5a. There are 6 points in a plane. How many triangles can be formed with the points?
b. A family of 6 is to be seated in a row. In how many ways can this be done if the father and mother are not to sit together?
Leave your answer in whole numbers " abc."
6. The table shows the distribution of the ages of a group of people in a village.
| Ages(in years) | 15-18 | 19-22 | 23-26 | 27-30 | 31-34 | 35-38 |
| Frequency | 40 | 33 | 25 | 10 | 8 | 4 |
Using an assumed mean of 24.5. Calculate the mean distribution.
7a. A body of mass 5 kg resting on a smooth horizontal plane is acted upon by forces 6i + 2j, 5i + 4j, and 4i − j. Calculate: the velocity of the body
b. the magnitude of its velocity, after 4 seconds
8. An object is projected vertically upward with a velocity of 80 ms\(^{-1}\). Find the;
a. Maximum height reached (Leave your answer in whole number 'abc.')
b. Time taken to return to the point of projection [ g = 10m/s\(^2\)]
SECTION B
9a. Simplify \(\frac{\sqrt{75} - 3}{\sqrt{3} + 1}\), leaving your answers in the form a + b\(\sqrt{c}\), where a, b, and c are rational numbers.
bi. The points (7,3), (2,8), and (-3,3) lie on a circle. Find the equation
bii. Find the radius of the circle.
