemathi.v
1
answer
If A and B are symmetric matrices,then $(ii)\quad BA-2AB\;is\;a\;\text{_______}$
cbse
class12
ch3
q78
q78-2
p63
fitb
exemplar
easy
sec-a
math
asked
Apr 3, 2013
by
sreemathi.v
1
answer
If a matrix has 13 elements.What are the possible orders it can have? (Note: This question has been split into 2 questions)
cbse
class12
ch3
sec4
q1-2
p52
shortanswer
exemplar
easy
sec-a
math
asked
Mar 19, 2013
by
sreemathi.v
1
answer
If $\begin{vmatrix}4+x& 4-x & 4-x\\4-x & 4+x & 4-x\\4-x & 4-x & 4+x\end{vmatrix}$,then find the values of x.
cbse
class12
ch4
sec-b
q13
p78
shortanswer
exemplar
medium
math
asked
Mar 18, 2013
by
sreemathi.v
1
answer
If the coordinates of the vertices of an equilateral triangle with sides of length 'a' are $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ then \[{\begin{vmatrix}x_1 & y_1 &1\\x_2 & y_2 &1\\x_3 & y_3 & 1\end{vmatrix}}^2=\frac{3a^4}{4}.\]
cbse
class12
ch4
sec-b
q11
p78
short-answer
exemplar
difficult
math
asked
Mar 15, 2013
by
sreemathi.v
1
answer
If A+B+C=0,then prove that $\begin{vmatrix}1& cosC &cos B\\cos C& 1 &cos A\\cos B & cos A &1\end{vmatrix}=0.$
cbse
class12
ch4
sec-b
q10
p78
short-answer
exemplar
medium
math
asked
Mar 15, 2013
by
sreemathi.v
1
answer
Using the properties of determinants,\[\begin{vmatrix}a^2+2a &2a+1 & 1\\2a+1 & a+2 & 1\\3 & 3 & 1\end{vmatrix}=(a-1)^3\]
cbse
class12
ch4
sec-b
q9
p78
short-answer
exemplar
easy
math
asked
Mar 15, 2013
by
sreemathi.v
1
answer
Let X={1,2,3} and Y={4,5}.Find whether the following subsets of X x Y are functions from X to Y or not.$(iv)\quad k=\{(1,4),(2,5)\} $
cbse
class12
ch1
q12
q12-4
p11
exemplar
sec-a
easy
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Let X={1,2,3} and Y={4,5}.Find whether the following subsets of X x Y are functions from X to Y or not.$(iii)\quad h=\{(1,4),(2,5),(3,5)\} $
cbse
class12
ch1
q12
q12-3
p11
exemplar
sec-a
easy
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Let X={1,2,3} and Y={4,5}.Find whether the following subsets of X x Y are functions from X to Y or not.$(ii)\quad g=\{(1,4),(2,4),(3,4)\} $
cbse
class12
ch1
q12
q12-2
p11
exemplar
easy
sec-a
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
If $\;A=\small\frac{1}{\pi}$$\begin{bmatrix}sin^{-1}(\pi x) &tan^{-1}\big(\frac{\pi}{x}\big)\\ sin^{-1}\big(\frac{\pi}{x} \big)&cot^{-1}(\pi x)\end{bmatrix}\;$ and $\;B=\small\frac{1}{\pi} $$\begin{bmatrix}-cos^{-1}(\pi x) &tan^{-1}\big(\frac{x}{\pi}\big)\\ sin^{-1}\big(\frac{x}{\pi} \big)&-tan^{-1}(\pi x)\end{bmatrix}$ then $A-B$ is equal to
cbse
class12
ch3
q56
p60
objective
exemplar
easy
sec-a
math
jeemain
matrices-and-determinants
matrices
asked
Mar 10, 2013
by
sreemathi.v
1
answer
If possible,using elementary row transformations,find the inverse of the following matrices $\quad\begin{bmatrix}2 & 0 & -1\\5 & 1 & 0\\0& 1 & 3\end{bmatrix}$
cbse
class12
ch3
q51
q51-3
p59
exemplar
sec-c
math
asked
Mar 9, 2013
by
sreemathi.v
1
answer
If possible,using elementary row transformations,find the inverse of the following matrices $(ii)\quad\begin{bmatrix}2 & 3 & -3\\-1 & -2 & 2\\1& 1 & -1\end{bmatrix}$
cbse
class12
ch3
q51
q51-2
p59
exemplar
sec-a
easy
math
asked
Mar 9, 2013
by
sreemathi.v
1
answer
If $\begin{bmatrix}xy & 4\\z+6 & x+y\end{bmatrix}=\begin{bmatrix}8 & w \\ 0 & 6\end{bmatrix}$ then find the value of x,y,z and w
cbse
class12
ch3
q38
p57
short-answer
exemplar
easy
sec-a
math
asked
Mar 7, 2013
by
sreemathi.v
1
answer
Find inverse,by elementary row operations(if possible),of the following matrices$(ii)\quad\begin{bmatrix}1 &- 3\\-2 & 6\end{bmatrix}$
cbse
class12
ch3
q37
q37-2
p57
short-answer
exemplar
sec-a
easy
math
asked
Mar 7, 2013
by
sreemathi.v
1
answer
Show that the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\lambda \;and\;\frac{x-4}{5}=\frac{y-1}{2}=z=\mu\;$intersect. Also,find thier point of intersection.
cbse
class12
ch11
q3
p235
exemplar
medium
sec-a
math
asked
Mar 7, 2013
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}1 & 2\\4 & 1\\5 & 0\end{bmatrix},B=\begin{bmatrix}1 & 2\\6 & 4\\7 & 3\end{bmatrix},then\;verify\;that:(ii)\quad(A-B)'=A'-B'$.
cbse
class12
ch3
q28
q28-2
p56
short-answer
exemplar
sec-b
easy
math
asked
Mar 6, 2013
by
sreemathi.v
1
answer
$A=\begin{bmatrix}0 & -1 & 2\\4 & 3 & -4\end{bmatrix}\;and\;B=\begin{bmatrix}4 & 0\\1 & 3\\2 & 6\end{bmatrix},then\;verify \;that:(iii)\quad(KA)'=(KA')$
cbse
class12
ch3
q27
q27-3
p56
short-answer
exemplar
sec-a
easy
math
asked
Mar 6, 2013
by
sreemathi.v
1
answer
$A=\begin{bmatrix}0 & -1 & 2\\4 & 3 & -4\end{bmatrix}\;and\;B=\begin{bmatrix}4 & 0\\1 & 3\\2 & 6\end{bmatrix},then\;verify \;that:(ii)\quad(AB)'=B'A'$
cbse
class12
ch3
q27
q27-2
p56
short-answer
exemplar
easy
sec-b
math
asked
Mar 6, 2013
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}1 & 2\\-2 & 1\end{bmatrix},B=\begin{bmatrix}2 & 3\\3 & -4\end{bmatrix}\;and\;C=\begin{bmatrix}1 & 0\\-1 & 0\end{bmatrix},verify:(ii)\;A(B+C)=AB+AC$
cbse
class12
ch3
q22
q22-2
p55
shortanswer
exemplar
sec-b
medium
math
asked
Mar 5, 2013
by
sreemathi.v
1
answer
Each of the following defines a relation on $N : (iii)\quad x\;y\;is\;square\; of\; an\; integer\;x,y\quad N$
cbse
class12
ch1
q22-3
p12
exemplar
sec-a
math
asked
Mar 4, 2013
by
meena.p
1
answer
Each of the following defines a relation on $ N : (ii)\quad x+y=10,x,y\quad N$
cbse
class12
ch1
q22-2
p12
exemplar
sec-b
easy
math
asked
Mar 4, 2013
by
meena.p
1
answer
Let A=[-1,1].Then,dicuss whether the following functions defined on A are one-one,onto or bijective:$ (iv)\quad k(x)\;=\;x^2$
cbse
class12
ch1
q21-4
p12
exemplar
sec-a
medium
math
asked
Mar 4, 2013
by
meena.p
1
answer
Let A=[-1,1].Then,dicuss whether the following functions defined on A are one-one,onto or bijective$(iii)\quad h(x)\;=\;x|x| $
cbse
class12
ch1
q21-3
p12
exemplar
sec-a
medium
math
asked
Mar 4, 2013
by
meena.p
1
answer
If $X=\begin{bmatrix}3 & 1 & 1\\5 & 2 & 3\end{bmatrix}$ and $Y=\begin{bmatrix}2 & 1 & 1\\7 & 2 & 4\end{bmatrix}$, find a matrix $Z$ such that $X+Y+Z$ is a zero matrix.
cbse
class12
ch3
q7
q7-3
p53
shortanswer
exemplar
sec-a
math
asked
Mar 4, 2013
by
sreemathi.v
1
answer
If $X=\begin{bmatrix}3 & 1 & 1\\5 & 2 & 3\end{bmatrix}$ and $Y=\begin{bmatrix}2 & 1 & 1\\7 & 2 & 4\end{bmatrix}$, find $2X-3Y$
cbse
class12
ch3
q7
q7-2
p53
short-answer
exemplar
sec-a
math
asked
Mar 4, 2013
by
sreemathi.v
1
answer
Construct $a_{2\times 2}$ matrix where $a_{ij} =|2i+3j|$
cbse
class12
ch3
q3
q3-2
p53
short-answer
exemplar
sec-a
math
asked
Mar 4, 2013
by
sreemathi.v
1
answer
In the matrix $A=\begin{bmatrix} a & 1 & x \\ 2 & \sqrt 3 & x^2 y \\ 0 & 5 & \frac{2}{5} \end{bmatrix}$, write the elements $a_{23}$, $a_{31}$, $a_{12}$
cbse
class12
ch3
q2
q2-3
p52
shortanswer
exemplar
sec-a
math
asked
Mar 4, 2013
by
sreemathi.v
1
answer
In the matrix $A=\begin{bmatrix} a & 1 & x \\ 2 & \sqrt 3 & x^2 y \\ 0 & 5 & \frac{2}{5} \end{bmatrix} write:(ii) Element\; of \;the\; matrices.$
cbse
class12
ch3
q2
q2-2
p52
shortanswer
exemplar
sec-a
easy
math
asked
Mar 4, 2013
by
sreemathi.v
1
answer
Let A=[-1,1].Then,dicuss whether the following functions defined on A are one-one,onto or bijective:$(ii)\quad g(x)\;=\;|\;x\;|$
cbse
class12
ch1
q21-2
p12
exemplar
sec-a
medium
math
asked
Mar 4, 2013
by
meena.p
1
answer
Give an example of a map$(iii)\quad which\; is\; neither\;one-one\;nor\;onto$
cbse
class12
ch1
q19-3
exemplar
sec-a
medium
math
asked
Mar 4, 2013
by
meena.p
1
answer
Give an example of a map$(ii)\quad which\;is\;not\;one-one\;but\; not\; onto$
cbse
class12
ch1
q19-2
exemplar
sec-a
easy
math
asked
Mar 4, 2013
by
meena.p
1
answer
Are the following set of ordered pairs function? If so,examine whether the mapping is injective or subjective $\;\{(a,b)\;:\;a\;$ is a person,$b\;$ is an ancestor of $a\}$
cbse
class12
ch1
q8
q8-2
p11
short-answer
exemplar
sec-a
easy
math
asked
Mar 1, 2013
by
meena.p
1
answer
Differentiate each of the following w.r.t $x$: $tan^{-1}\large\frac{3a^2x-x^3}{a^3-3ax^2}$, $\frac{1}{\sqrt 3}< \frac{x}{a} <\frac{-1}{\sqrt 3}$
cbse
class12
ch5
q42
p110
short-answer
exemplar
sec-a
difficult
math
asked
Feb 19, 2013
by
sreemathi.v
1
answer
Find the simplified form of $cos^{-1}(\frac{3}{5}cos x+\frac{4}{5}sin x),$where $x\in (\frac{-3}{4},\frac{3}{4})$
cbse
class12
ch2
q13
p36
exemplar
medium
sec-b
math
asked
Feb 19, 2013
by
sreemathi.v
1
answer
Prove that $tan^{-1}\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}=\frac{\pi}{4}+\frac{1}{2}cos^{-1}x^2$
cbse
class12
ch2
q12
p36
exemplar
sec-b
math
asked
Feb 19, 2013
by
sreemathi.v
1
answer
Show that $2tan^{-1}(-3)=\frac{-\pi}{2}+tan^{-1}\bigg(\frac{-4}{3}\bigg)$
cbse
class12
ch2
q6
p35
exemplar
difficult
sec-b
math
asked
Feb 19, 2013
by
sreemathi.v
1
answer
Find the value of $tan^{-1}\frac{-1}{\sqrt 3}+cot^{-1}\frac{1}{\sqrt 3}-tan^{-1}sin\frac{\pi}{2}$
cbse
class12
ch2
q4
p35
exemplar
easy
sec-a
math
asked
Feb 19, 2013
by
sreemathi.v
1
answer
Prove that \[cot(\frac{\pi}{4}-2cot^{-1}3)=7\]
cbse
class12
ch2
q3
p35
exemplar
medium
sec-b
math
asked
Feb 19, 2013
by
sreemathi.v
1
answer
Evaluate $cos\bigg(cos^{-1}\bigg(\frac{-\sqrt{3}}{2}\bigg)+\frac{\pi}{6}\bigg)$
cbse
class12
ch2
q2
p35
exemplar
easy
sec-a
math
asked
Feb 19, 2013
by
sreemathi.v
1
answer
True-or-False: The differential equation of all non horizontal lines in a plane is $\large\frac{d^2y}{dy^2}$$=0$.
cbse
class12
ch9
q77xi
p203
true-or-false
exemplar
easy
sec-a
math
asked
Jan 21, 2013
by
sreemathi.v
1
answer
True-or-False: Solution of $x\frac{dy}{dx} - y = x\tan\frac{y}{x}$ is $\sin\bigg(\frac{y}{x}\bigg)=kx$.
cbse
class12
ch9
sec-a
q77x
p203
true-or-false
exemplar
medium
math
asked
Jan 21, 2013
by
sreemathi.v
1
answer
True-or-False: The solution of the differential equation $\large\frac{dy}{dx} = \frac{x+2y}{x}$ is $x+y=kx^2$.
cbse
class12
ch9
sec-a
q77ix
p203
true-or-false
exemplar
medium
math
asked
Jan 21, 2013
by
sreemathi.v
1
answer
True-or-False: Differential equation representing the family of curves $y=e^x(A\cos x+B\sin x)$ is $\frac{d^2y}{dx^2} - 2\frac{dy}{dx} + 2y = 0$.
cbse
class12
ch9
sec-a
q77viii
p203
true-or-false
exemplar
medium
math
asked
Jan 21, 2013
by
sreemathi.v
1
answer
True-or-False: The solution of $\large\frac{dy}{dx}$$=\bigg(\large\frac{y}{x}\bigg)^\frac{1}{3}$ is $y^{\large\frac{2}{3}}-x^{\large\frac{2}{3}}=c$.
cbse
class12
ch9
sec-a
q77vii
p203
true-or-false
exemplar
easy
math
asked
Jan 20, 2013
by
sreemathi.v
1
answer
True-or-False: The differential equation representing the family of circles $x^2+(y-a)^2=a^2$ will be of order two.
cbse
class12
ch9
q77vi
p203
true-or-false
exemplar
sec-a
math
asked
Jan 20, 2013
by
sreemathi.v
1
answer
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