(a) Express \(\frac{2\sqrt{2}}{\sqrt{48} - \sqrt{8} - \sqrt{27}}\) in the form \(p + q\sqrt{r}\), where p, q and r are rational numbers. 

(b) If \(V = A\log_{10} (M + N)\), express N in terms of M, V and A.

If the quadratic equation \((2x - 1) - p(x^{2} + 2) = 0\), where p is a constant, has real roots :

(a) show that \(2p^{2} + p - 1 < 0\);

(b) find the values of p.

The equation of a curve is \(y = x(3 - x^{2})\). Find the equation of its normal of the point where x = 2.

If \(3x^{2} + 2y^{2} + xy + x - 7 = 0\), find \(\frac{\mathrm d y}{\mathrm d x}\) at the point (-2, 1).

Five students are to be selected from a large population. If 60% of them are boys and the rest are girls, find the probability that :

(a) exactly 3 of them are boys;

(b) at least 3 of them are girls.