Recent questions tagged 2005

The average number,in lakhs,of working days lost in strikes during each year of the period 1981-90 was :

asked Apr 18, 2013 by sreemathi.v

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Calculate the index number for the year 1979 with 1970 as base from the following data using weighted average of price relatives :

asked Apr 18, 2013 by sreemathi.v

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Prove that $\overrightarrow{a}.(\overrightarrow{b}+\overrightarrow{c})\times (\overrightarrow{a}+2\overrightarrow{b}+3\overrightarrow{c})=[\overrightarrow{a}\;\overrightarrow{b}\;\overrightarrow{c}].$

asked Apr 17, 2013 by sreemathi.v

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$\overrightarrow{a}$ and $\overrightarrow{b}$ are unit vectors such that $2\overrightarrow{a}-4\overrightarrow{b}$ and $10\overrightarrow{a}+8\overrightarrow{b}$ are perpendicular to each other.Find the angle between the vectors $\overrightarrow{a}$ and $\overrightarrow{b}.$

asked Apr 17, 2013 by sreemathi.v

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Find the least distance of the plane $12x+4y+3z=327$ from the sphere $x^2+y^2+z^2+4x-2y-6z=155.$

asked Apr 17, 2013 by sreemathi.v

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A plane passes through the point (4,2,4) and is perpendicular to the planes $2x+5y+4z+1=0$ and $4x+7y+6z+2=0$.Find the equation of the plane.

asked Apr 17, 2013 by sreemathi.v

1 answer

Solve the differential equation : $\tan x\large\frac{dy}{dx}\normalsize+2y=\sec x$

asked Apr 17, 2013 by sreemathi.v

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Using Demoivre's theorem,find the least value of $n\in N$ for which the expression $(i+1)^n+(1-i)^n$ is equal to $-2^{\large\frac{n+2}{2}}$

asked Apr 17, 2013 by sreemathi.v

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A candidate is selected for interview of management trainees for 3 companies.For the first company,there are 12 candidates,for the second there are 15 candidates and for the third,there are 10 candidates.Find the probability that he is selected in at least one of the companies.

asked Apr 17, 2013 by sreemathi.v

1 answer

In a certain city,the probability of not reading the morning newspaper by the residents is $\large\frac{1}{2}$ and that of not reading the evening newspaper is $\large\frac{2}{5}$.The probability of reading both the newspapers is $\large\frac{1}{5}$.Find the probability that a resident reads either the morning or evening or both the papers.

asked Apr 17, 2013 by sreemathi.v

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There are two series of index numbers : P for price index and S for stock of a commodity.The mean and standard deviation of P are 100 and 8 and of S are 103 and 4 respectively.The correlation coefficient between the two series is 0.4,with these data,obtain the regression lines of P on S and S on P.

asked Apr 17, 2013 by sreemathi.v

1 answer

Internal and External assessments were conducted on a group of 10 students who were studying in a post graduate class in a college.The following marks were obtained in the assessments :

asked Apr 17, 2013 by sreemathi.v

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Calculate the area bounded by the curve $y=x(2-x)$ and the lines $x=0,y=0,x=2$.This area is rotated through four right angles about the $x$-axis.Calculate the volume of the solid so formed.

asked Apr 17, 2013 by sreemathi.v

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Prove that $\int_0^{\large\frac{\pi}{2}}\large\frac{3\sin\theta+4\cos\theta}{\sin\theta+\cos\theta}\normalsize d\theta=\large\frac{7\pi}{4}$

asked Apr 17, 2013 by sreemathi.v

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Prove that the area of right-angled traingle of a given hypotenuse is maximum when the triangle is isosceles.

asked Apr 17, 2013 by sreemathi.v

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Examine the validity and conclusion of Rolle's theorem for the function $f(x)=e^x\sin x,\forall x\in [0,\pi]$.

asked Apr 17, 2013 by sreemathi.v

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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

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

asked Apr 17, 2013 by sreemathi.v

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Find the angle and the equation of the bisectors of the angle between the pair of lines given by $2x^2-7xy+3y^2=0$.

asked Apr 17, 2013 by sreemathi.v

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The equation $2x^2-3xy-py^2+x+qy=0$ represents two perpendicular lines.Find the values of $p$ and $q$.

asked Apr 17, 2013 by sreemathi.v

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Given the matrix $A=\begin{vmatrix}1 & 0 & 2\\-2 & 1 & 0\\0 & -1 & 2\end{vmatrix}$,compute $A^{-1}$.

asked Apr 17, 2013 by sreemathi.v

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Using properties of determinants,show that $\begin{vmatrix}a^2+1 & ab & ac\\ba & b^2+1 & bc\\ca & cb & c^2+1\end{vmatrix}=a^2+b^2+c^2+1$

asked Apr 17, 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

0 answers

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

0 answers

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

asked Apr 17, 2013 by sreemathi.v

0 answers

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

0 answers

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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Evaluate: $\lim\limits_{y \to 0}\large\frac{(x+y)\sec(x+y)-x\sec{x}}{y}$

asked Jan 30, 2013 by fingeazy

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Differentiate $\sin \sqrt{x}$ w.r.t. x from first principles

asked Jan 30, 2013 by fingeazy

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If x = $a \begin{pmatrix} \large\frac{1 + t^2}{1 - t^2}\end{pmatrix}$ and y = $\large\frac{2t}{1-t^2}$ find $\large\frac{dy}{dx}$

asked Jan 30, 2013 by fingeazy

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The surface area of a spherical bubble is increasing at the rate of 2 $cm^2$/sec. Find the rate at which the volume of the bubble is increasing at the instant its radius is 6 cm.

asked Jan 30, 2013 by fingeazy

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Evaluate: $\int \large\frac{2x -1}{(x-1))(x+2)(x-3)}$$dx$

asked Jan 30, 2013 by fingeazy

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Evaluate: $\int\limits_0^{\large \pi}\large\frac{dx}{5 + 4\cos x}$

asked Jan 29, 2013 by fingeazy

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Using matrices, solve the following system of linear equations: $$x + y + z = 4$$ $$2x - y + z = -1 $$ $$2x + y - 3z = -9$$

asked Jan 29, 2013 by fingeazy

1 answer

If $A= \begin{bmatrix} 3 & 1 \\[0.3em] 7 & 5 \end{bmatrix}$ find x and y such that $A2 + xl = yA$. Hence find A - 1.

asked Jan 29, 2013 by fingeazy

0 answers

A wire of length 36 cm is cut into two pieces. One of the pieces is turned in the form of a square and the other in the form of an equilateral triangle. Find the length of each piece so that the sum of the areas of the two be minimum.

asked Jan 29, 2013 by fingeazy

1 answer

Find the area bounded by the curve $x^2 = 4y$ and the straight line 4y - 2 = x

asked Jan 28, 2013 by fingeazy

0 answers

Express the vector $\overset \rightharpoonup {a} = 5\hat{i} - 2\hat{j} + 5\hat{k}$ as sum of two vectors such that one is parallel to the vector $\overset \rightharpoonup {b} = 3\hat{i} + \hat{k}$ and the other is perpendicular to $\overset \rightharpoonup {b}$

asked Jan 28, 2013 by fingeazy

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If the vectors $a\hat{i} + a\hat{j} + c\hat{k}$. $\hat{i} + \hat{k}$ and $c\hat{i} + c\hat{j} + b\hat{k}$ be coplanar, show that $c^2$ = ab

asked Jan 28, 2013 by fingeazy

0 answers

A car, traveling with a uniform acceleration, has a velocity of 18 km/hour at a certain time and 54 km/hour after covering a distance of 500m. How much further will it travel to attain a velocity of 72 km/hour?

asked Jan 28, 2013 by fingeazy

0 answers

A body falls freely from the top of a tower; It covers $\large\frac{5}{9}$th second. Find the height of the tower and the total by the body to fall down. of the whole distance in the last

asked Jan 28, 2013 by fingeazy

0 answers

A cricket ball is project with a velocity of 29.4 m/sec. Find (a) The greatest range on the horizontal plane; and (b) The angle of projection to give a range of 44.10 m.

asked Jan 28, 2013 by fingeazy

0 answers

Find the co-ordinates of the foot of the perpendicular drawn from the point A(1,8,4,) to the line joining the points B(0,-1,3) and C(2,-3,-1).

asked Jan 28, 2013 by fingeazy

0 answers

$\overset \rightharpoonup {P}$ and $\overset \rightharpoonup {Q}$ are two unlike parallel forces. When the magnitude of $\overset \rightharpoonup {P}$ is doubled, it is found that the line of action of $\overset \rightharpoonup {Q}$ is midway between the lines of action of the new and the original resultants, find the ratio of P and Q.

asked Jan 28, 2013 by fingeazy

0 answers

Three forces acting on a particle are in equilibrium. If the angle between the first force and the second force be 120 0 and that between the second force and the third force be 135 0 , find the ratio of their magnitudes.

asked Jan 24, 2013 by fingeazy

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