The sum of the first twelve terms of an Arithmetic Progression is 168. If the third term is 7, find the values of the common difference and the first term.
Two panel of judges, X and Y, rank 8 brands of cooking oil as follows :
| Cooking oil type | A | B | C | D | E | F | G | H |
| X | 8 | 5 | 1 | 7 | 2 | 6 | 3 | 4 |
| Y | 6 | 3 | 4 | 8 | 5 | 7 | 1 | 2 |
Calculate the Spearmann's rank correlation coefficient.
(a) The probability that Kunle solves a particular question is \(\frac{1}{3}\) while that of Tayo is \(\frac{1}{5}\). If both of them attempt the question, find the probability that only one of them will solve the question.
(b) A committee of 8 is to be chosen from 10 persons. In how many ways can this be done if there is no restriction?
Given that \(m = 3i - 2j ; n = 2i - 3j\) and \(p = -i + 6j\), find \(4m + 2n - 3p\).
A body of mass 20kg moving with a velocity of 80ms\(^{-1}\) collides with another body of mass 30kg moving with a velocity of 50ms\(^{-1}\). If they both moved in the same direction after collision, find their common velocity if they moved in the :
(a) same direction before collision ; (b) opposite direction before collision.
