The position vectors of points A, B and C are , and respectively. If C divides the line segment joining A and B in the ratio 3 : 1, find the values of λ and μ.

The two vectors and represent the two sides AB and AC, respectively of Find the length of the median through A.
From the differential equation of equation y = a cos 2x + b sin 2x, where a and b are constant.
If P(F) = 0·35 and P(E U F) = 0·85 and E and F are independent events. Find P(E).
Find the area of the parallelogram whose diagonals are represented by the vectors = and
A couple has 2 children. Find the probability that both are boys, if it is known that
(i) one of them is a boy
(ii) the older child is a boy.