(a) Forces \(F_{1} = (3N, 210°)\) and \(F_{2} = (4N, 120°)\) act on a particle of mass 7kg which is at rest. Calculate the  :

(i) acceleration of the particle ; (ii) velocity of the particle after 3 seconds.

(b) \(F_{1} = (2i + 3j)N, F_{2} = (-5j)N \) and \(F_{3} = (6i - 4j)N\) act on a body. Find the magnitude and direction of the fourth force that will keep the body in equilibrium.

(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).