A tent has been constructed which is in the form of a right circular cylinder surmounted by a right circular cone whose axis coincides with the axis of the cylinder. If the radius of the base is 50 m, the height of the cylinder is 10 m and the total height of the tent is 15 m, then what is the capacity of the tent in cubic meters?

Two rectangular sheets of sizes 2π × 4π and π × 5π are available. A hollow right circular cylinder can be formed by joining a pair of parallel sides of any sheets. What is the maximum possible volume of the cylinder that can be formed this way?

Consider the following statements in respect of three straight lines A, B and C on a plane:

1. If A and C are parallel and B and C are parallel, then A and B are parallel

2. If A is perpendicular to C and B is perpendicular to C, then A and B are parallel

3. If the acute angle between A and C is equal to the acute angle between B and C; then A and B are parallel

Which of the above statements are correct?

An arc of a circle subtends an angle π at the centre. If the length of the arc is 22 cm, then what is the radius of the circle?

(Take π = 22/7)

There are 8 lines in a plane, no two of which are parallel. What is the maximum number of points at which they can intersect?

A closed polygon has six sides and one of its angles is 30° greater than each of the other five equal angles. What is the value of the equal angles?

Consider the following statements:

(1) The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.

(2) The point of intersection of the perpendicular drawn from the vertices to the opposite side of a triangle may lie on two sides.

Which of the above statements is/are correct?

Frequency density of a class is computed by the ratio

A small company pays each of its 5 category ‘C’ workers Rs. 20,000, each of its 3 category ‘B’ workers Rs. 25,000 and a category ‘A’ worker Rs. 65,000. The number of workers earning less than the mean salary is

A man travelled 12 km at a speed of 4 km/h and further 10 km at a speed of 5 km/hr. What was his average speed?