Find \(\overrightarrow {BO} \)  in terms of  \(\vec a\) , \(\vec b\)  or  \(\vec c\).

Find  \(A\),  if   \(\dfrac{{\sin \theta }}{{1 – \cos \theta }} – \dfrac{{\sin \theta }}{{\sin \theta + 1}} = \dfrac{A}{{\tan \theta }}\).

If  \({\cos ^4}\theta – {\sin ^4}\theta = a\cos \left( {b\theta } \right)\),  find  \(a\)  and  \(b\).

Find  \(p\) and \(q\),   if  \(\int {\dfrac{{3x}}{{\sqrt {{x^2} + 8} }}} dx = p\sqrt {{{\left( {{x^2} + 8} \right)}^q}} + C\).

Find the area of the region bounded by   \(y = {x^3}\) and \(y = {x^2} + 2x\),   correcting to two decimal place.

Find \(a\) and \(b\),  if the volume of the solid formed when  \(y = {x^2} \)  for  \(2 \le x \le 4\)  is revolved through  \(2\pi \) or \(360^\circ \) about the \(y\)-axis is  \(a\pi \)  where  \(a\) and \(b\)  have no common factors.

A binomial random variable has a mean of 8 and a variance of 6.4. Find \(\Pr \left( {X = 10} \right)\), correcting to four significant figures.

A fair coin is tossed five times. Find the probability of obtaining two Heads and three Tails.

Find the positive value of \(k\),   correcting to three significant figures,   if the length of  \( \begin{pmatrix} k \\ – 3 \end{pmatrix} \)  is 7.2.

Find the first two values of \(t\) when \(h = 5\) given \(y = 3 + 4\cos \dfrac{\pi }{3}\left( {t – 4} \right)\).