**SECTION —A**

**Question numbers 1 to 6 carry 1 mark each.**

**3.At what points of the ellipse 16x ^{2} + 9y^{2} = 400, does the coordinates decrease at the same rate at which the abscissa increases.**

**4.Write the direction cosines of the line joining the points (1,0,0) and (0,1,1).**

**5.Find the differential equation y = e**

^{x}+ 1.**SECTION — B**

**Question numbers 7 to 19 carry 4 mark each.**

**18.For 6 trials of an experiment, let x be a binomial variate which satisfies the relation 9p(x = 4) = p(x = 2). Find the probability of success.**

**SECTION — C**

**Question numbers 20 to 26 carry 6 mark each.**

**23.Prove that the radius of the cylinder of greatest curved surface area that can be inscribed in a given cone is half of that of a cone.**

**24.A company has two plants to manufacture motorcycles. 70% of motorcycles are manufactured at the first plant, while 30% are manufactured at the second plant. At first plant 00% motorcycle are rated of the standard quality, while at the second plant, 90% are rated of standard quality.**

**25.Find the angle between the planes 4x + 8y + z- 8 = 0 and y + z- 4 = 0.**

**26.A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of 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, while 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 lamp and shades that he produces, how should he schedule his daily production in order to maximize his profit ?**