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Recent questions tagged misc
Questions
Prove that \[cos^{-1} \frac {4}{5} +cos^{-1} \frac{12}{13}=cos^{-1} \frac{33}{65}\]
cbse
class12
bookproblem
ch2
misc
q5
p51
medium
sec-b
math
asked
Nov 29, 2012
by
vaishali.a
1
answer
Prove that \[ cos^{-1} \frac {12}{13} +sin^{-1} \frac{3}{5}=sin^{-1} \frac{56}{65}\]
cbse
class12
bookproblem
ch2
misc
q6
p51
medium
sec-b
math
asked
Nov 29, 2012
by
vaishali.a
1
answer
Prove that \[tan^{-1} \frac{1}{5}+ tan^{-1} \frac{1}{7}+tan^{-1}\frac{1}{3}+tan^{-1} \frac{1}{8}= \frac{\pi}{4}\]
cbse
class12
bookproblem
ch2
misc
q8
p51
sec-c
medium
math
asked
Nov 29, 2012
by
vaishali.a
1
answer
Prove that \[tan^{-1} \sqrt{x} = \frac{1}{2} cos^{-1} \;\; \bigg(\frac{1-x}{1+x}\bigg), x\in [0,1]\]
cbse
class12
bookproblem
ch2
misc
q9
p52
medium
sec-b
math
asked
Nov 29, 2012
by
vaishali.a
1
answer
Let A = $\begin{bmatrix} 1 & sin\theta & 1 \\ -sin\theta & 1 & sin\theta \\ -1 & -sin\theta & 1 \end{bmatrix}$, where $0 \leq \theta \leq 2\pi$. Then: \[ \begin{array} ((A) \, Det(A) = 0 \quad& (B) \, Det(A) \in (2, \infty) \\[0.5em] (C) \, Det(A) \in (2, 4) \quad &(D) Det(A) \in [2,4] \end{array} \]
cbse
class12
bookproblem
ch4
misc
q19
p143
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
If x, y, z are nonzero real numbers, then the inverse of matrix A = $\begin{bmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{bmatrix}$ is
cbse
class12
bookproblem
ch4
misc
q18
p143
medium
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Choose the correct answer. If a, b, c, are in A.P, then the determinant $\begin{vmatrix} x+2 & x+3 &x+2a \\ x+3 & x+4 &x+2b \\ x+4 & x+5 &x+2c \end{vmatrix}$ is: \[\] $(A)\;0 \hspace{20 mm} (B)\;1 \hspace{20 mm} (C)\; x \hspace{20 mm} (D)\; 2x $
cbse
class12
bookproblem
ch4
misc
q17
p143
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Solve the system of equations: $\large \frac{2}{x}+\frac{3}{y}+\frac{10}{z}=$$4.\quad $ $\large \frac{4}{x}-\frac{6}{y}+\frac{5}{z}$$=1.\quad $ $\large \frac{6}{x}+\frac{9}{y}-\frac{20}{z}$$=2.$
cbse
class12
bookproblem
ch4
misc
q16
p142
difficult
sec-c
modelpaper
q23
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Using properties of determinants, prove that: $\begin{vmatrix} sin\alpha&cos\alpha&cos(\alpha+\delta)\\ sin\beta&cos\beta&cos(\beta+\delta)\\ sin\gamma&cos\gamma&cos(\gamma+\delta)) \end{vmatrix}= 0.$
cbse
class12
bookproblem
ch4
misc
q15
p142
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Using properties of determinants, prove that: $\begin{vmatrix} 1&1+p&1+p+q\\ 2&3+2p&4+3p+2q\\ 3&6+3p&10+6p+3q \end{vmatrix}= 1.$
cbse
class12
bookproblem
ch4
misc
q14
p142
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Using properties of determinants, prove that: $\begin{vmatrix} 3a&-a+b&-a+c\\ -b+a&3b&-b+c\\ -c+a&-c+b&3c \end{vmatrix}= 3(a+b+c)(ab+bc+ca)$
cbse
class12
bookproblem
ch4
misc
q13
p142
medium
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Using properties of determinants, prove that: $ \begin{vmatrix} x &x^2 &1 & px^3\\ y &y^2 &1 & py^3\\ z &z^2 &1 & pz^3 \end{vmatrix}= (1+pxyz) (x-z) (y-z)(z-x), $ where p is any scalar.
cbse
class12
bookproblem
ch4
misc
q12
p142
medium
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Using properties of determinants, prove that: $\begin{vmatrix} \alpha & \alpha^2 & \beta+\gamma\\ \beta & \beta^2 & \alpha+\gamma\\ \gamma & \gamma^2 & \alpha+\beta \end{vmatrix} = (\beta-\gamma) (\gamma - \alpha) (\alpha-\beta) (\alpha+\beta+\gamma)$
cbse
class12
bookproblem
ch4
misc
q11
p142
easy
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Evaluate $\begin{vmatrix} 1 & x & y\\ 1 & x+y & y\\ 1 & x & x+y \end{vmatrix}$
cbse
class12
bookproblem
ch4
misc
q10
p142
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Evaluate $ \begin{vmatrix} x & y & x+y\\ y & x+y & x\\ x+y & x & y \end{vmatrix}$
cbse
class12
bookproblem
ch4
misc
q9
p142
easy
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Let A = $\begin{bmatrix} 1 & -2 & 1\\ -2 & 3 & 1\\ 1 & 1 & 5 \end{bmatrix}$. Verify that \[\] $(i)\ \; \left [adj A \right ]^{-1} = adj(A^{-1}) \;\;\;\; $
cbse
class12
bookproblem
ch4
misc
q8
q8-1
p142
medium
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
$If \; A^{-1}=\begin{bmatrix} 3 &-1 & 1\\ -15&6 &-5 \\ 5& -2&2 \end{bmatrix} \; and \; B = \begin{bmatrix} 1 & 2 & -2\\ -1 & 3 & 0\\ 0 & -2 & 1 \end{bmatrix}, \; find \; (AB)^{-1} $
cbse
class12
bookproblem
ch4
misc
q7
p141
medium
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Prove that $ \begin{vmatrix} a^2&bc&ac+c^2\\ a^2+ab& b^2& ac\\ ab&b^2+bc&c^2 \end{vmatrix}=4\,a^2\;b^2\;c^2. $
cbse
class12
bookproblem
ch4
misc
q6
p141
medium
sec-b
modelpaper-2012
modelpaper-2014
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Solve the equation $ \begin{vmatrix} x+a & x & x \\ x & x+a & x\\ x & x & x+a \end{vmatrix}=0, \; a \neq 0. $
cbse
class12
bookproblem
ch4
misc
q5
p141
easy
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
If a, b and c are real numbers, and $\Delta = \begin{vmatrix} b+c & c+a & a+b \\ c+a & a+b & b+c\\ a+b & b+c & c+a \end{vmatrix}=0, $ show that either $a+b+c=0$ or $a=b=c.$
cbse
class12
bookproblem
ch4
misc
q4
p141
difficult
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Evaluate $ \begin{vmatrix} cos\alpha \; cos\beta & cos\alpha \; sin\beta & -sin\alpha \\ -sin\beta & cos\beta & 0 \\ sin \alpha \; cos\beta & sin\alpha \; sin\beta & cos\alpha \end{vmatrix} $
cbse
class12
bookproblem
ch4
misc
q3
p141
medium
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Without expanding the determinant, prove that $ \begin{vmatrix} a &a^2 &bc \\ b &b^2 &ca \\ c &c^2 &ab \end{vmatrix}\; = \; \begin{vmatrix} 1 & a^2 & a^3 \\ 1 & b^2 & b^3 \\ 1 & c^2 & c^3 \end{vmatrix} $
cbse
class12
bookproblem
ch4
misc
q2
p141
medium
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
\[ \text{Prove that the determinant } \begin{vmatrix} x&sin\theta&cos\theta \\ -sin\theta&-x&1\\ cos\theta&1&x \end{vmatrix} \text{ is independent of } \theta \]
cbse
class12
bookproblem
ch4
misc
q1
p141
medium
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
verify that the given function (implicit or explicit) is a solution of the corresponding differential equation
cbse
class12
bookproblem
ch9
misc
q2
q2-1
p420
medium
math
sec-a
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Form the differential equation representing the family of curves given by $(x-a)^2+2y^2\;=\;a^2$, where $a$ is an arbitrary constant
cbse
class12
bookproblem
ch9
misc
q3
p420
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Prove that \(x^2-y^2\;=\;c(x^2+y^2)^2\)is the general solution of differential equation \((x^3-3x\;y^2)dx\;=\;(y^3-3x^2y)dy\) where \(c\) is a parameter.
cbse
class12
bookproblem
ch9
misc
q4
p420
difficult
math
sec-b
asked
Nov 29, 2012
by
sreemathi.v
1
answer
prove that \[tan^{-1} \left ( \frac {{\sqrt {1+x}}-{\sqrt {1-x}}}{{\sqrt {1+x}}+{\sqrt {1-x}}} \right ) = \frac {\pi}{4} -\frac{1}{2} cos^{-1}x,-\frac{1}{\sqrt2} \leq x \leq 1 \]
cbse
class12
bookproblem
ch2
misc
q11
p52
sec-b
medium
modelpaper
2012
q12
math
asked
Nov 29, 2012
by
vaishali.a
1
answer
Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.
cbse
class12
bookproblem
ch9
misc
q5
p420
medium
math
sec-b
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the general solution of the differential equation$\large\frac{dy}{dx}+\sqrt{\frac{1-y^2}{1-x^2}}\;$$=\;0$
cbse
class12
bookproblem
ch9
misc
q6
p420
easy
math
sec-b
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Prove that \[cot^{-1} \left ( \frac {{\sqrt {1+sinx}}+{\sqrt {1-sinx}}}{{\sqrt {1+sinx}}-{\sqrt {1-sinx}}} \right ) = \frac {x}{2} , x \in \left ( 0, \frac{\pi}{4} \right )\]
cbse
class12
bookproblem
ch2
misc
q10
p52
medium
sec-b
math
asked
Nov 29, 2012
by
vaishali.a
1
answer
Prove that \[\frac{9 \pi}{8} - \frac{9}{4} sin ^{-1}\frac{1}{3}= \frac{9}{4} sin^{-1}\frac{2\sqrt 2}{3}\]
cbse
class12
bookproblem
ch2
misc
q12
p52
difficult
sec-b
math
asked
Nov 29, 2012
by
vaishali.a
1
answer
Show that the general solution of the differential equation\(\large\frac{dy}{dx}+\large\frac{y^2+y+1}{x^2+x+1}=0\) is given by \((x+y+1)\;=\;A(1-x-y-2xy)\), where A is parameter
cbse
class12
bookproblem
ch9
misc
q7
p420
medium
math
sec-b
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Solve the following \[2tan^{-1} (cos x) = tan^{-1} (2\, cosec\, x) \]
cbse
class12
bookproblem
ch2
misc
q13
p52
medium
sec-b
math
asked
Nov 29, 2012
by
vaishali.a
1
answer
Solve the following $tan^{-1} \frac{1-x}{1+x} =\frac{1}{2} tan^{-1} x,(x>0)$
cbse
class12
bookproblem
ch2
misc
q14
p52
sec-b
medium
math
asked
Nov 29, 2012
by
vaishali.a
2
answers
Find the equation of the curve passing through the point\(\bigg(0,\large\frac{\pi}{4}\bigg)\) whose differential equation is $\sin x\cos y\;dx+\cos x\sin y\;dy\;=\;0$
cbse
class12
bookproblem
ch9
misc
q8
p420
easy
math
sec-b
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the particular solution of the differential equation $(1+e^{2x})dy + (1+y^2)e^xdx$ = 0, given that $y = 1$ when $x = 0$
cbse
class12
bookproblem
ch9
misc
q9
p420
medium
modelpaper
2012
q18
math
sec-a
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Solve the differential equation$y\;e^{\large\frac{x}{y}}\;dx=\bigg(x\;e^{\Large\frac{x}{y}}+y^2\bigg)dy\;(y\neq0)$
cbse
class12
bookproblem
ch9
misc
q10
p420
medium
math
sec-b
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find a particular solution of the differential equation \((x-y)(dx+dy) = dx - dy\),given that \( y=\;-1\),when \( x=\;0\)
cbse
class12
bookproblem
ch9
misc
q11
p420
medium
math
sec-b
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Solve the differential equation $\begin{bmatrix}\large\frac{e^{-2\sqrt{x}}}{\sqrt{x}}-\large\frac{y}{\sqrt{x}}\end{bmatrix}\large\frac{dx}{dy}$$=1(x\neq0)$
cbse
class12
bookproblem
ch9
misc
q12
p421
medium
math
sec-b
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find a particular solution of the differential equation $\frac{dy}{dx} + y\cot x=4x\:cosec\:x$, $(x\neq0)$, given that $y = 0$ when $x = \large\frac{\pi}{2}$
cbse
class12
bookproblem
ch9
misc
q13
p421
medium
modelpaper
q19
sec-a
math
asked
Nov 28, 2012
by
sreemathi.v
1
answer
Find a particular solution of the differential equation $(x+1)\frac{dy}{dx}=2e^{-y} -1$, given that $y = 0$ when $x = 0$.
cbse
class12
bookproblem
ch9
misc
q14
p421
difficult
math
sec-a
asked
Nov 28, 2012
by
sreemathi.v
1
answer
Choose the correct answer $\sin (\tan^{-1}x), |x| <1 $ is equal to
cbse
class12
bookproblem
ch2
misc
q15
p52
sec-a
easy
math
asked
Nov 28, 2012
by
vaishali.a
1
answer
The population of a village increases continuously at the rate proportional to the number of its inhabitants present at any time.If the population was 20,000 in 1999 and 25000 in the year of 2004,what will be the population of the village in 2009?
cbse
class12
bookproblem
ch9
misc
q15
p421
difficult
math
sec-b
asked
Nov 28, 2012
by
sreemathi.v
1
answer
Choose the correct answer. If \(\sin^{-1}(1-x) -2 \sin^{-1} x=\large\frac {\pi}{2}, \) then \(x\) is equal to
cbse
class12
bookproblem
ch2
misc
q16
p52
medium
sec-b
math
asked
Nov 28, 2012
by
vaishali.a
1
answer
What is the value of: \[tan^{-1} \bigg( \frac {x}{y} \bigg) -tan^{-1} \frac {x-y}{x+y} \]
cbse
class12
bookproblem
ch2
misc
q17
p52
medium
sec-b
math
asked
Nov 28, 2012
by
vaishali.a
1
answer
The general solution of the differential equation $\large\frac{ydx-xdy}{y}$$=0\;is$
cbse
class12
bookproblem
ch9
misc
q16
p421
easy
math
sec-a
asked
Nov 28, 2012
by
sreemathi.v
1
answer
The general solution of a differential equation of the type $\large\frac{dx}{dy}$$+p_1x=Q_1\;is$
cbse
class12
bookproblem
ch9
misc
q17
p421
easy
math
sec-a
asked
Nov 28, 2012
by
sreemathi.v
1
answer
The general solution of the differential equation$ e^xdy+(ye^x+2x)dx=0\; is$
cbse
class12
bookproblem
ch9
misc
q18
p421
easy
math
sec-a
asked
Nov 28, 2012
by
sreemathi.v
1
answer
For each of the differential equations given below,indicate its order and degree(if defined) $(i)\;\large\frac{d^2y}{dx^2}+5x\bigg(\frac{dy}{dx}\bigg)^2-6y=\log x$
cbse
class12
bookproblem
ch9
misc
q1
q1-1
p419
easy
math
sec-a
asked
Nov 28, 2012
by
sreemathi.v
1
answer
Choose the correct answer in the points on the curve \(9y^2 = x^3\), where the normal to the curve makes equal intercepts with the axes are
cbse
class12
bookproblem
ch6
misc
q24
p244
sec-b
easy
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
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