A vertical tower standing on a horizontal plane is surmounted by a vertical flagstaff. At a point 100 m away from the foot of the tower, the angle of elevation of the top and bottom of the flagstaff are 54° and 42° respectively. Find the height of the flagstaff. Give your answer correct to nearest metre.

The marks of 200 students in a test were recorded as follows :

Using graph sheet draw ogive for the given data and use it to find the,

(a) median

(b) number of students who obtained more than 65% marks

(c) number of students who did not pass, if the pass percentage was 35.

If x, y and z are in continued proportion, prove that :

$\dfrac{x}{y^2.z^2} + \dfrac{y}{z^2.x^2} + \dfrac{z}{x^2.y^2} = \dfrac{1}{x^3} + \dfrac{1}{y^3} + \dfrac{1}{z^3}$

A manufacturing company prepares spherical ball bearings, each of radius 7 mm and mass 4 gm. These ball bearings are packed into boxes. Each box can have maximum of 2156 cm³ of ball bearings. Find the :

(a) maximum number of ball bearings that each box can have.

(b) mass of each box of ball bearings in kg.

$\Big(\text{use } \pi = \dfrac{22}{7}\Big)$