Recent questions tagged q4

$y^{2}$=$x^{2}(1-x)$

asked Apr 24, 2013 by poojasapani_1

1 answer

The life of army shoes is normally distributed with mean $8$ months and standard deviation $2$ months. If $5000$ pairs are issued, how many pairs would be expected to need replacement within $12$ months.

asked Apr 22, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse whose foci are at $(-2,4)$ and $(4,4)$ and whose major and minor axes are 10 and 8 respectively.Also find the eccentricity of the ellipse.

asked Apr 22, 2013 by sreemathi.v

0 answers

If pairs of straight lines $x^2-2pxy-y^2=0$ and $x^2-2qxy-y^2=0$ be such that each pair bisects the angle between the other pair,prove that $pq=-1$.

asked Apr 22, 2013 by sreemathi.v

0 answers

Alpha particles are emitted by a radio active source at an average rate of $5$ in a $20$ minutes interval.Using poisson distribution find the probability that there will be at least $2$ emission in a particular $20$ minutes interval .$[e^{-5}=0.0067].$

asked Apr 21, 2013 by poojasapani_1

1 answer

Alpha particles are emitted by a radio active source at an average rate of $5$ in a $20$ minutes interval.Using poisson distribution find the probability that there will be $2$ emission.$[e^{-5}=0.0067].$

asked Apr 21, 2013 by poojasapani_1

1 answer

Four coins are tossed simultaneously .what is the probability of getting at most two heads

asked Apr 21, 2013 by poojasapani_1

1 answer

Four coins are tossed simultaneously.what is the probability of getting at least two heads

asked Apr 21, 2013 by poojasapani_1

1 answer

Four coins are tossed simultaneously .what is the probability of getting exactly $2$ heads

asked Apr 21, 2013 by poojasapani_1

1 answer

Two cards are drawn with replacement from a well shuffled deck of $52$ cards. Find the mean and variance for the number of aces.

asked Apr 20, 2013 by poojasapani_1

1 answer

A discrete random variable $x$ has the following probability distribution. Find the value of $a$ \[\] $\begin{array} {llllllll} X:& 0& 1& 2& 3& 4& 5& 6& 7& 8 &\\ {P(X):}& a& 3a &5a& 7a& 9a &11a &13a &15a&17a \end{array}$

asked Apr 18, 2013 by poojasapani_1

0 answers

A discrete random variable $x$ has the following probability distributioxs.Find $p(x<3)$\[\]$\begin{array} {llllllll} X:& 0& 1& 2& 3& 4& 5& 6& 7& 8 &\\ {P(X):}& a& 3a &5a& 7a& 9a &11a &13a &15a&17a \end{array}$

asked Apr 18, 2013 by poojasapani_1

1 answer

A discrete random variable $x$ has the following probability distributioxs. Find$ p(3$$<$$x$$<$$7)$\[\]$\begin{array} {llllllll} X:& 0& 1& 2& 3& 4& 5& 6& 7& 8 &\\ {P(X):}& a& 3a &5a& 7a& 9a &11a &13a &15a&17a \end{array}$

asked Apr 18, 2013 by poojasapani_1

1 answer

Find the equation of a plane through the point (-1,-1,2) and perpendicular to the planes $3x+2y-3z=1$ and $5x-4y+z=5.$

asked Apr 18, 2013 by sreemathi.v

0 answers

Find the radius of the circular section of the sphere $x^2+y^2+z^2=49$ cut by a plane $2x+3y-z-5\sqrt{14}=0.$

asked Apr 18, 2013 by sreemathi.v

0 answers

If $x^py^q=(x+y)^{p+q}$.Prove that $\large\frac{dy}{dx}=\large\frac{y}{x}$.

asked Apr 17, 2013 by sreemathi.v

0 answers

Prove that : $\cot \begin{pmatrix}\large\frac{\pi}{4}\normalsize -2\cot^{-1}3\end{pmatrix}=7.$

asked Apr 17, 2013 by sreemathi.v

0 answers

The rate at which the population of a city increases at any time is propotional to the population at that time. If there were $1,30,000$ people in the city in $1960 $ and $1,60,000$ in $1990$ what population may be anticipated in $2020$.$[\log_{e}(\large\frac{16}{13})=$$.2070;$$e^{.42}=1.52]$

asked Apr 17, 2013 by poojasapani_1

1 answer

Prove that $\left ( 1+\mathit{i} \right )^{4n}$ and $\left ( 1+\mathit{i} \right )^{4n+2}$ are real and purely imaginary respectively.

asked Apr 16, 2013 by geethradh

1 answer

Prove that $\left ( 1+ \cos \; \theta + \mathit{i}\sin \; \theta \right )^{\mathit{n}} + \left ( 1+ \cos \; \theta - \mathit{i}sin \; \theta \right )^{\mathit{n}} = 2^{\mathit{n+1}} \cos ^{\mathit{n}}\left ( \large\frac{\theta}{2} \right )$$ \cos \;\large\frac{n\theta }{2}$

asked Apr 16, 2013 by geethradh

1 answer

Prove that $\left ( 1+ \mathit{i\sqrt{3}} \right )^{\mathit{n}} + \left ( 1- \mathit{i\sqrt{3}} \right )^{\mathit{n}} = 2^{n+1} \cos \; \large\frac{n\pi}{3}$

asked Apr 16, 2013 by geethradh

1 answer

Prove that $\left ( 1+\mathit{i} \right )^{\mathit{n}} + \left ( 1-\mathit{i} \right )^{\mathit{n}} = 2^{\large\frac{n+2}{2}} \cos \; \large\frac{n\pi}{4}$

asked Apr 16, 2013 by geethradh

1 answer

If $y=\large\frac{\sin^{-1}x}{\sqrt{1-x^2}}$,prove that $(1-x^2)\large\frac{dy}{dx}-\normalsize xy=1.$

asked Apr 16, 2013 by sreemathi.v

0 answers

Show that : $\sin^{-1}\bigg(\large\frac{1}{\sqrt {17}}\bigg)\normalsize+\cos^{-1}\bigg(\large\frac{9}{\sqrt{85}}\bigg)\normalsize=\tan^{-1}\bigg(\large\frac{1}{2}\bigg).$

asked Apr 16, 2013 by sreemathi.v

0 answers

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

asked Apr 16, 2013 by poojasapani_1

1 answer

If $\sin y=x\sin (a+y),$show that $\large\frac{dy}{dx}=\large\frac{\sin^2(a+y)}{\sin a}$.

asked Apr 16, 2013 by sreemathi.v

0 answers

Prove that : $2\tan^{-1}\bigg(\large\frac{1}{3}\bigg)\normalsize +\cot ^{-1}(4)=\tan^{-1}\bigg(\large\frac{16}{13}\bigg).$

asked Apr 16, 2013 by sreemathi.v

0 answers

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

Solve the following $ yx^{2}dx+e^{-x}dy=0$

asked Apr 15, 2013 by poojasapani_1

1 answer

Find $\large\frac{dy}{dx}$ if $y=\tan^{-1}\large \frac{\sqrt{1-x^2}-1}{x}$

asked Apr 15, 2013 by sreemathi.v

0 answers

Solve for x : $\tan^{-1}(x-1)+\tan^{-1}x+\tan^{-1}(x+1)=\tan^{-1}3x.$

asked Apr 15, 2013 by sreemathi.v

0 answers

A standard rectangular hyperbola has its vertices at $(5 , 7 )$ and $(-3 , -1 ) $ find its equation and asymptotes.

asked Apr 13, 2013 by poojasapani_1

1 answer

Find the equation of the two tangents that can be drawn, from the point $(1 , 2 )$ to the hyperbola $2x^{2}-3y^{2}=6$

asked Apr 13, 2013 by poojasapani_1

1 answer

Find the equation of the two tangents that can be drawn, from the point $(1 , 3 )$ to the ellipse $4x^{2}+9y^{2}=36$

asked Apr 13, 2013 by poojasapani_1

1 answer

Find the equation of the two tangents that can be drawn,from the point $(2 , -3 )$ to the parabola $y^{2}=4x $

asked Apr 13, 2013 by poojasapani_1

1 answer

Using a suitable substitution find the derivative of $\tan^{-1}\large\frac{4\sqrt x}{1-4x}$ with respect to x.

asked Apr 12, 2013 by sreemathi.v

0 answers

If $\sin^{-1}x+\sin^{-1}y+\sin^{-1}z=\pi,$prove that : $x^2-y^2-z^2+2yz\sqrt{1-x^2}=0.$

asked Apr 12, 2013 by sreemathi.v

0 answers

$x$,$y$ and $z$ represent three switches in an 'ON' position and $x',y'$ and $z'$ represent the same three switches in an 'OFF' position.Construct a switching circuit representing the polynomial $(x+y)(x'+z)+y(y'+z').$Using the laws of Boolean Algebra,show that the above polynomial is equivalent to $xz+y$ and construct an equivalent switching circuit.

asked Apr 12, 2013 by sreemathi.v

0 answers

Prove that : $\sin\begin{bmatrix}2 \tan^{-1}\frac{3}{5}-\sin^{-1}\frac{7}{25}\end{bmatrix}=\large\frac{304}{425}$

asked Apr 12, 2013 by sreemathi.v

0 answers

Show that the locus of a point which moves so that the difference of its distance from the points $(5 , 0 ) $ and $(-5 , 0 )$is $8 $ is $9x^{2}-16y^{2}=144$

asked Apr 11, 2013 by poojasapani_1

1 answer

Find the equation of the hyperbola whose foci are (0,$\pm$ 13) and the length of the conjugate axis is 20.

asked Apr 11, 2013 by sreemathi.v

0 answers

Verify Lagrange's mean value theorem for the function $f(x)=\sin x-sin 2x$ in the interval [0,$\pi$].

asked Apr 11, 2013 by sreemathi.v

0 answers

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 and length of major and minor axes of $16x^{2}+9y^{2}+32x-32y-92=0$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equations and length of major and minor axes of $9x^{2}+4y^{2}=20$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equations and length of major and minor axes of $5x^{2}+9y^{2}+10x-36y-4=0$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equations and length of major and minor axes of $9x^{2}+25y^{2}=225$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse with its centre at $(4,-1)$ focus at $(1,-1)$ and given that it passes through $(8,0).$

asked Apr 10, 2013 by sreemathi.v

0 answers

Verify Rolle's theorem for the function : $f(x)=log\left \{\Large \frac{x^2+ab}{(a+b)+x}\right\}$ in the interval [a,b] where,$0 \notin [a,b]$.

asked Apr 10, 2013 by sreemathi.v

0 answers

The focus of a parabolic mirror is at a distance of $8cm$ from its centre (vertex) ,if the mirror is $25cm$ deep, find the diameter of the mirror.

asked Apr 9, 2013 by poojasapani_1

1 answer

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