If the height and base area of a solid hemisphere and a solid cylinder are same, then the ratio of their volume is (a) 1 : 3 (b) 1 : 2 (c) 2 : 3 (d) 3 : 4

The radius of a right circular cylinder and a hemisphere is equal and their volumes are also equal. The height of the hemisphere is greater than the height of the cylinder by (a) 25% (b) 50% (c) 100% (d) 200%

Find the ratio of the volumes of a solid right circular cylinder and a solid right circular cone of equal radii and equal heights.

The shape of a pencil with one end sharpened is the combination of a and a _____.

A life insurance agent found the following distribution of ages of 100 policy holders: Age (years) Frequency Cumulative frequency 20–25 2 2 25–30 4 6 30–35 12 18 35–40 20 38 40–45 28 66 45–50 22 88 50–55 8 96 55–60 4 100 On a graph sheet, draw an ogive using the given data. Take 2 cm = 5 years along one axis and 2 cm = 10 policy holders along the other axis. Use your graph to find: (a) the median age. (b) the number of policy holders whose age is above 52 years.

The given histogram represents the number of plants of different heights grown on a school campus. Study the graph carefully and answer the following questions: (a) Make a frequency table with respect to the class boundaries and their corresponding frequencies. (b) State the modal class. (c) Identify and write the mode of the distribution. (d) Find the number of plants whose height is between 80 cm and 90 cm.

Oil is stored in a spherical vessel, occupying of its full capacity. The radius of the spherical vessel is 28 cm. This oil is then poured into a cylindrical vessel with radius 21 cm. Find the height of the oil in the cylindrical vessel, correct to the nearest centimetre. (Take π = )

If : (a) Find . (b) Hence, using properties of proportion, find a : b.

The angles of elevation of the top of a 100 m high tree from two points A and B on opposite sides of the tree are 52° and 45° respectively. Find the distance AB, to the nearest metre.

The figure shows a circle of radius 9 cm with O as the centre. The diameter AB produced meets the tangent PQ at P. If PA = 24 cm, find the length of tangent PQ.

Solve the following quadratic equation for x and give your answers correct to three significant figures: 2x² − 10x + 5 = 0

Mr Gupta invested ₹33,000 in buying ₹100 shares of a company at 10% premium. The dividend declared by the company is 12%. Find: (a) the number of shares purchased by him. (b) his annual dividend.