Recent questions tagged medium

Find the general solution of the differential equation $\large\frac{dy}{dx}$$+2y=\sin x$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $\cos^2x\large\frac{dy}{dx}$$+y=\tan x\bigg(0\leq x<\large\frac{\pi}{2}\bigg)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $x\large\frac{dy}{dx}$$+2y=x^2\log x$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $x \log x\large\frac{dy}{dx}$$+y=\large\frac{2}{x}$$\log x$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $(1+x^2)dy+2xy\;dx=\cot x\;dx\;(x\neq0)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $x\large\frac{dy}{dx}$$+y-x+xy\cot x=0\;(x\neq0)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $(x+y)\large\frac{dy}{dx}$$=1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $y\;dx+(x-y^2)dy=0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $(x+3y^2)\large\frac{dy}{dx}=y$$\;(y>0)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition$\large\frac{dy}{dx}$$+2y\tan x=\sin x;\;y=o\;when\;x=\large\frac{\pi}{3}$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $(1+x^2)\large\frac{dy}{dx}$$+2xy=\large\frac{1}{1+x^2}$$;y=0\;when\;x=1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $\large\frac{dy}{dx}-$$3y\cot x=\sin 2x;\;y=2\;when\;x=\large\frac{\pi}{2}$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the equation of curve passing through the origin given that the slope of the tangent to the curve at any point $(x,y)$ is equal to the sum of the coordinates of the point .

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the cartesian equation of the line which passes through the point (-2, 4, -5) and parallel to the line given by $\frac{\large x+3}{\large 3} = \frac{\large y-4}{\large 5} = \frac{\large z+8}{\large 6}$.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Prove that \[sin^{-1} \frac{8}{17} +sin^{-1} \frac{3}{5} =tan^{-1} \frac{77}{36}\]

asked Nov 29, 2012 by vaishali.a

1 answer

Prove that \[cos^{-1} \frac {4}{5} +cos^{-1} \frac{12}{13}=cos^{-1} \frac{33}{65}\]

asked Nov 29, 2012 by vaishali.a

1 answer

Prove that \[ cos^{-1} \frac {12}{13} +sin^{-1} \frac{3}{5}=sin^{-1} \frac{56}{65}\]

asked Nov 29, 2012 by vaishali.a

1 answer

What does $\sin^{-1} \frac{5}{13}+\cos^{-1} \frac {3}{5}$ reduce to?

asked Nov 29, 2012 by vaishali.a

1 answer

Prove that \[tan^{-1} \frac{1}{5}+ tan^{-1} \frac{1}{7}+tan^{-1}\frac{1}{3}+tan^{-1} \frac{1}{8}= \frac{\pi}{4}\]

asked Nov 29, 2012 by vaishali.a

1 answer

Prove that \[tan^{-1} \sqrt{x} = \frac{1}{2} cos^{-1} \;\; \bigg(\frac{1-x}{1+x}\bigg), x\in [0,1]\]

asked Nov 29, 2012 by vaishali.a

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

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using properties of determinants, prove that: $\begin{vmatrix} 3a&-a+b&-a+c\\ -b+a&3b&-b+c\\ -c+a&-c+b&3c \end{vmatrix}= 3(a+b+c)(ab+bc+ca)$

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.

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}) \;\;\;\; $

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} $

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. $

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} $

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} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

\[ \text{Prove that the determinant } \begin{vmatrix} x&sin\theta&cos\theta \\ -sin\theta&-x&1\\ cos\theta&1&x \end{vmatrix} \text{ is independent of } \theta \]

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

asked Nov 29, 2012 by sreemathi.v

1 answer

Solve system of linear equations, using matrix method: $5x+2y=3$ $3x+2y=5$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method: $4x-3y=3$ $3x-5y=7$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method: $2x-y=-2$ $3x+4y = 3$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method: $5x+2y=4 $ $7x+3y = 5$

asked Nov 29, 2012 by balaji.thirumalai

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

asked Nov 29, 2012 by sreemathi.v

1 answer

Solve the following Linear Programming Problems graphically: Minimise $Z = x + 2y$, subject to $2x + y \geq 3, x + 2y \geq 6, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Show that the minimum of $Z$ occurs at more than two points. Minimise and Maximise $Z = 5x + 10 y$ subject to $x + 2y \leq 120, x + y \geq 60, x – 2y \geq 0, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Show that the minimum of Z occurs at more than two points. Minimise and Maximise $Z = x + 2y$ subject to $ x + 2y \geq 100, 2x – y \leq 0, 2x + y \leq 200; x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

prove that \[tan^{-1} \left ( \frac {{\sqrt {1+x}}-{\sqrt {1-x}}}{{\sqrt {1+x}}+{\sqrt {1-x}}} \right ) = \frac {\pi}{4} -\frac{1}{2} cos^{-1}x,-\frac{1}{\sqrt2} \leq x \leq 1 \]

asked Nov 29, 2012 by vaishali.a

1 answer

Show that the minimum of Z occurs at more than two points. Maximise $z = – x + 2y$, subject to the constraints: $ x \geq 3, x + y \geq 5, x + 2y \geq 6, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

\[ \text{For the matrix A = } \begin{bmatrix} 3 & 2 \\ 1 & 1 \end{bmatrix}, \text{ find the numbers a and b such that } A^{2} + aA + bI = O \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.

asked Nov 29, 2012 by sreemathi.v

1 answer

\[ \text{If A = } \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}, \text{show that } A^{2} -5A +7I = 0. \text{ Hence find } A^{-1}\]

asked Nov 29, 2012 by balaji.thirumalai

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

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

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

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