Given that nC\(_4\), nC\(_5\) and nC\(_6\) are the terms of a linear sequence (A.P), find the :

i. value of n

ii. common differences of the sequence.

A solid rectangular block has a base that measures 3x cm by 2x cm. The height of the block is ycm and its volume is 72cm\(^3\).

i. Express y in terms of x.

ii. An expression for the total surface area of the block in terms of x only;

iii. the value of x for which the total surface area has a stationary value.

A basket contains 12 fruits: orange, apple and avocado pear, all of the same size. The number of oranges, apples and avocado pear forms three consecutive integers.

Two fruits are drawn one after the other without replacement. Calculate the probability that:

i. the first is an orange and the second is an avocado pear.

ii.both are of same fruit;

iii. at least one is an apple

The table shows the corresponding values of two variables X and Y.

a. plot a scatter diagram to represent the data

b i. Calculate:x̄, the mean of X and ȳ, the mean of Y;

ii. Caculate:
x̄1, the mean of X values below x̄ and ȳ1, the mean of the corresponding Y values below x̄

c.  Draw the line of best fit through (x̄,ȳ) and (x̄1,ȳ1).

d. From the graph, determine the relationship between X and Y;

ii. From the graph, determine the value of Y when X is 20.

A particle initially at rest moves in a straight line with an acceleration of (10t - 4t\(^2\))m/s\(^2\)
Find the:
a. velocity of the particle after t seconds;

ii. average acceleration of the particle during the 4th second.

b. A load of mass 120kg is placed on a lift. Calculate the reaction between the floor of the lift and the load when the lift moves upwards at a constant velocity. [Take g = 10m/s\(^2\)]

ii. with an acceleration of 3m/s\(^2\). [Take g = 10m/s\(^2\)]