CBSE Guess > Papers > Important Questions > Class XII > 2010 > Maths > Mathematics By Mr Vasu Raj CBSE CLASS XII Q. 1. Find the maximum slope of the curve y = -x3 + 3x2+ 2x - 27. and what point is it Q. 2. A right circular cone of maximum volume is inscribed in a sphere of radius r. find its altitude. Also show that the maximum volume of the cone is 8/27 times the volume of the sphere. Q. 3. A point on the hypotenuse of a triangle is at a distance a and b from the sides of the triangle. Show that the maximum length of the hypotenuse is Q. 4. From a piece of tin 20cm. in square, a simple box without top is made by cutting a square from each corner and folding up the remaining rectangular tips to form the sides of the box. What is the dimension of the squares is cut in order that the volume of the box is maximum. Q. 5. If length of three sides of a trapezium other than base are equal to 10cm, then find the area of the trapezium when it is maximum. Q. 6. Find the shortest distance of the point (o,c) from the parabola y = x2, where 0 £ x £ 5. Q. 7. A window consists of a rectangle surmounted by a semicircle. If the perimeter of the window is p centimetres, show that the window will allow the maximum possible light when the radius of the semi circles Q. 8. Show that the semi vertical angle of the cone of given surface area and maximum volume is Q. 9. A wire of length a is cut into two parts which are bent respectively in the form of a square and a circle. Show that the least value of the areas so formed is Q. 10. Show that the volume of the greatest cylinder which can be inscribed in a cone of height h and semi vertical angle a is Q. 11. An open tank with square base and vertical sides is to be constructed from metal sheet so as to hold a given quantity of water. Show that the cost of material will be least when the depth of the tank is half the width. Q. 12. Find the area of the greatest isosceles triangle that can be inscribed in a given ellipse Q. 13. Find the maximum and minimum points for the following: Q. 14. The section of a window consists of a rectangle surmounted by an equilateral triangle. If the perimeters be given as 16m. find the dimensions of the window in order that the maximum amount of light may be admitted. Q. 15. A square tank of capacity 250 cu.m has to be dug out. The cost of land is Rs. 50.per sq.m. The cost of digging increases with the depth and for the whole tank is 400(depth)2 rupees. Find the dimensions of the tank for the least total cost. Q. 16. Find the dimensions of the rectangle of greatest area that can be inscribed in a semi circle of radius r. Q. 17. A running track of 440 ft is to be laid out enclosing a football field, the shape of which is rectangle with semicircle at each end. If the area of the rectangular portion is to be maximum find the length of the sides. Q. 18. Find the maximum and minimum values of y = |4-x2|, -3 £ x £ 3. Also determine the greatest and least values. Paper By Mr Vasu Raj |
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