Recent questions tagged jun-2006

Solve : $x^4+4=0$

asked Jun 12, 2013 by sreemathi.v

1 answer

If $\cos \alpha +\cos \beta + \cos \gamma = 0 = \sin \alpha + \sin \beta + \sin \gamma$, prove that $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = 0$

asked Jun 11, 2013 by sreemathi.v

1 answer

The random variable $X$ follows normal distribution $f(x)=ce\large\frac{-1/2(x-100)^{2}}{25}$ Then the value of $c$ is

asked Jun 3, 2013 by poojasapani_1

1 answer

Var $(4X+3)$ is

asked May 28, 2013 by poojasapani_1

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In the multiplicative group of $n{ th } $ roots of unity, the inverse of $\omega^{k}$ is $(k<n)$

asked May 27, 2013 by poojasapani_1

1 answer

In the set of integers with operation $^{\ast}$ defined by $a ^{\ast} b=a+b-ab,$ the value of $3^{\ast}(4^{\ast} 5)$ is

asked May 24, 2013 by poojasapani_1

1 answer

The number of rows in the truth table of $\sim[p\land(\sim q)]$ is

asked May 24, 2013 by poojasapani_1

1 answer

The particular integral of the differential equation $f(D)y=e^{ax}$ where $\;.f(D)=(D-a)g(D).g(a)\neq 0$ is

asked May 24, 2013 by poojasapani_1

1 answer

On putting $y=vx,$ the homogeneous differential equation $x^{2}dy+y(x+y)dx=0$ becomes

asked May 24, 2013 by poojasapani_1

1 answer

If $y=ke^{\lambda x}$ then its differential equation is

asked May 23, 2013 by poojasapani_1

1 answer

Volume of solid obtained by revolving the area of the ellipse $\large\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}$=$1$ about major and minor axes are in the ratio

asked May 22, 2013 by poojasapani_1

1 answer

The area between the ellipse $\large\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}$=$1$ and its auxillary circle is

asked May 22, 2013 by poojasapani_1

1 answer

The area of the region bounded by the graph of $y=\sin x$ and $y=\cos x $ between $x=0$ and $x=\large\frac{\pi}{4}$ is

asked May 22, 2013 by poojasapani_1

1 answer

An asymptote to the curve $y^{2}(a+2x)=x^{2}(3a-x)$ is

asked May 21, 2013 by poojasapani_1

1 answer

If $u=\log\begin{pmatrix}\large\frac{x^{2}+y^{2}}{xy}\end{pmatrix}$ then $x\large\frac{\partial u}{\partial x}+$$y\large\frac{\partial u}{\partial y}$ is

asked May 21, 2013 by poojasapani_1

1 answer

The curve $y=ax^{3}+bx^{2}+cx+d$ has a point of inflexion at $x=1$ then

asked May 20, 2013 by poojasapani_1

1 answer

The eccentricity of the hyperbola whose latus rectum is equal to half of its conjugate axis is

asked May 14, 2013 by poojasapani_1

1 answer

If $\omega$ is a cube root of unity then the value of $(1-\omega+\omega^{2})^{4}+(1+\omega-\omega^{2})^{4}$ is

asked May 13, 2013 by poojasapani_1

1 answer

The value of $i+i^{22}+i^{23}+i^{24}+i^{25}$ is

asked May 12, 2013 by poojasapani_1

1 answer

If $p$ represents the veriable complex number $z$ and if $|2z-1|=2|z|$ then the locus of $p$ is

asked May 12, 2013 by poojasapani_1

1 answer

The following two lines are $ \large\frac{x-1}{2}=\frac{y-1}{-1}=\frac{z}{1}$ and $\large\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z-1}{2}$ is

asked May 11, 2013 by poojasapani_1

1 answer

If $|\overrightarrow{a+b}|=|\overrightarrow{a-b}|$ then

asked May 9, 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 May 8, 2013 by poojasapani_1

1 answer

If the equation $-2x+y+z=i\;;x-2y+z=m\;;x+y-2z=n$ such that $i+m+n=0,$ then the system has

asked May 8, 2013 by poojasapani_1

1 answer

In a system of $3$ linear non-homogeneous equation with three unknowns,if $\bigtriangleup=0\;$ and $\;\bigtriangleup_{x}=0 ,\bigtriangleup_y\neq 0 $ and $ \bigtriangleup_z=0$ then the system has

asked May 7, 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

1 answer

Find the intervals of concavity and the points of inflection of the following functions: $f(x)=x^{4}-6x^{2}$

asked May 6, 2013 by poojasapani_1

1 answer

Verify Lagrange's theorem for the following function;\[\]$f(x)=x^{3}-5x^{2}-3x\;[1,3]$

asked May 3, 2013 by poojasapani_1

1 answer

Find the perimeter of the circle with radius $a$.

asked Apr 30, 2013 by poojasapani_1

1 answer

Marks in an aptitude test given to $800$ students of a school was found to be normally distributed. $10\%$ of the students scored below $40$ marks and $10\%$ of the students scored above $90$ marks. Find the number of students scored between $40$ and $90$.

asked Apr 23, 2013 by poojasapani_1

1 answer

The number of accidents in a year involving taxi drivers in a city follows a poisson distribution with mean equal to $3$ out of $1000$ taxi drivers find approximately the number of driver with more than $3$ accidents in a year $[e^{-3}=0.0498].$

asked Apr 21, 2013 by poojasapani_1

1 answer

The number of accidents in a year involving taxi drivers in a city follows a poisson distribution with mean equal to $3$. Out of $1000$ taxi drivers find approximately the number of driver with no accident in a year .$[e^{-3} = 0.0498].$

asked Apr 21, 2013 by poojasapani_1

1 answer

Solve the following differential equation;$\large\frac{d^{2}y}{dx^{2}}$$-3\large\frac{dy}{dx}$$+2y=2e^{3x}$ when $x =\log$$2$,$y=0,$ and when $x=0,y=0$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following $x^{2}\large\frac{dy}{dx}$ =$ y^{2}+2xy$ given that $y=1,$ when $x=1$

asked Apr 15, 2013 by poojasapani_1

1 answer

Find the equation of the hyperbola if its asymptotes are parallel to $x+2y-12=0$ and $x-2y+8=0, (2 , 4 ) $ is the centre of the hyperbola and it passes through $(2 , 0 )$

asked Apr 13, 2013 by poojasapani_1

1 answer

A cable of a suspension bridge is in the form of a parabola whose span is $40mts$ . The road way is $5mts$ below the lowest point of the cable . if an extra support is provided across the cable $30mts$ above the ground level, Find the length of the support if the height of the pillars are $55mts$.

asked Apr 9, 2013 by poojasapani_1

1 answer

If $ \cos\;\alpha + \cos\;\beta + \cos\;\gamma = 0 = \sin \;\alpha + \sin \;\beta + \sin \;\gamma $, prove that $\sin 2\alpha + \sin 2\beta + \sin 2\gamma = 0$

asked Apr 8, 2013 by geethradh

1 answer

Show that the lines $\large \frac{x-1}{1}=\frac{y+1}{-1}=\frac{z}{3}$ and $\large\frac{x-2}{1}=\frac{y-1}{2}=\frac{-z-1}{1}$ intersect and find their point of intersection.

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equation of the line through the point $(3 , -4 , -2 )$ and parallel to vector $\overrightarrow{9i} +\overrightarrow{6j} +\overrightarrow{2k}$.

asked Apr 6, 2013 by poojasapani_1

1 answer

Discuss the solutions of the system of equations for all values of $\lambda$. $ x+y+z=2\;,2x+y-2z=2\;,\lambda\;x+y+4z=2$

asked Apr 2, 2013 by poojasapani_1

1 answer

If$A=\begin{bmatrix} 5 & 2 \\7 & 3 \end{bmatrix}$ and$B=\begin{bmatrix} 2 & -1 \\-1 & 1 \end{bmatrix}$ verify that $(AB)^{-1}=B^{-1}A^{-1}$

asked Mar 28, 2013 by poojasapani_1

1 answer

Show that the set G of all positive rationals forms a group under the composition $$ defined by $a b = (\large\frac{ab}{3})$ for all $a, b \in G.$

asked Nov 27, 2012 by balaji.thirumalai

1 answer

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