Q. 24. If the surface area of a sphere is 616cm2, find its volume.(205.3 cm3)
Q. 25. Find the angle of elevation of the sun (Sun’s altitude) when the length of shadow of a vertical pole is equal to its height. (45)
Q. 26. What is the probability that an ordinary year has 53 Sundays?(1/7)
Q. 27. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides. Using this theorem, find the area of DABC if AB = 10 cm and area of D PQR= 12
cm2, PQ = 11cm. 
(10 cm2)
Q. 28. A solid cone, with height and base radius of 28 cm each, is cut along a plane parallel to its base so that the bottom and top radii of the remaining part are in the ratio 1 : 4. Find its volume. Also find the cost of painting its outer surface @ Re 0.70 per sq.cm.
Q. 29. A wooden toy is conical at the top, cylindrical in the middle and hemispherical at the bottom (see figure). If the height and radius of the cylindrical portion are both equal to 21 cm and the total height of the toy is 70 cm, find the cost of painting it @ Re 0.70 per sq.cm and the amount of wood used to make it.(5497.8)
Q. 30. The diagonals of a cyclic quadrilateral are at right angles. Prove that the perpendicular from the point of their intersection on any side when produced backward bisects the opposite side.
Q. 31. Prove that any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally (i.e. in the same ratio) .
Q. 32. The following table gives weekly wages in rupees of workers in a certain commercial organization. The frequency of class 49-52 is missing. It is known that the mean frequency distribution is 47.2. Find the missing frequency.(44)
| Weekly Wages (Rs.) | 40-43 | 43-46 | 46-49 | 49-52 | 52-55 |
| Number of workers | 31 | 58 | 60 | ? | 27 |
Q. 33. The area of an equilateral triangle is 17300 cm2. With each vertex of the triangle as centre, a circle is drawn with a radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circles.( π = 3.14 and √3 =1.73 )(1600cm2)
Q. 34. A solid composed of a cylinder with hemi spherical ends . The whole height of the solid is 19cm and the radius of the cylinder is 3.5cm. Find the weight of the solid if 1cm3 of the metal weighs 4.5g. (2111.8g or 2.1kg)
Q. 35. Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level will rise by 21cm.(2 hour)
Q. 36. Find the zeroes of the polynomial 
and verify the relationship between zeroes and coefficients.(-2 , 0)
Q. 37. For what value of c does the following system of equations represent parallel lines? 
(c=6,)
Q. 38. Using Fundamental theorem of arithmetic, find the LCM of 2231 and 2813(6275803)
Q. 39. Show that 
is irrational
