Recent questions tagged q1

Prove that $2(\tan^{-1}1+\tan^{-1}\large\frac{1}{2}\normalsize+\tan^{-1}\large\frac{1}{3}\normalsize)=\pi$

asked Apr 18, 2013 by sreemathi.v

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Integrate : $\int\large\frac{1+\tan^2x}{\sqrt{1+\tan^2x}}\normalsize dx$.

asked Apr 18, 2013 by sreemathi.v

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If the matrix $A=\begin{pmatrix}2 & 3\\5 & -2\end{pmatrix}$,show that $A^{-1}=\large\frac{1}{19}\normalsize A.$

asked Apr 18, 2013 by sreemathi.v

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If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two vectors such that $\mid \overrightarrow{a}+\overrightarrow{b}\mid=\mid\overrightarrow{a}\mid $ then show that vector $(2\overrightarrow{a}+\overrightarrow{b})$ is perpendicular to $\overrightarrow{b}$.

asked Apr 18, 2013 by sreemathi.v

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What is the probability that a leap year has 53 Sundays?

asked Apr 18, 2013 by sreemathi.v

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Find the angle between the line $\large\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}$ and the plane $x+y+2z=0.$

asked Apr 18, 2013 by sreemathi.v

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If $x^yy^x$=5 show that $\large\frac{dy}{dx}=-\begin{pmatrix}\large\frac{\log y+\Large\frac{y}{x}}{\log x+\Large\frac{x}{y}}\end{pmatrix}$

asked Apr 18, 2013 by sreemathi.v

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The directrix of a conic section is $3x+4y=1$ and focus is (2,3).Find the equation of the conic section if its eccentricity is $\large\frac{1}{\sqrt 2}$

asked Apr 18, 2013 by sreemathi.v

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Find the value of 'p' for which the following equation represents a pair of straight lines : $x^2+pxy-2y^2+3gx+3fy=0.$

asked Apr 18, 2013 by sreemathi.v

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

asked Apr 17, 2013 by sreemathi.v

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Find the amplitude of the complex number $\sin\large\frac{6\pi}{5}\normalsize+i\begin{pmatrix}1-\cos\large\frac{6\pi}{5}\end{pmatrix}$.

asked Apr 17, 2013 by sreemathi.v

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A performance test was conducted among seven candidates.They scored the following marks : 7,10,12,15,17,19,25.Calculate the interquartile range and the standard deviation.

asked Apr 17, 2013 by sreemathi.v

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Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random.What is the probability that the ticket has a number which is a multiple of 3 or 7.

asked Apr 17, 2013 by sreemathi.v

1 answer

The points (0,4) and (0,2) are the vertex and focus of a parabola.Find the equation of the parabola.

asked Apr 17, 2013 by sreemathi.v

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Evaluate $\int\large\frac{\cos x}{\sin x+\sqrt \sin x}\normalsize dx.$

asked Apr 17, 2013 by sreemathi.v

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If $\sin(xy)+\cos(xy)=1$ and $\tan(xy)\neq 1$,then show that $\large\frac{dy}{dx}=-\frac{y}{x}$

asked Apr 17, 2013 by sreemathi.v

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Find the foci and latus rectum for the hyperbola $\large\frac{x^2}{4}-\frac{y^2}{5}=\frac{1}{2}$

asked Apr 17, 2013 by sreemathi.v

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A straight line $y=mx$ passes through the intersection of the straight lines $x+2y-1=0$ and $2x-y+3=0.$Find the value of m.

asked Apr 17, 2013 by sreemathi.v

1 answer

Given that $A=\begin{bmatrix}\cos x & \sin x\\-\sin x& \cos x\end{bmatrix}$ and $A(adj. A)=K\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$,find the value of K.

asked Apr 17, 2013 by sreemathi.v

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Radium disappears at a rate propotional to the amount present .If $5\%$ of the original amount disappears in $50$ years , how much will remain at the end of $100$ years [Take $A_{0}$ as a intial amount.]

asked Apr 17, 2013 by poojasapani_1

1 answer

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

asked Apr 16, 2013 by sreemathi.v

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Express $\large\frac{1-2i}{2+i}+\frac{3+i}{2-i}$ in the form $ a+ib$.

asked Apr 16, 2013 by sreemathi.v

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One set of 100 observations has the mean as 15 and another set of 150 observations has the mean as 16.Find the mean of 250 observations by combining the two sets of given observations.

asked Apr 16, 2013 by sreemathi.v

1 answer

The probability of A,B and C solving a problem are $\large\frac{1}{3},\frac{2}{7}$ and $\large\frac{3}{8}$respectively.If all the three try and solve the problem simultaneously,find the probability that only one of them will solve it.

asked Apr 16, 2013 by sreemathi.v

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Find the equation of the ellipse whose eccentricity is $\large\frac{1}{2}$ and whose foci are the points $(\pm 2,0).$

asked Apr 16, 2013 by sreemathi.v

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Evaluate $\int x^2(e^{x^3})\cos (2e^{x^3})dx.$

asked Apr 16, 2013 by sreemathi.v

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If $y=e^{\sin x^2}$,find $\large\frac{dy}{dx}$.

asked Apr 16, 2013 by sreemathi.v

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A straight line $2x+y+p=0$ is a focal chord of the parabola $y^2=-8x$.Find the value of $p.$

asked Apr 16, 2013 by sreemathi.v

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A straight line is parallel to the x-axis and passes through the intersection of the lines $x+2y+1=0$ and $y=x+7$.Find the equation of the straight line.

asked Apr 16, 2013 by sreemathi.v

1 answer

Solve for x and y : $\begin{bmatrix}x^2\\y^2\end{bmatrix}+2\begin{bmatrix}2x\\3y\end{bmatrix}=3\begin{bmatrix}7\\-3\end{bmatrix}$

asked Apr 16, 2013 by sreemathi.v

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Solve the following differential equation; $(D^{2}+7D+12)$y$=e^{2x}$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following. $\large\frac{dy}{dx}$$+y\;=\;x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the differential equation $\tan y dx+\sec^2y\tan x dy=0$.

asked Apr 16, 2013 by sreemathi.v

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Find the modulus and amplitude of the complex number $\large\frac{2+3i}{3+2i}$.

asked Apr 16, 2013 by sreemathi.v

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Five students scored marks as follows : 8,10,15,20,22.

asked Apr 16, 2013 by sreemathi.v

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Kamal and Monika appear for an interview for two vacancies.The probability of Kamal's selection is $\large\frac{1}{3}$ and that of Monika's selection is $\large\frac{1}{5}$.Find the probability that only one of them will be selected.

asked Apr 16, 2013 by sreemathi.v

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Find the equation of the ellipse whose minor axis is 4 and which has a distance of 6 units between its foci.

asked Apr 16, 2013 by sreemathi.v

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Solve $\int\large\frac{1}{x\cos^2(1+\log x)}\normalsize dx$.

asked Apr 16, 2013 by sreemathi.v

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If $e^{x+y}=xy,$show that $\large\frac{dy}{dx}\normalsize=\large\frac{y(1-x)}{x(y-1)}$.

asked Apr 16, 2013 by sreemathi.v

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Find the equation of the parabola having focus at (3,-4) and directrix as $x+y=2.$

asked Apr 16, 2013 by sreemathi.v

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Find the equation of the line passing through the intersection of the straight lines $2x+3y=1$ and $3x+4y=6$ and perpendicular to the line $5x-2y=7$.

asked Apr 16, 2013 by sreemathi.v

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If $A\begin{bmatrix}1 & 2\\2 & 1\end{bmatrix}$,show that $A^2-3I=2A$.

asked Apr 16, 2013 by sreemathi.v

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Solve the following $\large\frac{dy}{dx}+\frac{y}{x}=\frac{y^{2}}{x^{2}}$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $\sec 2x dy -\sin 5x \sec^{2} ydx=0$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the differential equation : $(x+1)\large\frac{dy}{dx}\normalsize-y=e^{3x}(x+1)^2$.

asked Apr 15, 2013 by sreemathi.v

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Find the value of $x$,$y$,given that $(x+iy)(2-3i)=4+i.$

asked Apr 15, 2013 by sreemathi.v

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In a standard deviation of the numbers,2,3,11 and x is $3\large\frac{1}{2}$,find the value of $x$.

asked Apr 15, 2013 by sreemathi.v

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In a single throw of two dice,find the probability of getting a total of at most 9.

asked Apr 15, 2013 by sreemathi.v

1 answer

Find the equation of tangents to the hyperbola $3x^2-y^2=3$ which are perpendicular to the line $x+3y=2$.

asked Apr 15, 2013 by sreemathi.v

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Evaluate $\int \large\frac{x^2}{(x^2-4)}\normalsize dx.$

asked Apr 15, 2013 by sreemathi.v

0 answers

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