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 lower part of an ice-cream is conical and upper part is hemispheric with same circular base. If the height of the cone is 9cm and radius of the base 2.5 cm. Find the volume of the ice-cream.

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%

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

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

Assertion (A): The 9th term of the G.P. 6, −12, 24, −48, … is positive. Reason (R): (−2)⁸ is positive. (a) A is true and R is false. (b) A is false and R is true. (c) Both A and R are true and R is the correct explanation of A. (d) Both A and R are true but R is not the correct explanation of 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 letters A, D, M, N, O, S, U and Y of the English alphabet are written on separate cards and put in a box. The cards are well shuffled and one card is drawn at random. What is the probability that the card drawn is a letter: (a) of the word MONDAY? (b) which does not appear in MONDAY? (c) which appears both in SUNDAY and MONDAY?

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.

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.

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.

In the given diagram, an isosceles △ABC is inscribed in a circle with centre O. PQ is a tangent to the circle at C. OM is perpendicular to chord AC and ∠COM = 65°. Find: (a) ∠ABC (b) ∠BAC (c) ∠BCQ

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 = )