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Recent questions tagged additionalproblem
Questions
Find the equation of the plane passing through the point (1,6,3) and perpendicular to the plane 2x+3y-z = 7
cbse
class12
additionalproblem
kvquestionbank2012
ch11
q5
p37
math
asked
Feb 5, 2013
by
meena.p
1
answer
Find the value of k for which the two lines $ \large\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}\; and \;\frac{x-3}{1}=\frac{y-k}{2}=z$ intersect at a point?
cbse
class12
additionalproblem
kvquestionbank2012
ch11
q4
p37
math
asked
Feb 5, 2013
by
meena.p
0
answers
What are the conditions that the planes $ a_1x+b_1y+c_1z=d_1\;and\; a_2x+b_2y+c_2z=d_2 $ are (i) parallel (ii) perpendicular to each other?
cbse
class12
additionalproblem
kvquestionbank2012
ch11
q3
p37
math
asked
Feb 5, 2013
by
meena.p
0
answers
Find the equation of the plane passing through the point (1,4,-2) and parallel to the plane -2x+y-3z=7
cbse
class12
additionalproblem
kvquestionbank2012
ch11
q2
p37
math
asked
Feb 5, 2013
by
meena.p
0
answers
Show that the line $ \bar{r}=(2\bar{i}-2\bar{j}+3\bar{k})+\lambda(\bar{i}-\bar{j}+4\bar{k})$ is parallel to the plane.$\bar{r}.(\bar{i}+5\bar{j}+\bar{k})=5$
cbse
class12
additionalproblem
kvquestionbank2012
ch11
q1
p37
math
asked
Feb 5, 2013
by
meena.p
0
answers
If D, E & F are the mid-points of the sides of a triangle ABC, prove by vector method that area of \[\bigtriangleup DEF=\frac{1}{4}(area\;of\;\bigtriangleup ABC).\]
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q26
p36
math
asked
Feb 5, 2013
by
meena.p
0
answers
If a, b & c are the lengths of the sides opposite respectively to the angles A, B & C of a $\bigtriangleup ABC,$ using vector method show that \[a)\cos A=\frac{b^2+c^2-a^2}{2bc} \qquad b)\;a=b\cos C+c \cos B.\]
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q25
p36
math
asked
Feb 5, 2013
by
meena.p
0
answers
Prove by vector method, that the parallelogram on the same base and between the same parallels are equal in area.
cbse
class12
additionalproblem
kvquestionbank2012
q24
p36
math
asked
Feb 5, 2013
by
meena.p
0
answers
Using vector method, show that the diagonals of a Rhombus bisect each other at right angles.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q23
p36
difficult
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
Using vector method, prove that if two medians of a triangle are equal, then it is an isosceles.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q22
p36
difficult
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
Using vector method, prove that if the diagonals of a parallelogram are equal in length, then it is a rectangle.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q21
p36
difficult
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
Prove that the perpendicular bisectors of a triangle are concurrent.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q20
p36
difficult
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
Prove that the altitudes of a triangle are concurrent.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q19
p36
difficult
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
Using vector method, find the angle between two diagonals of a cube?
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q18
p36
medium
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
Using vector method prove that : $a)\;\sin (A+B)=\sin A\cos B+\cos A\sin B$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q17
q17-a
p36
medium
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
In a triangle ABC, prove that $\Large\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q16
p36
difficult
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
If $\Large\frac{1}{a},\frac{1}{b},\frac{1}{c}$are the $\large p^{th},q^{th}and\;r^{th}\;$ terms of an AP and $ \bar{u}=(q-r)\bar{i}+(r-p)\bar{j}+(p-q)\bar{k}\;and\;\bar{v}=\large\frac{1}{a}\bar{i}+\frac{1}{b}\bar{j}+\frac{1}{c}\bar{k}$ then prove that $\bar{u}\; and\;\bar{v}$ are orthogonal vectors.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q15
p35
difficult
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
Prove that the area of a paralellogram with diagonals $\bar{a}\;and\;\bar{b}\;is\;\frac{1}{2}|\bar{a} \times \bar{b}|$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q14
p35
difficult
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
Let $ \bar{a},\bar{b},\;and\;\bar{c}$ be three vectors such that $|\bar{a}|=3,|\bar{b}|=4,|\bar{c}|=5$ and each one of them being perpendicular to sum of the other two, find $ |\bar{a}+\bar{b}+\bar{c}|$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q13
p35
medium
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
L and M are the mid-points of sides BC & DC of a paralellogram ABCD. Prove that $ \overline{AL}+\overline{AM}=\frac{3}{2}\overline{AC}$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q12
p35
difficult
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
Vectors $ 2\bar{i}-\bar{j}+2\bar{k}\;and\;\bar{i}+\bar{j}-3\bar{k}$ act along two adjacent sides of a parallelogram. Find the angle between the diagonals of the parallelogram.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q11
p35
easy
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
What is the area of the parallelogram having diagonals $ 3\bar{i}+\bar{j}-2\bar{k}\;and\;\bar{i}-3\bar{j}+4\bar{k}$?
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q10
p35
easy
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
Show that in a triangle ABC the perpendicular of the point $ C $ from the line joining $ the\:points\:A\:and\:B\:is\;\Large\frac{|\bar{a} \times \bar{b}+\bar{b} \times \bar{c}+\bar{c} \times \bar{a}|}{|\bar{b}-\bar{a}|}$(Hint : use area of triangle =$\frac{1}{2}$bh)
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q9
p35
math
asked
Feb 4, 2013
by
meena.p
0
answers
If $ \hat{a}\;and\;\hat{b}$ are unit vectors inclined at an angle $\theta$,then prove that\[(a)\;\cos \frac{\theta}{2}=\frac{1}{2}|\hat{a}+\hat{b}|\qquad(b)\;\tan \frac{\theta}{2}=\frac {|\hat{a}-\hat{b}|}{|\hat{a}+\hat{b}|}\]
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q8
p35
difficult
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
Prove that angle in a semi-circle is a right angle.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q7
p35
medium
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
If $ \bar{a}\;and\;\bar{b}$ are vectors,prove that $ |\bar{a} \times \bar{b}|^2+(\bar{a}.\bar{b})^2=|\bar{a}|^2.|\bar{b}|^2$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q6
p35
easy
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
Prove Cauchy - Schawarz inequality : $(\bar{a}.\bar{b})^2\leq|\bar{a}|^2.|\bar{b}|^2$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q5
p35
math
asked
Feb 4, 2013
by
meena.p
0
answers
Prove the triangle inequality $\bigg|\overrightarrow{a}+\overrightarrow{b}\bigg|\leq\bigg|\overrightarrow{a}\bigg|+\bigg|\overrightarrow{b}\bigg|$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q4
p35
medium
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
If $ \overrightarrow {a}+ \overrightarrow {b}+ \overrightarrow {c}=\overrightarrow 0$ show that $ \overrightarrow {a} \times \overrightarrow {b}=\overrightarrow {b} \times \overrightarrow {c}=\overrightarrow {c} \times \overrightarrow {a}$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q3
p35
medium
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
If $\bar{\alpha}=3\bar{i}-\bar{j}\;and\;\bar{\beta}=2\bar{i}+\bar{j}-\bar{k}.$ Express $ \bar{\beta}$ as a sum of two vectors $ \bar{\beta_1}\;and\;\bar{\beta_2},\;where \; \bar{\beta_1}$ is parallel to $ \bar{\alpha}\;and\; \bar{\beta_2}$ is prependicular to $ \bar{\alpha}$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q2
p35
difficult
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
Find the unit vector perpendicular to both the vectors\[\bar{a}=4\bar{i}-\bar{j}-3\bar{k}\;and\;\bar{b}=2\bar{i}+2\bar{j}-\bar{k}\]
cbse
class12
additionalproblem
kvquestionbank2012
ch10
p35
math
asked
Feb 4, 2013
by
meena.p
0
answers
Newtons law of cooling states that the rate of change of the temperature T of an object is proportional to the difference between T and the (constant) temperature t of the surrounding medium. We can write it as \[\frac{dT}{dt}=-K(T-t),K>0\; constant.\]A cup of coffee is served at $ 185^\circ F$ in a room where the temperature is $65^\circ F .$ Two minutes later the temperature of the coffee has dropped to $155^\circ F.$(log 3/4=0.144, log3 = 1.09872). Find the time required for coffee to have $105^\circ F$ temperature.
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q25
p34
sec-c
math
asked
Feb 4, 2013
by
meena.p
0
answers
A curve passing through the point (1,1) has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of p from the x-axis. Determine the equation of the curve.
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q24
p34
sec-b
math
asked
Feb 4, 2013
by
meena.p
0
answers
The surface area of a balloon being inflated, changes at a rate proportional to time t. If initially its radius is 1 unit and after 3 seconds it is 2 units, find the radius after time 't'.
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q23
p34
sec-a
math
asked
Feb 4, 2013
by
meena.p
1
answer
A wet porous substance in the open air losses its moisture at a rate proportional to the moisture content. If a sheet hung in the wind loses half of its moisture during the first hour, when will it have lost 95% moisture, weather conditions remaining the same.
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q22
p34
sec-b
math
asked
Feb 4, 2013
by
meena.p
0
answers
A population grows at the rate of 8% per year. How long does it take for the population to double?
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q21
p34
sec-b
math
asked
Feb 4, 2013
by
meena.p
0
answers
When the interest is compounded continuously, the amount of money invested increases at a rate proportional to its size. If Rs.1000 is invested at 10% compounded continuously, in how many years will the original investment double itself?
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q20
p34
sec-c
math
asked
Feb 4, 2013
by
meena.p
0
answers
Solve: \[\frac{xdx+ydy}{xdy-ydx}=\sqrt{\frac{a^2-x^2-y^2}{x^2+y^2}}\] (Hint : take $ x=r\cos \theta,y=r \sin \theta,$ so that $x^2+y^2=r^2)$
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q19
p34
sec-c
math
asked
Feb 4, 2013
by
meena.p
0
answers
Solve:\[\frac{dy}{dx}=\frac{x^2+y^2+1}{2xy},\;where\; y(1)=1\]
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q18
p34
sec-c
math
asked
Feb 4, 2013
by
meena.p
0
answers
Solve:\[(x^3-3xy^2)dx=(y^3-3x^2y)dy\]
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q17
p34
sec-b
math
asked
Feb 4, 2013
by
meena.p
0
answers
Solve:\[\frac{dy}{dx}=\frac{y^2+y+1}{x^2+x+1}=0.\]
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q16
p34
sec-b
math
asked
Feb 4, 2013
by
meena.p
0
answers
Solve the differential equation :\[(x^2y+y^2x)dy=(x^3+y^3)dx\]
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q15
p33
sec-b
math
asked
Feb 4, 2013
by
meena.p
0
answers
Solve:\[\sqrt{1-y^2}dx=[\sin^{-1}y-x]dy\]
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q14
p33
sec-b
math
asked
Feb 4, 2013
by
meena.p
0
answers
Solve:\[(x^3-3xy^2)dx=(y^3-3x^2y)dx\]
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q13
p33
sec-b
math
asked
Feb 4, 2013
by
meena.p
0
answers
Solve:\[(x^3y^3+xy)\frac{dy}{dx}=1\]
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q12
p33
sec-b
math
asked
Feb 4, 2013
by
meena.p
0
answers
Solve:\[\frac{dy}{dx}=\cos ^3x\sin^4x+x\sqrt {2x+1}\]
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q11
p33
sec-b
math
asked
Feb 4, 2013
by
meena.p
0
answers
Solve:\[\bigg[x\sqrt {x^2+y^2}-y^2\bigg]dx+xydy=0\]
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q10
p33
sec-b
math
asked
Feb 4, 2013
by
meena.p
0
answers
Solve:\[ydx-(x+2y)^2dy=0\]
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q9
p33
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
Solve:\[x\frac{dy}{dx}=y(log y-log x+1)\]
class12
cbse
additionalproblem
kvquestionbank2012
ch9
q8
p33
sec-b
math
asked
Feb 4, 2013
by
meena.p
0
answers
Solve:\[(x+y)^2\frac{dy}{dx}=a^2\]
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q7
p33
sec-b
math
asked
Feb 4, 2013
by
meena.p
0
answers
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