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Recent questions tagged modelpaper-2012

Solve the following differential equation : $ x\: \log\: x\: \frac{dy}{dx}+y=\large\frac{2}{x}$$\log\:x $

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Find the area of the smaller region boundary by the ellipse \( \large\frac{x^2}{9}+\large\frac{y^2}{4}=1\) and the straight line \(\large \frac{x}{3}+\frac{y}{2}=1 \).

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Prove that $ \begin{vmatrix} a^2&bc&ac+c^2\\ a^2+ab& b^2& ac\\ ab&b^2+bc&c^2 \end{vmatrix}=4\,a^2\;b^2\;c^2. $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

The sum of the perimeter of a circle and square is \(k\), where \(k\) is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.

asked Nov 28, 2012 by thanvigandhi_1

1 answer

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?

asked Nov 16, 2012 by fingeazy

1 answer

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