Given that (\(_r^n\)) = \(^nC_r\), simplify (\(^{2x + 1}_{3}\)) - (\(^{2x - 1}_3\)) - 2(\(^x_2\))

(a) Solve, for \(x\) and \(y\), the simultaneous equations \[3\log_2 x = y \qquad\text{and}\qquad \log_2 4x = y + 4.\] (b) Using the value of \(y\) obtained ...

Find the equation of the circle centre (2. 3) which passes through the y - intercept of the line 3x - 2y + 6 = 0

If \(\alpha\) and \(\beta\) are the roots of the equation 3x\(^2\) + 4x - 5 = 0, find the value of (\(\alpha - \beta\)), leaving the answer in surd form.

Differentiate from first principles, with respect to x, (3x\(^2\) + 2x - 1)

Find the angle between \(\over {OP}\) = (\(^{-3}_{-4}\)) and \(\over{OQ}\) = (\(^8_{-15}\))

Three soldies, X, Y and Z have probabilities \(\frac{1}{3}, \frac{1}{5}\) and \(\frac{1}{4}\) respectively of hitting a target. If each of them fires once, f...

The distribution of the masses of a group of persons is shown in the following table Mass/kg 10.5 - 14.4 14.5 - 24.4 24.5 - 44.4 44.5 - 47.4 47.5 - 49.4 Numb...

In the diagram, a mass of 12kg hanging from a light inextensible string is pulled aside by a horizontal force, R, such that the string is inclined at 45\(^o\...