The table shows the distribution of ages of a number of children in a school. If the mean of the distribution is 7, find the;

(a) value of x, (b) standard deviation of their ages.

(a) In the diagram, O is the centre of the circle XYZ. angle ZXO=34 ° and angle XOY=146 ° . Find angle OYZ. 

(b) The exterior angles of a polygon are 42, 38,57, x, (x+ y)°. (2x- 15)° and (3x -y)º? If x is 7 less than y, find the values of x and y.

(a) The probability that an athlete will not win any of three races is 1/4.If the athlete runs in all the races, what is the probability that the athlete will win;

(i) only the second race; (ii) all the three races; (ii) only two of the races?

(b) A cone with perpendicular height 24cm has a volume of 1200cm\(^3\). Find the volume of a cone with same base radius and height 84cm. [Take pi = \(\frac{22}{7}\)]

(a) The diameter of a cylinder closed at both ends is 7cm. If the total surface area is 209cm\(^2\), calculate the height. [Take pi = 22/7].

(b) The points X and Y, 19m apart are on the same side of a tree. The angles of elevation of the top, T, of the tree from X and Y on the horizontal ground with the foot of the tree are 43º and 38° respectively.

(i) Illustrate the information in a diagram. (ii) Find, correct to one decimal place, the height of the tree.

How many different 8 letter words are possible using the letters of the word SYLLABUS?