Recent questions tagged q9

Solve the following differential equation : $(1+x^2)\large\frac{dy}{dx}$$-2xy=(x^2+2)(x^2+1)$

asked Jul 16, 2013 by sreemathi.v

1 answer

A man pushes a truck initially at rest and weighting $2.5$ tonne along a horizontal rail with a steady force of $200 N$. The resistance to the motion amounts to $30 N$ per tonne. The velocity of the truck at the end of 30 seconds is

asked Jul 4, 2013 by meena.p

1 answer

Two resistances are expressed as $R_1=(4\pm0.5) \Omega$ and $R_2=(12 \pm 0.5) \Omega$. what is the net resistance when they are connected 1) series 2) in parallel, with percentage error ?

asked Jun 17, 2013 by meena.p

1 answer

The equation of the normal to the curve $\theta =\large\frac{1}{t}$ at the point $(-3 , -1/3)$ is

asked May 15, 2013 by poojasapani_1

1 answer

If $A$ is a square matrix of order $n$ then |adj$A$| is

asked May 7, 2013 by poojasapani_1

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At what angle $\theta $ do the curves $y=a^{x}$ and $y=b^{x}$ intersect $(a{\neq}b)$?

asked May 3, 2013 by poojasapani_1

1 answer

Gravel is being dumped from a conveyor belt at a rate of $30\;ft^{3}/min$ and its coarsened such that it forms a pile in the shape of the cone whose base diameter and hight are always equal. How fast is the hight of the pile increasing when the pile is $10$ ft hight?

asked May 1, 2013 by poojasapani_1

1 answer

Find the common area enclosed by the parabolas $4y^{2}=9x$ and $3x^{2}=16y$

asked Apr 28, 2013 by poojasapani_1

1 answer

Evaluate the following problems using properties of integration: $\int\limits_{0}^{1} x(1-x)^{10}dx$

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate the following problems using second fundamental theorem: $\int\limits_{0}^{\large\frac{\pi}{2}}\sin 2x \cos x dx$

asked Apr 27, 2013 by poojasapani_1

1 answer

Find the value of $x$,if $1\ast(x\ast 2)=8$,where the operation $\ast$ is defined by $a\ast b=a+b+\large\frac{ab}{2}\normalsize,\forall a,b,\in R$.

asked Apr 22, 2013 by sreemathi.v

0 answers

A set $S=\{x : x\in R,x\neq -2 \}$ is given.A binary operation $ \ast $ on S is defined by $a \ast b=a+b+\large\frac{ab}{2}\normalsize,\forall a,b,\in R$.Prove that $(S,\ast)$ is an abelian group.

asked Apr 22, 2013 by sreemathi.v

0 answers

If $x\;=\cos\;\alpha +i\sin\;\alpha\;;\; y\;= \cos\;\beta + i\sin \;\beta $ prove that $x^{m}y^{n} \;+\large \frac{1}{x^{m}y^{n}}$$= \;2\cos \;\left ( m\alpha + n\beta \right )$

asked Apr 19, 2013 by geethradh

1 answer

A continuous random variable $x$ has the p.d.f defined by $f(x) = \left\{ \begin{array}{1 1} ce^{-ax} & \quad 0 < x < \infty \\ 0 & \quad \text{else where} \end{array} \right.$ Find the value of $c$ if $a>0$

asked Apr 19, 2013 by poojasapani_1

1 answer

Prove the right cancellation law in a group.

asked Apr 19, 2013 by sreemathi.v

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Consider the non empty set S={0,1,2,3,4}.Show that $(S,\oplus_5)$ is a group where $\oplus_5$ represents addition modulo 5.Also find 'x' if $x\oplus_5$ 3=4,$x\in S$.

asked Apr 19, 2013 by sreemathi.v

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Solve the differential equation : $\tan x\large\frac{dy}{dx}\normalsize+2y=\sec x$

asked Apr 17, 2013 by sreemathi.v

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Using Demoivre's theorem,find the least value of $n\in N$ for which the expression $(i+1)^n+(1-i)^n$ is equal to $-2^{\large\frac{n+2}{2}}$

asked Apr 17, 2013 by sreemathi.v

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Solve the differential equation : $y dx-(x+2y^2)dy=0$.

asked Apr 16, 2013 by sreemathi.v

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Find the cube roots of -27 and show that the sum of the cube roots is equal to zero.

asked Apr 16, 2013 by sreemathi.v

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Solve the following differential equation; $D^{2}$$y=-9\sin$$3x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Show that the equation of the curve whose slope at any point is equal to $y+2x$ and which passes through the origin is $y\;=\;2(e^{x}-x-1)$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the differential equation : $x\large\frac{dy}{dx}\normalsize-y=\sqrt {x^2+y^2}$.

asked Apr 16, 2013 by sreemathi.v

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Prove that $(1+i\sqrt 3)^8+(1-i\sqrt 3)^8=-2^8$ by using De Moiver's Theorem.

asked Apr 16, 2013 by sreemathi.v

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Solve : $(x^2+y^2)dx-2xydy=0$,given that $y=0$,when $x=1$.

asked Apr 15, 2013 by sreemathi.v

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If the ratio $\large\frac{z-i}{z-1}$ is purely imaginary,prove that the point $z$ lies on the circle whose centre is the point $\large\frac{1}{2}\normalsize(1+i)$ and radius is $\large\frac{1}{\sqrt 2}$.

asked Apr 15, 2013 by sreemathi.v

0 answers

Solve the following differential equation for a particular solution : $dy=(5x-4y)dx;$ when $y=0$ and $x=0$.

asked Apr 12, 2013 by sreemathi.v

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If $z=\large\frac{13-5i}{4-9i}$,prove by using De Moivre's theorem that $z^6=-8i$.

asked Apr 12, 2013 by sreemathi.v

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Find the locus of a complex number $z=x+iy$,satisfying the relation $\mid 3z-4i\mid \leq \mid 3z+2\mid.$Illustrate the locus in the Argand plane.

asked Apr 12, 2013 by sreemathi.v

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Solve the differential equation : $(y+\log x)dx-xdy=0$,given that $y=0$,when $x=1$.

asked Apr 12, 2013 by sreemathi.v

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Solve the following differential equation for a particular solution : $y-x\large\frac{dy}{dx}\normalsize=x+y\large\frac{dy}{dx}$,when $y=0$ and $x=1$.

asked Apr 11, 2013 by sreemathi.v

0 answers

Using De moivre's theorem,find the value of : $(1+i\sqrt 3)^6+(1-i\sqrt 3)^6$

asked Apr 11, 2013 by sreemathi.v

0 answers

The orbit of the planet mercury around the sun is in elliptical shape with sun at a focus. The semi-major axis is of length $36$ million miles and the eccentricity of the orbit is $0.206$ The greatest possible distance between mercury and sun.

asked Apr 11, 2013 by poojasapani_1

1 answer

The orbit of the planet mercury around the sun is in elliptical shape with sun at a focus. The semi-major axis is of length $36$ million miles and the eccentricity of the orbit is $0.206$ Find how close the mercury gets to sun?

asked Apr 11, 2013 by poojasapani_1

1 answer

Solve the differential equation :$\Large \frac{dy}{dx}\normalsize -3y cot\;x=sin \;2x$,given y=2,when $x=\Large \frac{\pi}{2}$

asked Apr 10, 2013 by sreemathi.v

0 answers

Using De Moivre's theorem prove that : $\bigg(\large \frac{1+cos\; \theta+isin\;\theta}{1+cos\; \theta-i sin\;\theta}\bigg)^n\normalsize$$ =cos \;n\theta+i \sin n\theta,$where $i=\sqrt {-1}.$

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the vector and cartesian equation to the plane through the point $(-1 , 3 , 2 ) $ and perpendicular to the planes $x+2y+2z=5$ and $3x+y+2z=8.$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the angle between the lines $\overrightarrow{r}=\overrightarrow{5i}-\overrightarrow{7j}+\mu (-\overrightarrow{i}+\overrightarrow{4j}+\overrightarrow{2k}) \overrightarrow{r}=-\overrightarrow{2i}+\overrightarrow{k}+\lambda (\overrightarrow{3i}+\overrightarrow{4k})$

asked Apr 7, 2013 by poojasapani_1

1 answer

For any vector $\overrightarrow{a}$ Prove that $\overrightarrow{i} \times (\overrightarrow{a}\times\overrightarrow{i})+ \overrightarrow{j} \times (\overrightarrow{a}\times\overrightarrow{j})+ \overrightarrow{k } \times(\overrightarrow{a}\times\overrightarrow{k})=\overrightarrow{2a}$

asked Apr 6, 2013 by poojasapani_1

1 answer

Show that the torque about the point $ A(3, -1, 3 )$ of a force $\overrightarrow{4i}+\overrightarrow{2j}\overrightarrow{k}$ throught the point $\overrightarrow\;B(5, 2, 4)$ is $\overrightarrow{i}+\overrightarrow{2j}-\overrightarrow{8k}$.

asked Apr 5, 2013 by poojasapani_1

1 answer

Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ be unit vectors such that $\overrightarrow{a}.\overrightarrow{b}=\overrightarrow{a}.\overrightarrow{c}=0$ and the angle between $\overrightarrow{b}$ and $\overrightarrow{c}$ is $\Large\frac{\pi}{6}.$ Prove that $\overrightarrow{a}=\pm 2(\overrightarrow{b}\times\overrightarrow{c})$

asked Apr 4, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}\;,\overrightarrow{b}\;,\overrightarrow{c}$ are three mutually perpendicular unit vectors,than prove that $|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|=\sqrt{3}$

asked Apr 3, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method: $\large \frac{1}{x}+\frac{2}{y}-\frac{1}{z}=1\;;\frac{2}{x}+\frac{4}{y}+\frac{1}{z}=5\;;\frac{3}{x}-\frac{2}{y}-\frac{2}{z}=0$

asked Mar 29, 2013 by poojasapani_1

1 answer

If $A=\Large\frac{1}{3}$$\begin{bmatrix} 2 & 2 & 1 \\-2 & 1 & 2 \\1 & -2 & 2 \end{bmatrix}$ prove that $A^{-1}=A^T$.

asked Mar 29, 2013 by poojasapani_1

1 answer

If Matrix A = $\begin{bmatrix} 3 &-3 \\ -3 & 3 \end{bmatrix}$, and $A^2=\lambda A$, then write the value of $\lambda$.

asked Mar 22, 2013 by sreemathi.v

1 answer

If Matrix A = $\begin{bmatrix} 2 &-2 \\ -2 & 2 \end{bmatrix}$, and $A^2=pA$, then write the value of $p$.

asked Mar 22, 2013 by sreemathi.v

1 answer

Find the length of the perpendicular drawn from the origin to the plane 2X-3Y+6Z+21=0.

asked Mar 20, 2013 by sreemathi.v

1 answer

Using the properties of determinants,\[\begin{vmatrix}a^2+2a &2a+1 & 1\\2a+1 & a+2 & 1\\3 & 3 & 1\end{vmatrix}=(a-1)^3\]

asked Mar 15, 2013 by sreemathi.v

1 answer

Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $(vi)\;\; a \ast b = {ab}^2$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $(v)\;\; a \ast b = \frac{ab}{4}$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

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