Recent questions tagged bookproblem

Find the general solution of the differential equation$\large\frac{dy}{dx}+\sqrt{\frac{1-y^2}{1-x^2}}\;$$=\;0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Prove that \[cot^{-1} \left ( \frac {{\sqrt {1+sinx}}+{\sqrt {1-sinx}}}{{\sqrt {1+sinx}}-{\sqrt {1-sinx}}} \right ) = \frac {x}{2} , x \in \left ( 0, \frac{\pi}{4} \right )\]

asked Nov 29, 2012 by vaishali.a

1 answer

\[ \text{Let A = } \begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix} \text{and B = } \begin{bmatrix} 6 & 8 \\ 7 & 9 \end{bmatrix}. \text{Verify that } (AB^{-1}) = B^{-1}A^{-1}\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Prove that \[\frac{9 \pi}{8} - \frac{9}{4} sin ^{-1}\frac{1}{3}= \frac{9}{4} sin^{-1}\frac{2\sqrt 2}{3}\]

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

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the inverse of the matrix (if it exists): \[ \begin{bmatrix} 1&0&0 \\ 0&cos\alpha&sin\alpha \\ 0&sin\alpha&-cos\alpha \\ \end{bmatrix} \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the following \[2tan^{-1} (cos x) = tan^{-1} (2\, cosec\, x) \]

asked Nov 29, 2012 by vaishali.a

1 answer

Solve the following $tan^{-1} \frac{1-x}{1+x} =\frac{1}{2} tan^{-1} x,(x>0)$

asked Nov 29, 2012 by vaishali.a

2 answers

Find the inverse of the matrix (if it exists): $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \\ \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the inverse of the matrix (if it exists): $ \begin{bmatrix} 2 & 1& 3 \\ 4 &- 1 & 0 \\ -7 & 2 & 1 \\ \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the inverse of the matrix (if it exists): $\begin{bmatrix} 1 & 0 & 0 \\ 3 & 3 & 0 \\ 5 & 2 & -1 \\ \end{bmatrix}$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the inverse of the matrix (if it exists): $ \begin{bmatrix} 1&2&3 \\ 0&2&4 \\ 0&0&5 \\ \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the inverse of the matrix (if it exists): $ \begin{bmatrix} -1&5 \\ -3&2 \\ \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the inverse of the matrix (if it exists): $ \begin{bmatrix} 2&-2 \\ 4&3 \\ \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Verify A (adj A)= (adj A) A = | A | I: \[ \begin{bmatrix} 1&-1&2 \\ 3&0&-2 \\ 1&0&3 \\ \end{bmatrix} \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Verify A (adj A)= (adj A) A = | A | I: \[ \begin{bmatrix} 2&3 \\ - 4&-6 \\ \end{bmatrix} \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the adjoint of the matrix: $\begin{bmatrix} 1&-1&2 \\ 2&3&5 \\ -2&0&1 \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the adjoint of the matrix: $\begin{bmatrix} 1&2 \\ 3&4 \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the equation of the curve passing through the point$\bigg(0,\large\frac{\pi}{4}\bigg)$ whose differential equation is $\sin x\cos y\;dx+\cos x\sin y\;dy\;=\;0$

asked Nov 29, 2012 by sreemathi.v

1 answer

If $\Delta = \begin{vmatrix} a_11&a_12&a_13 \\ a_21&a_22&a_23 \\ a_31&a_32&a_33 \end{vmatrix} $ and $A_y$ is Cofactor of $a_y$, then value of $\Delta$ is:

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using Cofactors of elements of third column, evaluate $ \Delta = \begin{vmatrix} 1&x&yz \\ 1&y&zx \\ 1&z&xy \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using Cofactors of elements of second row, evaluate $ \Delta = \begin{vmatrix} 5&3&8 \\ 2&0&1 \\ 1&2&3 \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

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 $x = 0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Write Minors and Cofactors of the elements of following determinants: $ (i) \quad \begin{vmatrix} 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the differential equation$y\;e^{\large\frac{x}{y}}\;dx=\bigg(x\;e^{\Large\frac{x}{y}}+y^2\bigg)dy\;(y\neq0)$

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$

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)$

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 $x = \large\frac{\pi}{2}$

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 $x = 0$.

asked Nov 28, 2012 by sreemathi.v

1 answer

Choose the correct answer $\sin (\tan^{-1}x), |x| <1 $ is equal to

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?

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

asked Nov 28, 2012 by vaishali.a

1 answer

What is the value of: \[tan^{-1} \bigg( \frac {x}{y} \bigg) -tan^{-1} \frac {x-y}{x+y} \]

asked Nov 28, 2012 by vaishali.a

1 answer

The general solution of the differential equation $\large\frac{ydx-xdy}{y}$$=0\;is$

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$

asked Nov 28, 2012 by sreemathi.v

1 answer

The general solution of the differential equation$ e^xdy+(ye^x+2x)dx=0\; is$

asked Nov 28, 2012 by sreemathi.v

1 answer

For each of the differential equations given below,indicate its order and degree(if defined) $(i)\;\large\frac{d^2y}{dx^2}+5x\bigg(\frac{dy}{dx}\bigg)^2-6y=\log x$

asked Nov 28, 2012 by sreemathi.v

1 answer

The order of the differential equation $2x^2\large\frac{d^2y}{dx^2}$$-3\frac{dy}{dx}$$+y=0\;is$

asked Nov 28, 2012 by sreemathi.v

1 answer

Write Minors and Cofactors of the elements of following determinants: $ (i) \quad \begin{vmatrix} 2&-4 \\ 0&3 \end{vmatrix}$

asked Nov 28, 2012 by balaji.thirumalai

1 answer

If area of triangle is $35\; sq\; units$ with vertices $(2, -6), (5, 4)$ and $(k, 4)$. Then $k$ is

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Find equation of line joining (1, 2) and (3, 6) using determinants

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Find the value of $k$ if area of triangle is $4\; sq. units$ and vertices are: $(k, 0), (4, 0), (0, 2)$

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Show that the points A (a, b + c), B (b, c + a), C (c, a + b) are collinear.

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Find area of the triangle with vertices at the point given in (1, 0), (6, 0), (4, 3)

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Which of the following is correct:

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Let $A$ be a square matrix of order $3 \times 3$, then $ |kA|$ is equal to:

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} a^2+1&ab&ac \\ ab&b^2+1&bc \\ ca&cb&c^2+1 \end{vmatrix} = 1+a^2+b^2+c^2 \end{array} \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} 1+a^2-b^2&2ab&-2b \\ 2ab&1-a^2+b^2&2a \\ 2b&-2a&1-a^2-b^2 \end{vmatrix} = (1+a^2+b^2)^3 \end{array} \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} 1&x&x^2 \\ x^2&1&x \\ x&x^2&1 \end{vmatrix} = (1-x^3)^2 \end{array} \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Solve the following $\tan^{-1} \sqrt{3} -sec^{-1} (-2)$:

asked Nov 28, 2012 by vaishali.a

2 answers

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