The Mean of the following distribution is 52 and the frequency of class interval 30-40 is ‘f’. Find ‘f’.

Use the Remainder Theorem to factorise the following expression:

2x³ + x² – 13x + 6

If x, y, z are in continued proportion, prove that $\frac{(\mathrm{x} + \mathrm{y}{)}^2}{(\mathrm{y} + \mathrm{z}{)}^2} = \frac{\mathrm{x}}{\mathrm{z}}$

From the top of a light house 100 m high the angles of depression of two ships on opposite sides of it are 48$°$ and 36$°$ respectively. Find the distance between the two ships to the nearest metre.

Evaluate $\left[\begin{array}{cc}4\sin (30°)& 2\cos \left(60°\right)\\ \sin \left(90°\right)& 2\cos (0°)\end{array}\right]\left[\begin{array}{cc}4& 5\\ 5& 4\end{array}\right]$

In the given figure ABC is a triangle with$\angle$EDB =$\angle$ACB.

Prove that $∆$ABC $~ ∆$EBD. If BE = 6 cm, EC = 4 cm, BD = 5 cm. And area of
$∆$BED = 9
cm2. Calculate the

(i) length of AB

(ii) area of $∆\mathrm{ABC}$

27.

Vivek invests Rs 4500 in 8%. Rs. 10 shares at Rs. 15. He sells the shares when the price rises to Rs. 30, and invests the proceeds in 12% Rs. 100 shares at Rs. 125. Calculate.

(i) the sale proceeds

(ii) the number of Rs. 125 shares he buys.

(iii) the change in his annual income from dividend.

A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.

The monthly income of a group of 320 employees in a company is given below:

Draw an ogive the given distribution on a graph sheet taking 2 cm = Rs. 1000 on one axis and 2 cm = 50 employees on the other axis. From the graph determine:

(i) the median wage

(ii) the number of employees whose income is below Rs. 8500.

(iii) if the salary of a senior employee is above Rs. 11,500, find the number of senior employees in the company.

(iv) the upper quartile.

Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon.