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Recent questions tagged difficult
Questions
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
Show that the right-circular cone of least curved surface and given volume has an altitude equal to \( \sqrt 2 \) times the radius of the base.
cbse
class12
modelpaper
2012
sec-c
q24
difficult
math
asked
Feb 5, 2013
by
thanvigandhi_1
1
answer
A window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12 m, find the dimensions of the rectangle that will produce the largest area of the window.
cbse
class12
modelpaper
2012
sec-c
q24
difficult
math
asked
Feb 5, 2013
by
thanvigandhi_1
1
answer
Evaluate : $ \int \large\frac{6x+7}{\sqrt{(x-5)(x-4)}}$$dx $
cbse
class12
modelpaper
2012
sec-c
q25
difficult
math
asked
Feb 5, 2013
by
thanvigandhi_1
1
answer
Given three identical boxes I, II and III each containing two coins. In box I, both coins are gold coins, in box II, both are silver coins and in box III, there is one gold and one silver coin. A person chooses a box at random and takes out a coin. If the coin is of gold, what is the probability that the other coin in the box is also of gold?
cbse
class12
modelpaper
2012
sec-c
q28
difficult
math
asked
Feb 4, 2013
by
thanvigandhi_1
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
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
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
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
Evaluate:\[\int\limits_0^1 \sqrt{\frac{1-x}{1+x}}dx\]
cbse
class12
additionalproblem
kvquestionbank2012
ch7
q98
p30
difficult
math
asked
Feb 4, 2013
by
meena.p
1
answer
Evaluate:$\int \limits_1^4 [\; \left |x-1 \right|+\left |x-2 \right |+\left| x-3\right |\;]\;dx$
cbse
class12
additionalproblem
kvquestionbank2012
ch7
q86
p30
difficult
math
asked
Feb 4, 2013
by
meena.p
1
answer
If $ x\sqrt{1+y}+y\sqrt{1+x}=0,\normalsize\; Prove\; that\; \Large\frac{dy}{dx}=\frac{-1}{(1+x)^2}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q45
p14
difficult
math
sec-b
asked
Jan 28, 2013
by
meena.p
1
answer
Differentiate $ \cos^{-1} \bigg[\large\frac{3 \cos x-2 \sin x}{\sqrt {13}}\bigg] w.r.t \; \sin^{-1} \bigg[\large\frac{5\sin x +4 \cos x}{\sqrt{41}}\bigg]$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q43
p14
p406
difficult
math
sec-a
asked
Jan 28, 2013
by
meena.p
1
answer
If $ y^{ \cos x}+(\tan^{-1}x)^y=1,find \Large\frac{dy}{dx}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q41
p14
difficult
math
sec-b
asked
Jan 28, 2013
by
meena.p
1
answer
If $ y=f \bigg(\Large\frac{2x-1}{x^2+1}\bigg)\;\normalsize and\;f' (x)=\sin x^2,\;find\; \Large\frac{dy}{dx}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q40
p14
difficult
math
sec-b
asked
Jan 28, 2013
by
meena.p
1
answer
If $ y=\Large\frac{1}{\sqrt{b^2-a^2}} \normalsize log \bigg[\Large\frac{\sqrt{b+a}+\sqrt{b-a}\tan \frac{x}{2}} {\sqrt{b+a}-\sqrt{b-a}\tan \frac{x}{2}}\bigg]$ prove that $ \Large\frac {dy}{dx}=\frac{\sec^2\frac{x}{2}}{(b+a)-(b-a) \tan^2\frac{x}{2}}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q37
p14
difficult
math
sec-b
asked
Jan 28, 2013
by
meena.p
1
answer
If $ \sqrt { 1-x^2} +\sqrt {1-y^2}=a(x-y),\;prove\;that\;\Large\frac{dy}{dx}=\sqrt{\frac{1-y^2}{1-x^2}}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q36
p14
difficult
math
sec-b
asked
Jan 25, 2013
by
meena.p
1
answer
Prove that $ \Large\frac{d}{dx}\bigg[\Large\frac{1}{4 \sqrt 2} \normalsize log\bigg|\Large\frac{x^2+\sqrt 2 x+1}{x^2- \sqrt 2 x+1} \bigg|+\Large\frac {1}{2 \sqrt 2} \normalsize \tan^{-1} \Large\frac{\sqrt 2 x}{1-x^2}\bigg]=\Large\frac{1}{1+x^4}$
cbse
class12
kvquestionbank2012
ch5
q34
p13
difficult
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
Given that $ \cos \frac{x}{2}.\cos \frac{x}{4}.\cos \frac{x}{8}.......=\Large\frac {\sin x}{x},$ \[Prove\;that\;\frac{1}{2^2}\sec^2\frac{x}{2}+\frac{1}{2^4}\sec^2\frac{x}{4}+.......=cosec^2x-\frac{1}{x^2}\]
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q31
p13
difficult
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
If $ y=\frac{2}{\Large\sqrt {a^2-b^2}}\tan^{-1}\bigg[\sqrt{\frac{a-b}{a+b}}\tan \frac{x}{2} \bigg],$ prove that $ \Large\frac{dy}{dx}=\frac{1}{a+b \cos x}, \normalsize a>b>0 $
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q28
p13
difficult
math
sec-b
asked
Jan 25, 2013
by
meena.p
1
answer
Show that the function :$f(x)= \left\{ \begin{array}{1 1} \Large\frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}, & \quad when\;x\neq0 \\ 0, & \quad when\; x=0 \end{array} \right. $ is discontinuous at x = 0.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q12
p11
difficult
math
sec-b
asked
Jan 25, 2013
by
meena.p
1
answer
Solve for x : $ \tan^{-1} \bigg(\large \frac{x-1}{x+1} \bigg) + \tan^{-1} \bigg( \frac{2x-1}{2x+1} \bigg) = \tan^{-1} \bigg( \frac{23}{36} \bigg). $
cbse
class12
modelpaper
ch2
2012
sec-b
q17
difficult
math
asked
Jan 24, 2013
by
thanvigandhi_1
1
answer
Solve: $\sin\lfloor2\cos^{-1}\{\cot(2\tan^{-1}x)\}\rfloor=0$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q24
p6
difficult
sec-b
math
asked
Jan 24, 2013
by
meena.p
1
answer
Prove that $ \tan^{-1}\large\frac{yz}{xr}+ \tan^{-1}\frac{zx}{yr}+ \tan^{-1}\frac{xy}{zr}=\frac{\pi}{2}\;where\;x^2+y^2+z^2=r^2$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q22
p6
difficult
sec-c
math
asked
Jan 24, 2013
by
meena.p
1
answer
If $ x= cosec \lfloor\tan^{-1}\{\cos(\cot^{-1}(\sec(\sin^{-1}a)))\}\rfloor\; $ and $ y=\sec\lfloor\cot^{-1}\{\sin(\tan^{-1}(cosec(\cos^{-1}a)))\}\rfloor\;$ where $\;a\;\in [0,1]$ Find the relationship between $x$ and $y$ in terms of $a$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q17
p6
difficult
sec-c
math
asked
Jan 24, 2013
by
meena.p
1
answer
If $ \sin^{-1}x+\sin^{-1}y+\sin^{-1}z=\pi,$ prove that $x\sqrt{1-x^2}+y\sqrt{1-y^2}+z\sqrt{1-z^2}=2xyz$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q14
p5
difficult
sec-c
math
asked
Jan 23, 2013
by
meena.p
1
answer
If $x,y,z \in [-1,1]\;$ such that $\;\sin^{-1}x+\sin^{-1}y+\sin^{-1}z=\frac{3\pi}{2},$ find the value of $x^{2006}+y^{2007}+z^{2008}-\Large \frac{9}{x^{2006}+y^{2007}+z^{2008}}$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q12
p5
difficult
sec-a
math
asked
Jan 23, 2013
by
meena.p
1
answer
If $ tan^{-1} \bigg(\large \frac{x-1}{x-2} \bigg) $$+ \tan^{-1} \bigg(\large \frac{x+1}{x+2} \bigg) =\large \frac{\pi}{4}, $ find the value of x.
cbse
class12
modelpaper
ch2
2012
sec-b
q12
difficult
math
asked
Jan 22, 2013
by
thanvigandhi_1
1
answer
The general solution of $\frac{dy}{dx}-y=\sin x$ is
cbse
class12
ch9
sec-a
q76ix
p202
fitb
exemplar
difficult
math
asked
Jan 20, 2013
by
sreemathi.v
1
answer
The solution of $(1+x^2)\frac{dy}{dx}+2xy-4x^2=0$ is ___________.
cbse
class12
ch9
sec-a
q76vii
p202
fitb
exemplar
difficult
math
asked
Jan 20, 2013
by
sreemathi.v
1
answer
The solution of the differential equation $\large\frac{dy}{dx}+\frac{2xy}{(1+x^2)}=\frac{1}{(1+x^2)^2}$ is
cbse
class12
ch9
sec-a
q75
p201
objective
exemplar
difficult
math
asked
Jan 20, 2013
by
sreemathi.v
1
answer
The general solution of the differential equation $(e^x+1)ydy=(y+1)e^xdx$ is
cbse
class12
ch9
sec-a
q73
p201
objective
exemplar
difficult
math
asked
Jan 20, 2013
by
sreemathi.v
1
answer
Solution of the differential equation $\large\frac{dy}{dx}+\frac{y}{x}$$=\sin x$ is:
cbse
class12
ch9
sec-a
q72
p201
objective
exemplar
difficult
math
asked
Jan 20, 2013
by
sreemathi.v
1
answer
The solution of the differential equation $\Large \frac{dy}{dx}=\frac{1-y^2}{1-x^2}$ is:\begin{array}{1 1}(A)\;y=\tan^{-1}x & (B)\;y-x=k(1+xy)\\(C)\;x=tan^{-1}y & (D)\;\tan (xy)=k\end{array}
cbse
class12
ch9
sec-a
q54
p198
objective
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Integrating factor of the differential equation $(1-x^2)\Large \frac{dy}{dx}\normalsize -xy=1$ is \[(A)\;-x\quad(B)\;\frac{x}{1-x^2}\quad(C)\;\sqrt {1-x^2}\quad(D)\;\frac{1}{2}log(1-x^2)\]
cbse
class12
ch9
sec-a
q47
p197
objective
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
If $y=e^{-x}(A\cos x+B\sin x)$, then $y$ is a solution of
cbse
class12
ch9
differential-equations
sec-a
q37
p195
objective
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the equation of a curve passing through the point (1,1).If the tangent drawn at any point P(x,y) on the curve meets the coordinate axes at A and B such that P is the mid-point of AB.
cbse
class12
ch9
sec-b
q32
p195
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the equation of a curve passing through (2,1) if the slope of the tangent to the curve at any point (x,y) is $\Large \frac{x^2+y^2}{2xy}.$
cbse
class12
ch9
sec-b
q29
p194
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the general solution of $\large \frac{dy}{dx}$$+3y=\sin 2x$
cbse
class12
ch9
sec-b
q28
p194
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve :$\large\frac{dy}{dx}$$=\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
FInd the general solution of $(1+\tan y)(dx-dy)+2xdy=0$
cbse
class12
ch9
sec-a
q26
p194
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve:$y+\large\frac{d}{dx}$$(xy)=x(\sin x+log x)$
cbse
class12
ch9
sec-b
q25
p194
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve: $(x+y)(dx-dy)=dx+dy.$[Hint:Substitute x+y=z after separating dx and dy]
cbse
class12
ch9
sec-b
q19
p194
short-answer
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the general solution of $y^2dx+(x^2-xy+y^2)dy=0$
cbse
class12
ch9
sec-b
q18
p194
short-answer
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Form the differential equation of all circles which pass through origin and whose centers lie on y-axis as shown below:
cbse
class12
ch9
sec-b
q14
p194
short-answer
exemplar
math
difficult
jeemain
differential-equations
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The vector $\overrightarrow{a}+\overrightarrow{b}$ bisects the angle between the non-collinear vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ if__________.
cbse
class12
ch10
q34
p218
exemplar
difficult
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ represent the vertices of a triangle,then show that $\frac{1}{2}\mid\overrightarrow{b}\times\overrightarrow{c}+\overrightarrow{c}\times\overrightarrow{a}+\overrightarrow{a}\times\overrightarrow{b}\mid$ gives the vector area of the triangle .Hence deduce the condition that the three points $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are collinear.Also find the unit vector normal to the plane of the triangle.
cbse
class12
ch10
q16
p216
exemplar
difficult
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
If \( cos^{-1}x+cos^{-1}y+cos^{-1}z=\pi\) prove that \( x^2+y^2+z^2+2xyz=1\)
cbse
class12
modelpaper
ch2
2012
sec-b
q12
difficult
math
asked
Jan 17, 2013
by
thanvigandhi_1
1
answer
Prove that in any triangle ABC,$ cos A=\large \frac{b^2+c^2-a^2}{2bc}$,$where \overrightarrow{a},\overrightarrow{b} and \overrightarrow{c}$ are the vectors of sides BC, CA and AB respectively.
cbse
class12
ch10
q15
p216
exemplar
difficult
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
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