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Recent questions tagged q27
Questions
Given $ A=\begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$ such that $ |A|=-10.\;Find\;a_{11}c_{11}+a_{12}c_{12}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q27
p8
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
Using integration, find the area of triangle PQR, whose vertices are P(3, 0)Q(4, 5) and R(5, 1).
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 24, 2013
by
thanvigandhi_1
0
answers
A variable plane, which remains at a constant distance '3p' from the origin cuts the coordinate axes at A, B and C. Show that locus of the centroid of the triangle is \(\large \frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2} = \frac{1}{p^2} .\)
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 23, 2013
by
thanvigandhi_1
0
answers
Prove that relation R defined on the set N of natural numbers by \[x\;R\;y \Leftrightarrow 2x^2-3xy+y^2=0\] is not symmetric but it is reflexive.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q27
p4
math
sec-b
asked
Jan 23, 2013
by
meena.p
1
answer
Find the shortest distance between the lines $\large \frac{x-8}{3} = \frac{y+9}{-16} = \frac{z-10}{7}$$ \: and \: \large\frac{x-15}{3} = \frac{y-29}{8} = \frac{z-5}{-5} $ Also find equation of the shortest distance
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 22, 2013
by
thanvigandhi_1
0
answers
Find the distance of the point (-2, 3, -4) from the line \( \large \frac{x+2}{3} = \frac{2y+3}{4} = \frac{3z+4}{5} \) measured parallel to the plane \( 4x+12y-3z+1=0.\)
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 21, 2013
by
thanvigandhi_1
0
answers
Solve :$\large\frac{dy}{dx}$$=\cos (x+y)+\sin (x+y)$.[Hint :Substitute x+y=z]
cbse
class12
ch9
sec-b
q27
p194
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
If $\mid\overrightarrow a\mid=10,\mid\overrightarrow b\mid=2$ and $\overrightarrow a.\overrightarrow b=12$,then value of $\mid\overrightarrow a\times\overrightarrow b\mid$ is
cbse
class12
ch10
q27
p218
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Find the distance of a point (1, -2, 3) from the plane x-y+z=5, measured parallel to the line $\large\frac{x}{2}=\frac{y}{3}=\frac{z}{-6} $
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 16, 2013
by
thanvigandhi_1
0
answers
The area of the region in the first quadrant enclosed by the x-axis,the line y=x and the circle $x^2+y^2=32$ is \begin{array}{1 1}(A)\;16\pi\; sq.units & (B)\;4\pi \;sq.units\\(C)\;32\pi\; sq.units & (D)\;24\pi\;sq.units \end{array}
cbse
class12
ch8
q27
p178
objective
exemplar
sec-b
difficult
math
asked
Jan 16, 2013
by
sreemathi.v
2
answers
Find the image of (1, 3, 4) in the plane x-y+z=5.
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 15, 2013
by
thanvigandhi_1
0
answers
Evaluate the following as limits of sums: $\int\limits_0^2(x^2+3)dx$
cbse
class12
ch7
q27
p165
short-answer
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Find the maximum area of an isosceles triangle inscribed in the ellipse \( \frac{\large x^2}{\large a^2}+\frac{\large y^2}{\large b^2}=1\) with its vertex at one end of the major axis.
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 13, 2013
by
thanvigandhi_1
0
answers
A telephone company in a town has 500 subscribers on its list and collects fixed charges of Rs300/- per subscriber per year.The company proposes to increase the annual subscription and it is believed that for every increase of Re1/- one subscriber will discontinue the service.Find what increase will bring maximum profit?
cbse
class12
ch6
q27
p137
exemplar
math
sec-b
asked
Jan 11, 2013
by
sreemathi.v
0
answers
Find the shortest distance between the lines : $\overrightarrow r = (1+2\lambda ) \hat i + (2+3\lambda)\hat j + (3+4\lambda)\hat k $ and $ \overrightarrow r = (2+3\mu ) \hat i + 4(1+\mu)\hat j + 5(1+\mu)\hat k $
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 11, 2013
by
thanvigandhi_1
0
answers
Find the equation of plane passing through the (-1, -1, 2) and \( \bot \) to each of the following planes : \( 2x+3y-3z=2 \: and \: 5x-4y+z=6 \).
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 10, 2013
by
thanvigandhi_1
0
answers
Show that the planes \( 2x+y+3x-2 = 0 \: and \: x-2y+5=0\) are perpendicular to each other.
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
A biased die is such that $P(4)=\Large \frac{1}{10}$ and other scores being equally likely.The die is tossed twice.If X is the number of fours seen',find the variance of the random variable X.
cbse
class12
ch13
q27
p274
short-answer
exemplar
sec-a
easy
math
asked
Jan 9, 2013
by
sreemathi.v
1
answer
Show that the line joining the origin to the point (2, 1, 1) is perpendicular the line determined by the point (3, 5, -1),(4, 3, -1).
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 8, 2013
by
thanvigandhi_1
0
answers
Find the equation of the plane which contains the line of intersection of the planes $ \overrightarrow r. (\hat i + 2\hat j + 3\hat k ) -4 = 0 \overrightarrow r. (2\hat i + \hat j - \hat k ) + 5 = 0$ and which is perpendicular to the plane $\overrightarrow r. (5\hat i + 3\hat j - 6\hat k ) + 8 = 0 $ .
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 7, 2013
by
thanvigandhi_1
1
answer
If \( l_1, m_1, n_1 \: and \: l_2, m_2, n_2 \) are direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are \( m_1n_2-m_2n_1, n_1l_2-n_2l_1, l_1m_2-l_2m_1.\)
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 4, 2013
by
thanvigandhi_1
0
answers
Show that the straight lines whose direction cosines are given by $2l+2m-n=0\;and\;mn+nl+lm=0$ are at right angles.
cbse
class12
ch11
q27
p237
exemplar
difficult
sec-c
math
asked
Jan 4, 2013
by
sreemathi.v
1
answer
Find the vector equation of the line through the point ( 1, 2, -4 ) and perpendicular to the two lines $\large \frac{x-8}{3}=\frac{y+19}{-16}=\frac{z-10}{7} $ and, $ \large\frac{x-15}{3}=\frac{y-29}{8}=\frac{z-5}{-5} $
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 3, 2013
by
thanvigandhi_1
0
answers
Find the distance of the point ( -2, 3, -4 ) from the line \(\large \frac{x+2}{3}=\frac{2y+3}{4}=\frac{3z+4}{5}\), measured parallel to the plane \( 4x+12y-3z+1=0\).
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 2, 2013
by
thanvigandhi_1
0
answers
From the point P(1, 2, 4 ) a perpendicular is drawn on the plane \( 2x+y-2z+3 = 0 \). Find the equation of the length and coordinates of the foot of the \( \bot \)
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 2, 2013
by
thanvigandhi_1
1
answer
Differentiate the following w.r.t $x$ : $log\bigg(x+\sqrt{ x^2+a}\bigg)$.
cbse
class12
ch5
q27
p109
short-answer
exemplar
sec-b
easy
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Find the equation of plane determined by the points A(3, -1, 2), B(5, 2, 4) and C(-1, -1, 6). Also find the distance of the point P(6, 5, 9) from the plane.
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Dec 29, 2012
by
thanvigandhi_1
1
answer
The determinant $\begin{vmatrix}b^2 - ab & b - c & bc - ac\\ab - a^2 & a - b & b^2 - ab\\bc - ac & c - a & ab -a^2\end{vmatrix}$ equals
cbse
class12
ch4
sec-a
q27
p80
objective
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
Show that the lines $ \large\frac{x+3}{-3} = \frac{y-1}{1} = \frac{z-5}{5} $ and $\large \frac{x+1}{-1} = \frac{y-2}{2} = \frac{z-5}{5} $ are coplanar. Also find the equation of the plane.
cbse
class12
modelpaper
2011
sec-c
q27
math
asked
Dec 26, 2012
by
thanvigandhi_1
1
answer
Find the coordinates of the foot of the perpendicular distance of the poit (1, 3, 4) from the plane \( 2x - y + z + 3 = 0 \). Find also, the image of the point in the plane.
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Dec 25, 2012
by
thanvigandhi_1
0
answers
A point on the hypotenuse of a triangle is at distance 'a' and 'b' fro the sides of the triangle. Show that the minimum length of the hypotenuse is $ \bigg( a^{\large\frac{2}{3}} + b^{\large\frac{2}{3}} \bigg)^{\frac{2}{3}}. $
cbse
class12
modelpaper
2008
sec-c
q27
math
asked
Dec 24, 2012
by
thanvigandhi_1
0
answers
Evaluate \[ \int_{-2}^2 \mathrm \: | 1 - x^2 |dx \]
cbse
class12
modelpaper
2012
sec-b
q27
math
asked
Dec 22, 2012
by
thanvigandhi_1
0
answers
If $A=\begin{bmatrix}0 & -1 & 2\\4 & 3 & -4\end{bmatrix}\;and\;B=\begin{bmatrix}4 & 0\\1 & 3\\2 & 6\end{bmatrix},then\;verify \;that:(i)\quad(A')'=A$
cbse
class12
ch3
q27
q27-1
p56
short-answer
exemplar
sec-a
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
The value of $\sin(\tan^{-1}(.75))$ is equal to
cbse
class12
ch2
q27
p38
objective
exemplar
medium
sec-b
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
Coloured balls are distributed in three bags as shown in the table below, a bag is selected at random and then two balls are randomly drawn from the selected bag. They happen to be black and red. what is the probability that they came from bag 1 ?
cbse
class12
modelpaper
2009
sec-c
q27
math
asked
Dec 20, 2012
by
thanvigandhi_1
1
answer
Find the equation of the plane passing through the point ( -1, -1, 2 ) and perpendicular to each of the following planes : $2x + 3y - 3z = 2 \: and \: 5x - 4y + z = 6 $
cbse
class12
modelpaper
2008-1
sec-c
q27
math
asked
Dec 19, 2012
by
thanvigandhi_1
0
answers
Let * be binary operation defined on R by $ a*b=1+ab, a,b \in R.$ Then the operation * is
cbse
class12
ch1
q27
p13
exemplar
sec-b
math
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Integrate the function\[\sqrt{\sin2x}\cos2x\]
cbse
class12
bookproblem
ch7
sec2
q27
p305
sec-a
easy
math
asked
Dec 5, 2012
by
sreemathi.v
1
answer
By using the properties of definite integrals, evaluate the integral $\int\limits_0^\frac{\Large \pi}{\Large 2}(2 \log \sin x-\log \sin 2x)\;dx$
cbse
class12
bookproblem
ch7
sec11
q10
p347
sec-b
medium
modelpaper
2012
q27
math
asked
Dec 3, 2012
by
sreemathi.v
1
answer
Evaluate the definite integrals\[\int\limits_0^\frac{\pi}{2}\frac{\cos^2xdx}{\cos^2x+4\sin^2x}\]
cbse
class12
bookproblem
ch7
misc
q27
p353
sec-b
difficult
math
asked
Dec 3, 2012
by
sreemathi.v
1
answer
Choose the correct answer in the point on the curve \( x^2 = 2y\) which is nearest to the point \((0, 5)\) is
cbse
class12
bookproblem
ch6
sec5
q27
p234
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the line $y = x + 1$ is a tangent to the curve $y^2 = 4x$ at the point
cbse
class12
bookproblem
ch6
sec3
q27
p213
sec-a
easy
math
asked
Nov 26, 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^2 ,& \quad\text{ if $ x $ \(\leq 2\)}\\ 3,& \quad \text{if $x$ > 2}\\ \end{array} \right. \qquad at \;x = 2 $
cbse
class12
bookproblem
ch5
sec1
q27
p161
sec-b
easy
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
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