Two events M and N are such that P(M) = \(\frac{1}{2}\), P(N) =  \(\frac{9}{20}\) and P(M ∩ N) = \(\frac{11}{50}\)

(a) P(M ∩ N'):  (b) P(M' ∩ N)

The table shows the distribution of distance (in km) of 60 villages from a state capital.

The magnitude of two vectors u and v are 10N and 12N respectively. If the magnitude of their resultant is 15N, calculate the angle between them.

A body of mass 40 kg is placed on a rough inclined plane which makes an angle of 30\(^0\) with the horizontal. If a force of 420 N is applied upwards parallel to the plane. find the:

(a) maximum friction force that will keep the body in equilibrium;

(b) coefficient of friction.[Take g = 10ms\(^{-1}\)

                                                                          SECTION B (PART 1)

A curve is given by y = 8x + \(\frac{27}{2x^2}\),

FIND:

(a) an expression for \(\frac{dy}{dx}\),

(b) the coordinates of the stationary point on the curve and the nature of the stationary point;

(c) the equation of the normal to the curve at (2, 2).