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Recent questions tagged q12
Questions
Solve for x : \( 2\: tan^{-1}(\cos x)=tan^{-1}(2 cosec x) \)
cbse
class12
modelpaper
ch2
2012
sec-b
q12
math
asked
Jan 31, 2013
by
thanvigandhi_1
1
answer
$\Large\int \frac {\sin^2x-\cos^2x}{\sin^2x-\cos^2x} \normalsize dx=$\[(a)\;\tan x+\cot x \qquad (b)\;\tan x-\cot x \qquad(c)\;\tan x+\sec x \qquad(d)\;\tan x+cosec x\]
cbse
class12
additionalproblem
kvquestionbank2012
ch7
q12
p24
math
asked
Jan 31, 2013
by
meena.p
0
answers
Prove that $ 2\tan^{-1}\large\frac{1}{2}$$+ \tan^{-1}\large\frac{1}{7}$$= \tan^{-1}\large\frac{31}{17} $
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 30, 2013
by
thanvigandhi_1
0
answers
If x = $a \begin{pmatrix} \large\frac{1 + t^2}{1 - t^2}\end{pmatrix}$ and y = $\large\frac{2t}{1-t^2}$ find $\large\frac{dy}{dx}$
cbse
class12
modelpaper
2005
sec-a
q12
math
asked
Jan 30, 2013
by
fingeazy
0
answers
Show that $ \sin^{-1}\large\frac{12}{13}$$+\cos^{-1}\large\frac{4}{5}$$+\tan^{-1}\large\frac{63}{16} $$= \pi $
cbse
class12
modelpaper
ch2
2012
sec-b
q12
math
asked
Jan 29, 2013
by
thanvigandhi_1
1
answer
Solve for x : $ \sin \bigg(\sin^{-1} \large\frac{1}{5}$$+\cos^{-1}x \bigg) = 1 $.
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 29, 2013
by
thanvigandhi_1
0
answers
$f(x)=\Large\frac{x^2-1}{x^2+1} $ for every real number then minimum value of \begin{array}{1 1}(a)\;does\; not\; exist & \qquad(b)\;is\;not\;attained\;even\;though\;f\;is\;bounded\\(c)\;is\;equal\;to\;1 & \qquad(d)\;is\;equal\;to\;-1\end{array}
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q12
p17
math
asked
Jan 28, 2013
by
meena.p
0
answers
Prove that $\large \frac{9\pi}{8}-\frac{9}{4}$$\sin^{-1}\large\frac{1}{3}=\large\frac{9}{4}$$\sin^{-1}\large\frac{2\sqrt2}{3} $
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 28, 2013
by
thanvigandhi_1
0
answers
Solve for x : $ \tan^{-1}(x+1)+\tan^{-1}(x-1)=\tan^{-1}\large\frac{8}{31} $
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 27, 2013
by
thanvigandhi_1
0
answers
If $ \cos^{-1}\large\frac{x}{a}$$+\cos^{-1}\large\frac{y}{b}= \alpha $, prove that $\large \frac{x^2}{a^2}-\frac{2xy}{ab}$$\cos \alpha+\large\frac{y^2}{b^2}$$=\sin^2\alpha. $
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 27, 2013
by
thanvigandhi_1
1
answer
Prove that : $\sin^{-1}\frac{3}{5} + \sin^{-1}\frac{8}{17}=\sin^{-1}\frac{77}{85} $
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 25, 2013
by
thanvigandhi_1
1
answer
Show that the function :$f(x)= \left\{ \begin{array}{1 1} \Large\frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}, & \quad when\;x\neq0 \\ 0, & \quad when\; x=0 \end{array} \right. $ is discontinuous at x = 0.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q12
p11
difficult
math
sec-b
asked
Jan 25, 2013
by
meena.p
1
answer
Solve for x : $ \begin{vmatrix} 3x-8 & 3 & 3 \\ 3 & 3x-8 & 3 \\ 3 & 3 & 3x-8 \end{vmatrix} = 0$
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 25, 2013
by
thanvigandhi_1
1
answer
Using properties of determinants, prove the following : $ \begin{vmatrix} 1 & a^2+bc & a^3 \\ 1 & b^2+ca & b^3 \\ 1 & c^2+ab & c^3 \end{vmatrix} = (a-b)(b-c)(c-a)(a^2+b^2+c^2). $
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 25, 2013
by
thanvigandhi_1
1
answer
If $f(x)=3x^2-9x+7,$ then for a square matrix A, write f(A)
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q12
p7
math
sec-a
asked
Jan 24, 2013
by
meena.p
0
answers
Solve the differential equation $\bigg( y-x\large\frac{dy}{dx} \bigg)$$ = a \bigg( y^2+\large\frac{dy}{dx} \bigg). $
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 24, 2013
by
thanvigandhi_1
0
answers
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
Let $ f(x)=\frac{\alpha x}{x+1},x\;\neq\;-1,$ find the value of $\alpha$ such that $f(f(x))=x$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q12
p3
math
sec-a
asked
Jan 23, 2013
by
meena.p
0
answers
Solve for x : \[ tan^{-1} \bigg( \frac{2x}{1-x^2} \bigg) +cot^{-1} \bigg( \frac{1-x^2}{2x} \bigg) = \frac{\pi}{3}, x > 0\]
cbse
class12
modelpaper
ch2
2012
sec-b
q12
medium
math
asked
Jan 23, 2013
by
thanvigandhi_1
1
answer
If $ \sin \bigg( \sin^{-1} \large\frac{1}{5}$$+\cos^{-1}x \bigg) = 1,$ then find the value of x.
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 23, 2013
by
thanvigandhi_1
0
answers
If $ tan^{-1} \bigg(\large \frac{x-1}{x-2} \bigg) $$+ \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
Prove that : \[ sin^{-1}\frac{3}{5}+sin^{-1}\frac{8}{17}=cos^{-1}\frac{36}{85} \]
cbse
class12
modelpaper
ch2
2012
sec-b
q12
math
asked
Jan 21, 2013
by
thanvigandhi_1
1
answer
If y(t) is a solution of $(1+t)\Large\frac{dy}{dt}\normalsize-ty=1$ and $y(0)=-1,$ then show that y(1)=$-\Large \frac{1}{2}$
cbse
class12
ch9
sec-b
q12
p193
short-answer
exemplar
math
asked
Jan 18, 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
Solve: $ \tan^{-1}(x+1)+\tan^{-1}(x-1)=\tan^{-1}\large\frac{8}{31}$$;x > 0.$
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 17, 2013
by
thanvigandhi_1
0
answers
If $A,B,C,D$ are the points with position vectors $\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k},2\overrightarrow{i}+\overrightarrow{j}+3\overrightarrow{k},2\overrightarrow{i}-3\overrightarrow{k},3\overrightarrow{i}+2\overrightarrow{i}+\overrightarrow{k},$ respectively ,find the projection of $\overrightarrow{AB}$ along $\overrightarrow{CD}.$
cbse
class12
ch10
q12
p216
short-answer
exemplar
easy
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Prove that : $ \cos^{-1}\large \frac{4}{5}+\tan^{-1}\large\frac{3}{5}$$=\tan^{-1}\large\frac{27}{11} $
cbse
class12
modelpaper
ch2
2012
sec-b
q12
medium
math
asked
Jan 16, 2013
by
thanvigandhi_1
1
answer
Determine the area under the curve $y=\sqrt{a^2-x^2}$ included between the lines $x=0$ and $x=a$.
cbse
class12
ch8
q12
p177
short-answer
exemplar
sec-c
medium
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
Prove that $ \cot^{-1} \bigg( \large\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}} \bigg) = \large\frac{x}{2}$$, x \in \bigg( 0, \large\frac{\pi}{4} \bigg).$
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 15, 2013
by
thanvigandhi_1
0
answers
Find the value of $ \tan\large\frac{1}{2}$$ \bigg[ \sin^{-1}\large \frac{2x}{1+x^2}$$+\cos^{-1}\large\frac{1-y^2}{1+y^2} \bigg].$$ \: where \: |x| < 1, y > 0 \: and \: xy < 1.$
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 15, 2013
by
thanvigandhi_1
1
answer
Evaluate the following $\large\int\frac{ x^{\frac{1}{2}}}{1+x^{\frac{3}{4}}}dx$ $(Hint:Put\;x=z^4)$
cbse
class12
ch7
q12
p164
short-answer
exemplar
sec-b
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Using properties of determinants, prove the following : \( \begin{bmatrix} b+c & a & a \\ b & c+a & b \\ c & c & a+b \end{bmatrix} = 4abc.\)
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 11, 2013
by
thanvigandhi_1
0
answers
Using properties of determinants, prove the following : \( \begin{bmatrix} b+c & c+a & a+b \\ q+r & r+p & p+q \\ y+z & z+x & x+y \end{bmatrix} = 2 \begin{bmatrix} a & b & c \\ p & q & r \\ x & y & z \end{bmatrix}. \)
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 11, 2013
by
thanvigandhi_1
0
answers
Find the condition that the curves $2x=y^2$ and $2xy=k$ intersect orthogonally.
cbse
class12
ch6
q12
p136
short-answer
exemplar
difficult
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Prove that : $ \cot^{-1} \bigg[\large \frac{\sqrt{1+\sin\: x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}} \bigg] = \large \frac{x}{2}; $$x \in \bigg( 0, \large\frac{\pi}{2} \bigg). $
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 10, 2013
by
thanvigandhi_1
0
answers
Solve for x : $ \tan^{-1} (2x)+\tan^{-1}(3x)=\large\frac{\pi}{4}. $
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 10, 2013
by
thanvigandhi_1
0
answers
Evaluate : $ \sin \bigg[ \frac{\large \pi}{\large 3}-$$\sin^{-1} \bigg( -\frac{\large 1}{\large 2} \bigg) \bigg]. $
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
If X is the number of tails in three tosses of a coin ,determine the standard deviation of X.
cbse
class12
ch13
q12
p272
short-answer
exemplar
sec-a
easy
math
asked
Jan 8, 2013
by
sreemathi.v
1
answer
Prove that : $ \cot^{-1} \bigg(\large \frac{ \sqrt{1+\sin x}+\sqrt{1-\sin\: x}}{\sqrt{1+\sin\: x}-\sqrt{1-\sin x}} \bigg)=\frac{x}{2}.$
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 8, 2013
by
thanvigandhi_1
0
answers
A firm has to transport 1200 packages using large vans which can carry 200 packages each and small vans which can take 80 packages each.The cost for engaging each large van is Rs 400 and each small van is Rs 200.Not more than Rs 3000 is to be spent on the job and the number of large vans cannot exceed the number of small vans.Formulate this problem as a LPP given that the objective is to minimize cost.
cbse
class12
ch12
q12
p252
short-answer
exemplar
math
sec-a
asked
Jan 7, 2013
by
sreemathi.v
1
answer
Prove that :$ \sin^{-1}\bigg(\large\frac{ 4}{ 5} \bigg) $$+ \sin^{-1}\bigg(\large\frac{ 5}{ 13} \bigg)$$+ \sin^{-1}\bigg(\frac{\large 16}{\large 65}\bigg) = \frac{\large \pi}{\large 2}.$
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 6, 2013
by
thanvigandhi_1
0
answers
Solve for : \( x : tan^{-1}3x+tan^{-1}2x=\frac{\large \pi}{\large 4}. \)
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 6, 2013
by
thanvigandhi_1
0
answers
Using properties of determinants, prove the following : $\begin{bmatrix} 1+a^2-b^2 & 2ab & -2b \\ 2ab & 1-a^2+b^2 & 2a \\ 2b & -2a & 1-a^2=b^2 \end{bmatrix} = (1 + a^2 + b^2)^3. $
cbse
class12
modelpaper
2012
sec-b
q12
ch4
bookproblem
sec2
q13
p121
math
asked
Jan 4, 2013
by
thanvigandhi_1
0
answers
Using properties of determinants, prove the following : $ \begin{bmatrix} 3a & -a+b & -a+c \\ a-b & 3b & c-b \\ a-c & b-c & 3c \end{bmatrix} = 3(a + b + c)(ab+bc+ca) $
cbse
class12
modelpaper
2012
sec-b
q12
ch4
bookproblem
misc
q13
p142
medium
math
asked
Jan 4, 2013
by
thanvigandhi_1
0
answers
Find the angle between the lines whose direction cosines are given by the equations $l+m+n=0,l^2+m^2-n^2=0$
cbse
class12
ch11
sec-b
q12
p235
exemplar
difficult
math
asked
Jan 3, 2013
by
sreemathi.v
1
answer
Using properties of determinants, prove the following : $ \begin{bmatrix} \alpha & \beta & \gamma \\ \alpha^2 & \beta^2 & \gamma^2 \\ \beta+\gamma & \gamma+\alpha & \alpha+\beta \end{bmatrix} $
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 3, 2013
by
thanvigandhi_1
0
answers
Prove, using the properties of determinants $ \begin{bmatrix} a+b & b+c & c+a \\ b+c & c+a & a+b \\ c+a & a+b & b+c \end{bmatrix} = 2 \begin{bmatrix} a & b & c \\ b & c & a \\ c & a & b \end{bmatrix} $
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 3, 2013
by
thanvigandhi_1
0
answers
Prove that : \( tan^{-1}\bigg(\frac{1}{3} \bigg)+tan^{-1}\bigg(\frac{1}{5}\bigg)+tan^{-1}\bigg(\frac{1}{7}\bigg)+tan^{-1}\bigg(\frac{1}{8}\bigg)=\large\frac{\pi}{4} \)
cbse
class12
modelpaper
ch2
2012
sec-b
q12
difficult
math
asked
Jan 2, 2013
by
thanvigandhi_1
1
answer
Write the following functions in the simplest form : \[ (i) tan^{-1} \bigg( \frac{\sqrt{1+x^2} - 1}{x} \bigg), x \neq 0 \] \[(ii) tan^{-1} \frac{1}{\sqrt{x^2-1}} ,| x | > 1 \]
cbse
class12
modelpaper
ch2
2012
sec-b
q12
easy
math
asked
Dec 31, 2012
by
thanvigandhi_1
1
answer
Find the value of k in the following so that the function $f$ is continuous at the indicated point: $f(x)=\left \{\begin{array}{1 1}\frac{\large 2^{x+2}-16}{4^{\large x}-16}, & if\;x\neq 2\\k, & if\;x=2\end{array}\right.$ at $x=2$
cbse
class12
ch5
q12
p108
short-answer
exemplar
medium
sec-a
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
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