Recent questions tagged oct-2009

Use the truth table to establish which of the following statements are tautologies and which are contradictions.

asked Sep 13, 2013 by sreemathi.v

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Solve : $x^4+4=0$

asked Jun 12, 2013 by sreemathi.v

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For a poisson distribution with parameter $ \lambda=0.25$ the value of the $2^{nd}$ moment about the origin is

asked Jun 3, 2013 by poojasapani_1

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$\mu_{2}=20, \mu'_{2}=276$ for a discrete random variable $X$. Then the mean of the random variable $X$ is

asked May 28, 2013 by poojasapani_1

1 answer

If $f(x)=\large\frac{A}{\pi}\frac{1}{16+x^{2'}}$$-\infty<x<\infty$\[\]is a p.d.f of a continuous random variable $X,$ then the value of $A$ 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

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Which of the following is a contradiction ?

asked May 24, 2013 by poojasapani_1

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If a compound statement is made up of three simple statements, then the number of rows in the truth table is

asked May 24, 2013 by poojasapani_1

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The differential equation formed by eliminating $A$ and $B$ from the relation $y=e^{x}(A\cos x+ B\sin x) $ is

asked May 23, 2013 by poojasapani_1

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A particular integral of $(D^{2}-4D+4)y=e^{2x}$ is

asked May 23, 2013 by poojasapani_1

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Integrating factor of $\large\frac{dy}{dx}+\frac{1}{x\log x}$$.y=\large\frac{2}{x^{2}}$ is

asked May 22, 2013 by poojasapani_1

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The curved surface area of a sphere of radius $5,$ intercepted between two parallel planes of distance $2$ and $4$ from the centre is

asked May 22, 2013 by poojasapani_1

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The volume, When the curve $y=\sqrt{3+x^{2}}$ from $x=0$ to $x=4$ is rotated about $x$-axis is

asked May 22, 2013 by poojasapani_1

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The value of $\int\limits_{0}^{\pi}\sin^{4}x dx$ is

asked May 21, 2013 by poojasapani_1

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The curve $a^{2}y^{2}=x^{2}(a^{2}-x^{2})$ has

asked May 21, 2013 by poojasapani_1

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The curve $y^{2}(x-2)=x^{2}(1+x)$ has

asked May 21, 2013 by poojasapani_1

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$\;\lim \limits_{x \to 0}\Large\frac{a^{x}-b^{x}}{c^{x}-d^{x}}$ is

asked May 18, 2013 by poojasapani_1

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If $s=r^{3}-4t^{2}+7,$ the velocity when the acceleration is zero is

asked May 16, 2013 by poojasapani_1

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The slope of the normal to the curve $y=3x^{2}$ at the point whose $x$ coordinate is $2$ is

asked May 15, 2013 by poojasapani_1

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The eccentricity of the hyperbola $ 12y^{2}-4x^{2}-24x+48y-127=0$ is

asked May 14, 2013 by poojasapani_1

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The sum of the distance of any point on the ellipse $ 4x^{2}+9y^{2}=36 $ from $(\sqrt{5},0) and (-\sqrt{5} ,0) $ is

asked May 13, 2013 by poojasapani_1

1 answer

The length of the latus rectum of the parabola whose vertex is $(2 ,-3)$ and the directrix $ x=4 $ is

asked May 13, 2013 by poojasapani_1

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The point of intersection of the tangents at $t_{1}=t $ and $t_{2}=3t$ to the parabola $y^{2}=8x $ is

asked May 13, 2013 by poojasapani_1

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If $-i+2 $ is one root of the equation $ax^{2}-bx+c=0$, then the other root is

asked May 13, 2013 by poojasapani_1

1 answer

The modulus and amplitude of the complex number $[e^{3-i \pi/4}]^{3}$ is respectively

asked May 11, 2013 by poojasapani_1

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The shortest distance of the point $(2 , 10 ,1 )$ from the plane $\overrightarrow{r}.(\overrightarrow{3i}-\overrightarrow{j}+\overrightarrow{4k})=2\sqrt{26}$ is

asked May 10, 2013 by poojasapani_1

1 answer

If the projection of $\overrightarrow{a} $ on $\overrightarrow{b} $ and the projection of $\overrightarrow{b}$ on $\overrightarrow{a}$ are equal then the angle between $\overrightarrow{a}+\overrightarrow{b}$ and $\overrightarrow{a}-\overrightarrow{b}$ is

asked May 10, 2013 by poojasapani_1

1 answer

If $\overrightarrow{p} ,\overrightarrow{q}$ and $\overrightarrow{p}+\overrightarrow{q}$ are vectors of magnitude $\lambda$ than the magnitude of $|\overrightarrow{p}-\overrightarrow{q}|$ is

asked May 9, 2013 by poojasapani_1

1 answer

The area of the parallelogram having a diagonal $\overrightarrow{3i}+\overrightarrow{j}-\overrightarrow{k}$ and a side $\overrightarrow{i}-\overrightarrow{3j}+\overrightarrow{4k} $ is

asked May 9, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two unit vectors and $\theta $is the angle between them, then $(\overrightarrow{a}+\overrightarrow{b})$ is a unit vector if

asked May 8, 2013 by poojasapani_1

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Inverse of $\begin{bmatrix}2& -1 \\-5 & 3 \end{bmatrix}$ is

asked May 7, 2013 by poojasapani_1

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If the matrix $\begin{bmatrix} -1 & 3 & 2 \\1 & k & -3 \\1 & 4 & 5 \end{bmatrix}$ has an inverse than the value of $k$

asked May 7, 2013 by poojasapani_1

1 answer

If the rank of the matrix$\begin{bmatrix} \lambda & -1 & 0 \\0 & \lambda & -1 \\-1 & 0 & \lambda \end{bmatrix}$ is $2$, than $\lambda$ is

asked May 7, 2013 by poojasapani_1

1 answer

Find two numbers whose sum is $100 $ and whose product is a maximum.

asked May 5, 2013 by poojasapani_1

1 answer

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

asked May 3, 2013 by poojasapani_1

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Find the surface area of the solid generated by revolving the arc of the parabola$\;y^{2}=4ax$, bounded by its latus rectum about $x$- axis.

asked Apr 30, 2013 by poojasapani_1

1 answer

Using Euler's theorem prove the following: if$\;u=\tan^{-1}\large[\frac{x^{3}+y^{3}}{x-y}]$ prove that $x\large\frac{\partial u}{\partial x}$+$y\large\frac{\partial u}{\partial y}=$$\sin 2u$

asked Apr 26, 2013 by poojasapani_1

1 answer

Use differentials to find an approximate value for the given numbers $\sqrt{36.1}$

asked Apr 24, 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

Find the mean and variance for the following probability density functions $f(x) = \left\{ \begin{array}{l l} \alpha e^{-\alpha x} ,& \quad \text{if $x$$>$$0$}\\ 0 ,& \quad \text{otherwise} \end{array} \right.$

asked Apr 20, 2013 by poojasapani_1

1 answer

If $\alpha $ and $\beta$ are the roots of the equation $ x^{2}-2px+\left ( p^{2} + q^{2}\right )=0 $ and $ tan \; \theta =\large \frac{q}{y+p} $ show that $ \large\frac{\left (y+\alpha \right )^{n}-\left ( y+\beta \right )^{n}}{\alpha -\beta }$ = $ q^{n-1}\large\frac{sin \;n\theta }{sin\;^{n}\theta }$

asked Apr 18, 2013 by geethradh

1 answer

A cup of coffee at temperature $100^{\circ}$$C$ is placed in a room whose temperature is $15^ {\circ}$$C$ and it cools to $60^{\circ}$$C$ in $5$ minutes . Find its temperature after a further interval of $5$ minutes.

asked Apr 17, 2013 by poojasapani_1

1 answer

Solve the following. $(1+x^{2}) \large\frac{dy}{dx}$$+2xy\;=\; \cos$$ x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Find the eccentricity, centre , foci , and vertices of the following hyperbolas and draw their diagrams: $x^{2}-3y^{2}+6x+6y+18=0$

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

if $\ \overrightarrow{a}= \overrightarrow{2i}+ \overrightarrow{3j}- \overrightarrow{k} , \overrightarrow{b}= -\overrightarrow{2i}+ \overrightarrow{5k}, \overrightarrow{c}= \overrightarrow{j}- \overrightarrow{3k}. $ Verify that $ \overrightarrow{a}\times ( \overrightarrow{b}\times \overrightarrow{c})= (\overrightarrow{a}. \overrightarrow{c}) \overrightarrow{b}- (\overrightarrow{a}. \overrightarrow{b})c$

asked Apr 5, 2013 by poojasapani_1

1 answer

A force magnitude $5$ units acting parallel to $\overrightarrow{2i}-\overrightarrow{2j}+ \overrightarrow{k}$ displaces the point of application from $(1,2,3)$to $(5,3,7) $ find the work done.

asked Apr 4, 2013 by poojasapani_1

1 answer

For what valus of $k$, the system of equations $kx+y+z=1\;,x+ky+z=1\;,x+y+kz=1\;,$have (i) unique solution (ii) more than one solution (iii) no solution.

asked Apr 2, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method : $4x+5y=9\;,8x+10y=18 $

asked Mar 29, 2013 by poojasapani_1

1 answer

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