Recent questions tagged oct-2007

Find all the values of $\bigg(\large\frac{1}{2}$$-i\large\frac{\sqrt 3}{2}\bigg)^{\Large\frac{3}{4}}$ and hence prove that the product of the values is 1.

asked Jun 13, 2013 by sreemathi.v

1 answer

The marks secured by $400$ students in a Mathematics test were normally distributed with mean $65$. If $120$ students got more marks above $85$, the number of students securing marks between $45$ nd $65$ is

asked Jun 3, 2013 by poojasapani_1

1 answer

If in a poisson distribution $P(X=0)=k$ then the variance is

asked May 30, 2013 by poojasapani_1

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Given $E(X+c)=8$ and $E(X-c)=12$ then the value of $c$ is

asked May 28, 2013 by poojasapani_1

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Which of the following is correct?

asked May 27, 2013 by poojasapani_1

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The order of $[7]$ in $(Z_{9},+_{9})$ is

asked May 24, 2013 by poojasapani_1

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Which of the following is not a binary operation on $R$

asked May 24, 2013 by poojasapani_1

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If $\;p\;$ is $T$ and $\;q$ is $F$, then which of the following have the truth value$T$? \[\begin{array}{1 1}(1)p \vee q&(2)\sim p\vee q\\(3)p \vee \sim q&(4)p \wedge\sim q\end{array}\]

asked May 24, 2013 by poojasapani_1

1 answer

If $f '(x)=\sqrt{x}$ and $f(1)=2$ then $f(x)$ is

asked May 24, 2013 by poojasapani_1

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The amount present in a radio active element disintegrates at a rate proportional to its amount .The differential equation corresponding to the above statement is ($k$ is negative)

asked May 23, 2013 by poojasapani_1

1 answer

The differential equation of the family of lines $y=mx$ is

asked May 23, 2013 by poojasapani_1

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The volume generated by rotating the triangle with vertices at $(0,0),(3,0)$ and $(3,3) $ about $x$-axis is

asked May 22, 2013 by poojasapani_1

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The area of the region bounded by the graph of $y=\sin x$ and $y=\cos x $ between $x=0$ and $x=\large\frac{\pi}{4}$ is

asked May 22, 2013 by poojasapani_1

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The value of $\int\limits_{-\pi/2}^{\pi/2}\large\left(\frac{\sin x}{2+\cos x}\right)$$dx$ is

asked May 21, 2013 by poojasapani_1

1 answer

The curve $a^{2}y^{2}=x^{2}(a^{2}-x^{2})$ has

asked May 21, 2013 by poojasapani_1

1 answer

If $u=\log\begin{pmatrix}\large\frac{x^{2}+y^{2}}{xy}\end{pmatrix}$ then $x\large\frac{\partial u}{\partial x}+$$y\large\frac{\partial u}{\partial y}$ is

asked May 21, 2013 by poojasapani_1

1 answer

The least possible perimeter of a rectangle of area $100m^{2}$ is

asked May 18, 2013 by poojasapani_1

1 answer

$\;\lim \limits_{x \to \infty}\large\frac{x^{2}}{e^{x}}$ is

asked May 18, 2013 by poojasapani_1

1 answer

If a normal makes an angle $\theta$ with positive $x$-axis then the slope of the curve at the point where the normal is drawn is

asked May 16, 2013 by poojasapani_1

1 answer

The eccentricity of the hyperbola with asymptotes $x+2y-5=0 ,2x-y+5=0 $ is

asked May 14, 2013 by poojasapani_1

1 answer

If $\large\frac{1-i}{1+i}$ is a root of the equation $ax^{2}+bx+1=0$ where $a ,b $ are real then $(a , b) $is

asked May 13, 2013 by poojasapani_1

1 answer

The quadratic equation whose roots are $\pm\;i\sqrt{7} $is

asked May 13, 2013 by poojasapani_1

1 answer

$z_{1}=4+5i,z_{2}=-3+2i$ then $\large\frac{z_{1}}{z_{2}}$is

asked May 12, 2013 by poojasapani_1

1 answer

The polar form of the complex number $(i^{25})^{3}$ is

asked May 12, 2013 by poojasapani_1

1 answer

The shortest distance between the parallel lines $ \large\frac{x-3}{4}=\frac{y-1}{2}=\frac{z-5}{-3} $ and $\large\frac{x-1}{4}=\frac{y-2}{2}=\frac{z-3}{3}$ is

asked May 11, 2013 by poojasapani_1

1 answer

The point of intersection of the lines $\large\frac{x-6}{-6}=\frac{y+4}{4}=\frac{z-4}{-8} $ and $\large\frac{x+1}{2}=\frac{y+2}{4}=\frac{z+3}{-2}$ is

asked May 11, 2013 by poojasapani_1

1 answer

If $\overrightarrow{PR}=2\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}, \;\overrightarrow{QS}=-\overrightarrow{i}+\overrightarrow{3j}+\overrightarrow {2k},$ then the area of the quadrilateral $PQRS$ is

asked May 9, 2013 by poojasapani_1

0 answers

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two unit vectors and $\theta $is the angle between them, then $(\overrightarrow{a}+\overrightarrow{b})$ is a unit vector if

asked May 8, 2013 by poojasapani_1

1 answer

Inverse of $\begin{bmatrix}2& -1 \\-5 & 3 \end{bmatrix}$ is

asked May 7, 2013 by poojasapani_1

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If $A$ and $B$ are any two matrices such that $AB=O$ and $A$ is non-singular, then

asked May 7, 2013 by poojasapani_1

1 answer

If $A$ is a matrix of order $3$, then det($kA$)

asked May 7, 2013 by poojasapani_1

1 answer

If $A$ is a scalar matrix with scalar $k \neq 0$ of order $3$ than $A^{-1}$ is

asked May 7, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim \limits_{x \to 1 } x^{\large\frac{1}{x-1}}$

asked May 6, 2013 by poojasapani_1

1 answer

Let $P$ be a point on the curve $y=x^{3}$ and suppose that the tangent line at $P$ intersects the curve again at $Q$. Prove that the slope at $Q$ is four times the slope at $P$.

asked May 3, 2013 by poojasapani_1

1 answer

Find the area of the region bounded by the ellipse $\large\frac{x^{2}}{9}+\frac{y^{2}}{5}$$=1$ between the two latus rectums.

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate the following problems using properties of integration: $\int\limits_{\large\frac{\pi}{6}}^{\large\frac{\pi}{3}}\large\frac{dx}{1+\sqrt{\tan x}}$

asked Apr 27, 2013 by poojasapani_1

1 answer

Trace the curve $y$=$x^{3}$ Discuss the following curves for extence,symmetry,Asymptotes and loops

asked Apr 24, 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

Find the mean and variance for the following probability density functions $f(x) = \left\{ \begin{array}{l l} xe^{-x}, & \quad \text{if $x$$>$0}\\ 0, & \quad \text{otherwise} \end{array} \right.$

asked Apr 20, 2013 by poojasapani_1

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

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

asked Apr 15, 2013 by poojasapani_1

1 answer

Prove that the tangent at any point to the rectangular hyperbola forms with the asymptotes a tringle of constant area.

asked Apr 14, 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 vector and cartesian equations of the plane through the points $(1 , 2 , 3 )$and $(2 , 3 , 1 )$ perpendicular to the plane $ 3x-2y+4z-5=0$

asked Apr 8, 2013 by poojasapani_1

1 answer

Prove that sin $(A - B)$= sin $ A$ cos $B$ - cos $A$ sin $B$.

asked Apr 5, 2013 by poojasapani_1

1 answer

Examine the consistency of the following system of equation. If it is consistent than solve the same. $x+y+z=7\;,x+2y+3z=18\;,y+2z=6 $

asked Mar 30, 2013 by poojasapani_1

1 answer

A small seminar hall can hold 100 chairs.Three different colours(red,blue and green) of chairs are available. The cost of a red chair is Rs.240, cost of a blue chair is Rs.260, and the cost of a green chair is Rs.300. The total cost of chair is Rs.25,000. Find atleast 3 different solution of the number of chairs in each colour to be purchased.

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the adjoint of the following matrices $\begin{bmatrix} 3 & -1 \\2 & -4& \end{bmatrix}$

asked Mar 27, 2013 by poojasapani_1

1 answer

Show that the set G of all positive rationals forms a group under the composition $$ defined by $a b = (\large\frac{ab}{3})$ for all $a, b \in G.$

asked Nov 27, 2012 by balaji.thirumalai

1 answer

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