Recent questions tagged 2004

The position of a particle at time t is given by the equation $x(t) =\large\frac{v_0}{A}$$(1-e^{At})\; v_0=$ constant and $A > 0$ . Dimensions of $v_0$ and $A$ respectively are:

asked Nov 13, 2013 by meena.p

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Solve the differential equation $\large\frac{d^2y}{dx^2}\normalsize=\sin 2x$

asked Apr 19, 2013 by sreemathi.v

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Using DeMoivre's theorem find the value of $(2-2i)^{\large\frac{1}{3}}$.

asked Apr 19, 2013 by sreemathi.v

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Solve the differential equation $(1-x^2)\large\frac{dy}{dx}\normalsize-xy=x$. Given $y=2$ when $x=0$.

asked Apr 19, 2013 by sreemathi.v

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Given $z=x+iy$ and $z_1=1+2i$ determine the region in the complex plane represented by $I<\mid z-z_1\mid\leq 3$.Represent it on the Argand plane.

asked Apr 19, 2013 by sreemathi.v

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If $z=x+iy$ and $\mid 2z+1\mid=\mid z-2i\mid$ show that $3(x^2+y^2)+4(x+y)=3.$

asked Apr 19, 2013 by sreemathi.v

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Solve the differential equation $2\large\frac{dy}{dx}\normalsize=\large\frac{y}{x}\normalsize+\large\frac{y^2}{x^2}$ by substituting $y=vx$.

asked Apr 19, 2013 by sreemathi.v

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A bag has 4 red and 5 black balls,a second bag has 3 red and 7 black balls.One ball is drawn from the first bag and two from the second.Find the probability that two balls are black and one is red.

asked Apr 19, 2013 by sreemathi.v

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A dice is tossed three times.Getting a '3' or a '5' is considered a success.Find the probability of at least two successes.

asked Apr 19, 2013 by sreemathi.v

1 answer

Calculate the lower $(Q_1$) and upper $(Q_3)$ quartiles for the following distribution :

asked Apr 19, 2013 by sreemathi.v

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The number of letters in hundreds received in a town on each day of a fortnight is given below :

asked Apr 19, 2013 by sreemathi.v

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The mathematical aptitude score (MAS) of ten computer programmers with job performance rating (JPR) is given below.Calculate Spearman's rating of rank correlation and state whether those who have aptitude for maths are likely to be better programmers.

asked Apr 19, 2013 by sreemathi.v

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If a,b,c are elements of Boolean Algebra,prove that $ab+c(a'+b')=ab+c$.

asked Apr 19, 2013 by sreemathi.v

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Write the Boolean expression for the following circuit :

asked Apr 19, 2013 by sreemathi.v

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Prove the right cancellation law in a group.

asked Apr 19, 2013 by sreemathi.v

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Consider the non empty set S={0,1,2,3,4}.Show that $(S,\oplus_5)$ is a group where $\oplus_5$ represents addition modulo 5.Also find 'x' if $x\oplus_5$ 3=4,$x\in S$.

asked Apr 19, 2013 by sreemathi.v

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Find the unit vector perpendicular to the two vectors $\overrightarrow{i}+2\overrightarrow{j}-\overrightarrow{k}$ and $2\overrightarrow{i}+3\overrightarrow{j}+\overrightarrow{k}$.

asked Apr 19, 2013 by sreemathi.v

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Show that the sum of the squares on the sides a parallelogram is equal to the sum of the squares on the diagonals of the parallelogram.

asked Apr 19, 2013 by sreemathi.v

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If $x=\sin^3t$ and $y=a\cos^3t$,find $\large\frac{dy}{dx}$.

asked Apr 19, 2013 by sreemathi.v

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Sketch and shade the area of the region lying in the first quadrant and bound by $y=9x^2,x=0,y=1$ and $y=4$.Find the area of the shaded region.

asked Apr 19, 2013 by sreemathi.v

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A closed circular cylinder has a volume of 2156c.c.What will be the radius of its base so that its total surface area is minimum.Find the height of the cylinder when its total surface area is minimum.

asked Apr 19, 2013 by sreemathi.v

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

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

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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

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Find the equation of a pair of straight lines represented by $8x^2+8xy+2y^2+26x+13y+5=0$ and show that the angle between them is $0^{\circ}$.

asked Apr 18, 2013 by sreemathi.v

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If $A=\begin{pmatrix}3 & -4\\1 & -1\end{pmatrix}$,show by mathematical induction that for any positive integer n, $A^n=\begin{pmatrix}1+2n&-4n\\n &1-2n\end{pmatrix}$

asked Apr 18, 2013 by sreemathi.v

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If $C_0,C_1,C_2..........C_n$ denote the coefficient of successive terms in the expansion of the binomial $(1+x)^n$ prove that $C_0+C_2+C_4+.........=C_1+C_3+C_5+.....=2^{n-1}$

asked Apr 18, 2013 by sreemathi.v

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If $x\neq y\neq z$ and $\begin{vmatrix}x& x^2 & 1+x^3\\y & y & 1+y^3\\z & z^2 & 1+z^3\end{vmatrix}=0$.Then show that $xyz=-1$.

asked Apr 18, 2013 by sreemathi.v

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If $i=\sqrt{-1}$,prove the following : $(x+1+i)(x+1-i)(x-1+i)(x-1-i)=x^4+4$

asked Apr 18, 2013 by sreemathi.v

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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

0 answers

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

0 answers

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