Recent questions tagged q1

Solve the differential equation : $\large \frac{dy}{dx}=e^{x+y}+x^2e^y$

asked Apr 11, 2013 by sreemathi.v

0 answers

A word consists of 9 different alphabets,in which there are 4 consonants and 5 vowels.Three alphabets are chosen at random .What is the probability that more than one vowel will be selected?

asked Apr 11, 2013 by sreemathi.v

1 answer

Find the modulus and argument of the complex number $\large \frac{2+i}{4i+(1+i)^2}$

asked Apr 11, 2013 by sreemathi.v

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Evaluate : $\large \int_0^1\frac{xe^x}{(1+x)^2}\normalsize dx$

asked Apr 11, 2013 by sreemathi.v

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Evaluate : $\lim_{y\to 0}\large \frac{y-tan^{-1}y}{y-sin y}$

asked Apr 11, 2013 by sreemathi.v

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Evaluate : $\large \int \frac{cosec x}{\log \;\tan\big(\frac{x}{2}\big)}\normalsize dx.$

asked Apr 11, 2013 by sreemathi.v

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Two regression lines are represented by $2x+3y-10=0$ and $4x+y-5=0$.Find the line of regression of y on x.

asked Apr 11, 2013 by sreemathi.v

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Solve for x : $\sin(2\tan^{-1}x)=1$

asked Apr 11, 2013 by sreemathi.v

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Find the values of k,if the equation $8x^2-16xy+ky^2-22x+34y=12$ represents an ellipse.

asked Apr 11, 2013 by sreemathi.v

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If A=$\begin{bmatrix}3 & -2\\4 & -2\end{bmatrix}$,find x such that $A^2=xA-2I.$Hence find $A^{-1}$.

asked Apr 11, 2013 by sreemathi.v

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Find the equation of the ellipse if the vertices are $(\pm 4 , 0)$and $e=\large\frac{\sqrt{3}}{2}$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the foci are $(\pm 3 , 0 ),$ and the length of the latus rectum is $\large\frac{32}{5}$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the centre is$ (3 , -1 ),$ one of the foci is $(6 , -1)$ and passing through the point $(8 , -1)$.

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the length of the semi major axis, and the latus rectum are $7$ and $\large\frac{80}{7}$ respectively, the centre is $(2 , 5 )$ and the major axis is parallel to y- axis.

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the centre at the origin, the major axis is along $x$-axies,$e=\large\frac{2}{3}$ and passes through the point $(2 , \large\frac{-5}{3})$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the centre is $(3 , -4 ), $one of the foci is $(3+\sqrt{3},-4)$ and $e=\large\frac{\sqrt{3}}{2}$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the foci are $(\pm 3 , 0 )$ and the vertices are $(\pm 5 , 0)$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the foci are $(2 , -1 ) , (0 , -1 )$ and $e=\large\frac{1}{2}$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if One of the foci is$(0 , -1 )$, the corresponding directrix is $3x+16=0$ and $e=\large\frac{3}{5}$

asked Apr 10, 2013 by poojasapani_1

1 answer

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

asked Apr 10, 2013 by sreemathi.v

0 answers

Three persons A,B and C shoot to hit a target.If in trials,A hits the target 4 times in 5 shots,B hits 3 times in 4 shots and C hits 2 times in 3 trials.Find the probability that :

asked Apr 10, 2013 by sreemathi.v

1 answer

Evaluate : $\Large \int_1^2 \frac{\sqrt x}{\sqrt{3-x}+\sqrt x}\normalsize dx.$

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the locus of the complex number,Z=x+iy given $\bigg/ \Large \frac{x+iy-2i}{x+iy+2}\bigg/ \normalsize =\sqrt 2$.

asked Apr 10, 2013 by sreemathi.v

0 answers

Evaluate : $\lim_{x\to \Large {\frac{\pi}{2}}}(cos.log\;tan\;x).$

asked Apr 10, 2013 by sreemathi.v

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Evaluate : $\int e^x(tan \;x+log \;sec x)dx.$

asked Apr 10, 2013 by sreemathi.v

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From the equations of the two regression lines,4x+3y+7=0 and 3x+4y+8=0,find :

asked Apr 10, 2013 by sreemathi.v

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Find the equation of the hyperbola whose Transverse and Conjugate axes are the x and y axes respectively,given that the length of conjugate axis is 5 and distance between the foci is 13.

asked Apr 10, 2013 by sreemathi.v

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Prove that $sec^2(tan^{-1}2)+cosec^2(cot ^{-1}3)=15.$

asked Apr 10, 2013 by sreemathi.v

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Solve for x and y if $\left(\begin{array}{c}x^2\\y^2\end{array}\right)+2\left(\begin{array}{c}2x\\3y\end{array}\right)=3\left(\begin{array}{c}7\\-3\end{array}\right)$

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the equation of parabola if : Vertex $(2 , 3 )$ open upward ;and passing through the point $(6 , 4 )$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if :Vertex $(3 , -1 );$ open rightward ; the distance between the latus recturm and directrix is $4$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Vertex $(3 , -2 ); $ open downward and the length of the latus rectum is $8$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Vertex $(1 , 2 ) ;$ latus recturm :$y=5$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Vertex $(1 , 4 );$ focus :$(-2 , 4 ).$

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Vertex $(0 , 0 ); $ focus : $(0 , -4 )$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Focus: $(-1 , 3 )$; directrix $ 2x+3y=3$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Focus:$(2 , -3 );$ directrix :$2y-3=0$

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the vector equation of a sphere with centre having position vector $\overrightarrow{2i}-\overrightarrow{j}+\overrightarrow{3k}$ and radius $4$ units. Also find the equation in cartesian form.

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the angle between following plane:$r=(3i+j-k)=7 $ and $r=(i+4j-2k)=10$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the angle between following planes; $2x-3y+4z=1$ and $-x+y=4$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the angle between the followin planes: $2x+y-z=9 $and $x+2y+z=7$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the equations of the plane which contains the two lines $\large\frac{x+1}{2}=\frac{y-2}{-3}=\frac{z-3}{4}$ and $\large\frac{x-4}{3}=\frac{y-1}{2}=z-8$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equations of a plane which is at a distance of $18$ units from the origin and which is normal to the vector $\overrightarrow{2i}+\overrightarrow{7j}+\overrightarrow{8k}$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the shortest distance between the parallel lines $\large\frac{x-1}{-1}=\frac{y}{3}=\frac{z+3}{2} $ and $\large\frac{x-3}{-1}=\frac{y+1}{3}=\frac{z-1}{2} $

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the shortest distance between the parallel lines $\overrightarrow{r}=(\overrightarrow{2i}-\overrightarrow{j}-\overrightarrow{k}) + t (\overrightarrow{i}-\overrightarrow{2j}+\overrightarrow{3k})$ and $\overrightarrow{r}=(\overrightarrow{i}+\overrightarrow{2j}+\overrightarrow{k}) + s (\overrightarrow{i}-\overrightarrow{2j}+\overrightarrow{3k})$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the d . c. s of a vector whose direction ratios are $2 , 3 , -6.$

asked Apr 6, 2013 by poojasapani_1

1 answer

Show that the vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are coplanar if and only if $\overrightarrow{a}+\overrightarrow{b},\overrightarrow{b}+\overrightarrow{c},\overrightarrow{c}+\overrightarrow{a}$ are coplanar.

asked Apr 5, 2013 by poojasapani_1

1 answer

Find the area of parallelogram $A\;B\;C\;D$ whose vertices are $A(-5 ,2 ,5),B(-3 ,6 ,7),C(4 ,-1 ,5)$ and $D(2 ,-5 ,3)$

asked Apr 5, 2013 by poojasapani_1

1 answer

Simplify: $\Large\frac{\left ( cos2 \theta -\mathit{i}sin2 \theta \right )^{7} \left ( cos 3 \theta +\mathit{i} sin3 \theta \right )^{-5}}{\left (cos 4 \theta + \mathit{i} sin4 \theta \right )^{12} \left ( cos 5 \theta -\mathit{i}sin5 \theta \right )^{-6}}\Large$

asked Apr 4, 2013 by geethradh

1 answer

Is the function $f (x) = 5x – 3$ continuous at $x=5$?

asked Apr 4, 2013 by balaji.thirumalai

1 answer

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