Recent questions tagged 2012

Solve the differential equation : $ (1+e^{\large\frac{x}{y}})dx+e^{\large\frac{x}{y}} \bigg( 1- \large\frac{x}{y} \bigg)$$ dy=0$

asked Jan 30, 2013 by thanvigandhi_1

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Show that the lines : $\large\frac{x-5}{4} = \frac{y-7}{4}=\frac{z+3}{-5}$ and $\large \frac{x-8}{7} = \frac{y-4}{1}=\frac{z-5}{3}$ intersect.

asked Jan 30, 2013 by thanvigandhi_1

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Kellogg is a new cereal fromed of a mixture of bran and rice that contains at least 88 g of protein and at least 36 milligram of iron. Knowing that bran contains 80 g of protein and 40 milligram of iron per kilogram, and that rice contains 100 g of protein and 30 milligrams of iron per kilogram, find the minimum cost of producing this new cereal if bran costs Rs.5 per kilogram and rice costs Rs. 4 per kilogram.

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Let X denote the number of hours you study during a randomly selected school day. The probability that X can take the values X has the following form, where k is some unknown constant. \[ p(X=x) = \left\{ \begin{array}{l l}0.1, & \quad if{ x = 0}\\ kx, & \quad if{ x = 1 \: or\: 2} \\ k(5-x), & \quad if{ x = 3 \: or\: 5} \\ 0, & \quad \: otherwise \end{array}. \right. \] (i) Find the value of K (ii) What is the probability that you study atleast two hours? Exactly two hours? Atmost two hours?

asked Jan 30, 2013 by thanvigandhi_1

1 answer

If $ f: R \rightarrow R$ is defined by $ f(x)=x^2-3x+2,$ find $ f [ f(4) ]. $

asked Jan 29, 2013 by thanvigandhi_1

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Find the value of $ tan^{-1}\sqrt 3 - sec^{-1}(-2). $

asked Jan 29, 2013 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta &\cos\theta \end{bmatrix} $ and $A + A'= I$, then find the value of $ \theta $.

asked Jan 29, 2013 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} 2 & -2 \\ -3 & 4 \end{bmatrix} $, find $ -A^2+6A.$

asked Jan 29, 2013 by thanvigandhi_1

1 answer

If $ \begin{bmatrix} 2 & 4 \\ 5 & 1 \end{bmatrix} = \begin{bmatrix} 2x & 4 \\ 6 & x \end{bmatrix} $, then find x.

asked Jan 29, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int \large\frac{\sec^2(\log x)}{x}$$dx $

asked Jan 29, 2013 by thanvigandhi_1

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Evaluate : $ \int_{-\large\frac{\pi}{4}}^{\large\frac{\pi}{4}} x^3\sin^4x\: dx $

asked Jan 29, 2013 by thanvigandhi_1

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Find a unit vector perpendicular to the vectors $ \hat i + \hat j - \hat k $ and $ \hat i - 2\hat j + \hat k.$

asked Jan 29, 2013 by thanvigandhi_1

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Find $ |\overrightarrow X |$, if for a unit vector $ \overrightarrow a.(\overrightarrow x-\overrightarrow a).(\overrightarrow x+\overrightarrow a)=15.$

asked Jan 29, 2013 by thanvigandhi_1

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Find the distance of the point (2, -1,-4) from the plane $ 3x-4y+12z=9.$

asked Jan 29, 2013 by thanvigandhi_1

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Show that the function $ f ; R \rightarrow R$ given by $ f(x)=7x-11$ is a bijection.

asked Jan 29, 2013 by thanvigandhi_1

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Show that $ \sin^{-1}\large\frac{12}{13}$$+\cos^{-1}\large\frac{4}{5}$$+\tan^{-1}\large\frac{63}{16} $$= \pi $

asked Jan 29, 2013 by thanvigandhi_1

1 answer

Solve for x : $ \sin \bigg(\sin^{-1} \large\frac{1}{5}$$+\cos^{-1}x \bigg) = 1 $.

asked Jan 29, 2013 by thanvigandhi_1

0 answers

The total monthly earnings of a worker in a factory is given by $ I=p+qx+ry$, where X denotes the number of points of honesty and Y denotes the number of points of punctuality. Data for three months are as follows : (a) represent the above data by linear equations and write its matrix form. (b) Is it possible to solve the system of equations so obtained using matrices?

asked Jan 29, 2013 by thanvigandhi_1

0 answers

Show that the function 'f' given by $ f(x)=|x|+|x+1|, x \in R$ is continuous both at $ x=0 \: and \: x=1.$

asked Jan 29, 2013 by thanvigandhi_1

0 answers

If $ y=x\log \bigg( \large\frac{x}{a+bx} \bigg)$, find $\large\frac{d^2y}{dx^2} $.

asked Jan 29, 2013 by thanvigandhi_1

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If $ y = e^{\Large m\tan^{-1}x}$, prove that $ (1+x^2)\large\frac{d^2y}{dx^2}$$+(2x-m)\large\frac{dy}{dx}=0.$

asked Jan 29, 2013 by thanvigandhi_1

0 answers

Find the points on the curve $ y = 5x^2-2x^3$ at which the tangent is parallel to the line $ y-4x=5.$

asked Jan 29, 2013 by thanvigandhi_1

1 answer

Find the intervals in which the following function is (a) increasing (b) decreasing $ f(x)=2x^3-9x^2+12x+30 $

asked Jan 29, 2013 by thanvigandhi_1

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Obtain the differential equation by eliminating 'a' and 'b' from the equation $ y=e^x(a\cos \: x+b\sin \: x). $

asked Jan 29, 2013 by thanvigandhi_1

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Solve the differential equation : $ (x^3+y^3)dy-x^2ydx=0.$

asked Jan 29, 2013 by thanvigandhi_1

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Evaluate : $ \int\large\frac{\log x}{(1+\log x)^2}$$dx.$

asked Jan 29, 2013 by thanvigandhi_1

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Evaluate : $ \int \large\frac{5x-2}{1+2x+3x^2}$$dx.$

asked Jan 29, 2013 by thanvigandhi_1

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If $ \overrightarrow a,\overrightarrow b \: and \overrightarrow c $are three mutually perpendicular vectors of equal magnitude, prove that the angle which $ (\overrightarrow a+\overrightarrow b+\overrightarrow c)$ makes with any of the vectors $ \overrightarrow a, \overrightarrow b \: or \overrightarrow c$ is $ \cos^{-1}\large\frac{1}{\sqrt3}.$

asked Jan 29, 2013 by thanvigandhi_1

0 answers

Find the equation of the plane passing thriugh a point (3, -3, 1) and normal to the line joining the points (3, 4,-1) and (2, -1, 5).

asked Jan 29, 2013 by thanvigandhi_1

0 answers

To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200 bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected.

asked Jan 29, 2013 by thanvigandhi_1

1 answer

Solve the following system of equation by matrix method : $ u-2v+w=1, 2u+v+w=1 , u+v-2w=-2 $

asked Jan 29, 2013 by thanvigandhi_1

1 answer

Find the area of the smaller region bounded by the ellipse $\large\frac{x^2}{a^2}+\large\frac{y^2}{b^2}$$=1$ and the straight line $\large\frac{x}{a}+\frac{y}{b}$$=1$.

asked Jan 29, 2013 by thanvigandhi_1

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Find the area of the region $ \{(x,y); x^2+y^2 \leq 1 \leq x+y \}.$

asked Jan 28, 2013 by thanvigandhi_1

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A window is in the form of rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum sunlight through the whole opening.

asked Jan 28, 2013 by thanvigandhi_1

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Evaluate : $\int_0^{\pi} \cos 2x\log\sin\:x\: dx $

asked Jan 28, 2013 by thanvigandhi_1

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Evaluate : $ \int \large\frac{\sin x}{\sin 4x}$$dx$

asked Jan 28, 2013 by thanvigandhi_1

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Find the equation of the line passing through the point (-1, 3, -2) and perpendicular to each of the lines $ \large\frac{x}{1} = \frac{y}{2} = \frac{z}{3}$ and $\large\frac{x+2}{-3} = \frac{y-1}{2} = \frac{z+1}{5} $. Also, find its vector equation.

asked Jan 28, 2013 by thanvigandhi_1

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A company sells two different products A and B. The two products are produced in a common production process, which has a total capacity of 500 man-hours. It takes 5 hours to produce a unit of A and 3 hours to produce a unit of B. The market has been surveyed and company officials feel that the maximum number of units of A that can be sold is 70 and that of B is 125. If the profit is Rs.20 per unit for the product A and Rs.15 per unit for the product B, how many units for each product should be sold to maximize profit.

asked Jan 28, 2013 by thanvigandhi_1

0 answers

There are 40 workers in a factory who are participating in strike for increase in wages. Out of them 5 workers are sincere to management and believe that management know each thing and do the needful. Management selects 2 workers at random out of them. Write the probability distribution for the selected worker who are sincere. Also find the mean of the distribution.

asked Jan 28, 2013 by thanvigandhi_1

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Let * be binary operation on N given by $ ab = 1.c.m.(a,b),a,b \in N.$ Find (23)*6.

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Prove that $ \cos^{-1}(4x^3-3x)=3\cos^{-1}x.$

asked Jan 28, 2013 by thanvigandhi_1

1 answer

Find the values of x,y and z, if $ \begin{bmatrix} x+y+z \\ x+z \\ y+z \end{bmatrix} = \begin{bmatrix} 9 \\ 5 \\ 7 \end{bmatrix} $

asked Jan 28, 2013 by thanvigandhi_1

1 answer

If $A = \begin{bmatrix} 2 & 5 \\ 6 & -3 \end{bmatrix} $then show that : |5A|=25|A|.

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Find the co-factor of $ a_{13}$ in the following : $ \begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix} $

asked Jan 28, 2013 by thanvigandhi_1

1 answer

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

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_{-\pi}^{\pi} x^8\sin^5x dx. $

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Find a unit vector parallel to the sum of the vectors $ \overrightarrow a = 2\hat i + 4\hat j - 5\hat k \: and \: \overrightarrow b = \hat i + 2\hat j - 3\hat k $

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Show that the vectors $ 2\hat i - 3\hat j + 4\hat k\: and \: -4\hat i + 6\hat j - 8\hat k$ are collinear.

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Find the area of a parallelogram whose adjacent sides are given by $ \overrightarrow a = 3\hat i + \hat j + 4\hat k \: and \: \overrightarrow b = \hat i - \hat j + \hat k$

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Let A = set of workers in a publication house. Let a R b, if and only if a and b tell lie; $ a,b \in A $ (i) Is R symmetric relation? (ii) Is this relation an equivalence relation?

asked Jan 28, 2013 by thanvigandhi_1

0 answers

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