Recent questions tagged q5

The radius of a circular disc is given as $24cm$ with a maximum error in mesurement of $0.02cm$ Use differentials to estimate the maximum error in the calculated area of the dise.

asked Apr 24, 2013 by poojasapani_1

1 answer

$y^{2}$=$(x-a)(x-b)^{2};a,b>0,a>b,$

asked Apr 24, 2013 by poojasapani_1

1 answer

The mean weight of $500 $ male students in a certain college in $151$ pounds and the standard deviation is $15$ pounds. Assuming the weights are normally distributed, find how many students weigh more than $185$ pounds

asked Apr 22, 2013 by poojasapani_1

1 answer

The mean weight of $500 $ male students in a certain college in $151$ pounds and the standard deviation is $15$ pounds. Assuming the weights are normally distributed, find how many students weigh between $120$ and $155$ pounds

asked Apr 22, 2013 by poojasapani_1

1 answer

A sphere $x^2+y^2+z^2-3ax-3by-3cz=0$ has a constant radius $3r$.It cuts the axes at the point A,B and C.Show that the centroid of the triangle ABC lies on the sphere $x^2+y^2+z^2=4r^2$

asked Apr 22, 2013 by sreemathi.v

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Show that : $\sin^{-1}\large\frac{4}{5}\normalsize+\cos^{-1}\large\frac{2}{\sqrt 5}\normalsize =\cot^{-1}\large\frac{2}{11}$.

asked Apr 22, 2013 by sreemathi.v

0 answers

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

The overall percentage of passes in a certain examination is $80$.If $6$ candidates appear in the examination what is the probability that atleast $5$ pass the examination.

asked Apr 21, 2013 by poojasapani_1

1 answer

In a gambling game a man wins Rs.$10 $ if he gets all heads or all tails and loses Rs.$5$ if he gets $1$ or $2$ heads when $3$ coins are tossed once. Find his expectation of gain.

asked Apr 20, 2013 by poojasapani_1

1 answer

Evaluate :$\Large \int_{\normalsize 0}^{\large \frac{1}{2}} \large \frac{\sin^{-1}x}{(1-x^2)^\frac{3}{2}}$$dx$

asked Apr 18, 2013 by sreemathi.v

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show that the function $f(x)=x^2-6x+1$ satisfies the Lagrange's Mean value Theoem.Also find the co-ordinate of a point at which the tangent to the curve represented by the above function is parallel to the chord joining A(1,-4) and B(3,-8).

asked Apr 18, 2013 by sreemathi.v

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

Verify that the following are probability density functions.$f(x)=\large\frac{1}{\pi}\frac{1}{(1+x^{2})'}$$-\infty$$<$$x$$<\infty $

asked Apr 18, 2013 by poojasapani_1

1 answer

Verify that the following are probability density functions.$f(x) = \left\{ \begin{array}{l l} \frac { 2x}{9} & \quad \text{0 $\leq$ x$\leq$3}\\ 0 & \quad \text{elsewhere} \end{array} \right.$

asked Apr 18, 2013 by poojasapani_1

1 answer

Prove that the area of right-angled traingle of a given hypotenuse is maximum when the triangle is isosceles.

asked Apr 17, 2013 by sreemathi.v

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Examine the validity and conclusion of Rolle's theorem for the function $f(x)=e^x\sin x,\forall x\in [0,\pi]$.

asked Apr 17, 2013 by sreemathi.v

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A radioactive substance disintegrates at a rate proportional to its mass. When its mass is $10 $mgm, the rate of disintegration is $0.051$ mgm per day. How long will it take for the mass to be reduced from $10$mgm to $5$mgm.$ [\log_{e}$$2=0.6931]$

asked Apr 17, 2013 by poojasapani_1

1 answer

Find the volume of the largest cone that can be inscribed in a sphere of radius R.

asked Apr 16, 2013 by sreemathi.v

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Verify Rolle's theorem for the function $f(x)=e^{2x}(\sin 2x-\cos 2x)$ defined in the interval $\begin{bmatrix}\large\frac{\pi}{8},\frac{5\pi}{8}\end{bmatrix}$

asked Apr 16, 2013 by sreemathi.v

1 answer

Solve the following differential equation; $(D^{2}+1)$Y=$0$ when $x=0;y=2$ and when $x=\large\frac{\pi}{2};$$y=-2$

asked Apr 16, 2013 by poojasapani_1

1 answer

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

asked Apr 16, 2013 by poojasapani_1

1 answer

Show that the semi-vertical angle of a cone of maximum volume and of given slant height is $\tan^{-1}(\sqrt 2).$

asked Apr 16, 2013 by sreemathi.v

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Verify Lagrange's mean value theorem for the function $f(x)=3x^2-5x+1$ defined in interval $[2,5].$

asked Apr 16, 2013 by sreemathi.v

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Solve the following $(x^{2}+y^{2})dx+3xy dy$=$0$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $(x^{2}+5x+7) dy+\sqrt{9+8y-y^{2}}dx=0$

asked Apr 15, 2013 by poojasapani_1

1 answer

An open box with a square base is to be made out of a given quantity of cardboard whose area is $c^2$ square units.Show that the maximum volume of the box is $\large\frac{c^3}{6\sqrt 3}$cubic units.

asked Apr 15, 2013 by sreemathi.v

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Use Lagrange's mean value theorem to be determine a point P on the curve $y=\sqrt{x-2}$ defined in the interval [2,-3],where the tangent is parallel to the chord joining the end points on the curve.

asked Apr 15, 2013 by sreemathi.v

1 answer

Find the equation of the rectangular hyperbola which has its center at $(2 , 1 )$ one of its asymptotes $ 3x-y-5=0 $ and which passes through the point $(1 , -1 )$

asked Apr 13, 2013 by poojasapani_1

1 answer

Prove that the line $5x+12y=9$ touches the hyperbola $x^{2}-9y^{2}=9$ and find its point of contact.

asked Apr 13, 2013 by poojasapani_1

1 answer

A wire of length 20m is available to fence off a flower bed in the form of a sector of a circle.What must be the radius of the circle,if we wish to have a flower bed with the greatest possible area?

asked Apr 12, 2013 by sreemathi.v

1 answer

It is given that Rolle's theorem holds good for the function : $f(x)=x^3+ax^2+bx,x\in [1,2]$ at the point $x=\large\frac{4}{3}$.Find the values of a and b.

asked Apr 12, 2013 by sreemathi.v

1 answer

A closed right circular cylinder has volume $\large\frac{539}{2}$cubic units.Find the radius and the height of the cylinder so that the total surface area is minimum.

asked Apr 12, 2013 by sreemathi.v

1 answer

Using a suitable substitution,find the derivative of $tan^{-1}\large\sqrt{\frac{a-x}{a+x}}$ with respect to $x$.

asked Apr 12, 2013 by sreemathi.v

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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

Find the eccentricity, centre , foci , and vertices of the following hyperbolas and draw their diagrams: $x^{2}-4y^{2}+6x+16y-11=0$

asked Apr 11, 2013 by poojasapani_1

1 answer

Find the eccentricity, centre , foci , and vertices of the following hyperbolas and draw their diagrams: $\large\frac{y^{2}}{9}-\frac{x^{2}}{25}=$$1$

asked Apr 11, 2013 by poojasapani_1

1 answer

Find the eccentricity, centre , foci , and vertices of the following hyperbolas and draw their diagrams: $25x^{2}-16y^{2}=400$

asked Apr 11, 2013 by poojasapani_1

1 answer

Draw a rough sketch of the curves $y=(x-1)^2$ and $y=(x-1)$.Hence,find the area of the region bounded by these curves.

asked Apr 11, 2013 by sreemathi.v

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Evaluate : $\large\int\frac{x^2-5x-1}{x^4+x^2+1}\normalsize dx$.

asked Apr 11, 2013 by sreemathi.v

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A printed page is to have a total area of 80 sq.cm with a margin of 1 cm at the top and on each side and a margin of 1.5 cm at the bottom.What should be the dimensions of the page so that the printed area will be maximum?

asked Apr 10, 2013 by sreemathi.v

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If,$e^y(x+1)=1$,then show that : $\large \frac{d^2y}{dx^2}=\bigg(\frac{dy}{dx}\bigg)^2$

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the equations of directrices, latus rectum and lengths of latus rectums of the following ellipses: $3x^{2}+2y^{2}-30x-4y+23=0$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equations of directrices, latus rectum and lengths of latus rectums of the following ellipses: $x^{2}+4y^{2}-8x-16y-68=0.$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equations of directrices, latus rectum and lengths of latus rectums of the following ellipses: $9x^{2}+16y^{2}=144$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equations of directrices, latus rectum and lengths of latus rectums of the following ellipses: $25x^{2}+169y^{2}=4225$.

asked Apr 10, 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

Find the centre and radius of the following spheres: $\overrightarrow{r}^{2}-\overrightarrow{r} . (\overrightarrow{4i}+\overrightarrow{2j}-\overrightarrow{6k})-11=0$

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the centre and radius of the following spheres :$x^{2}+y^{2}+z^{2}+4x-8x+2z=5$

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the centre and radius of the following spheres : $|\overrightarrow{2r}+(\overrightarrow{3i}-\overrightarrow{j}+\overrightarrow{4k})|=4$

asked Apr 9, 2013 by poojasapani_1

1 answer

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