Solve the simultaneous equations : \(\log_{2} x - \log_{2} y = 2 ; \log_{2} (x - 2y) = 3\)

If the quadratic equation \((x + 1)(x + 2) = k(3x + 7)\) has equal roots, find the possible values of the constant k.

Given that \(\tan 2A = \frac{2 \tan A}{1 - \tan^{2} A}\), evaluate \(\tan 15°\), leaving your answer in surd form.

The probabilities of Rotey obtaining the highest mark in Mathematics, Physics and Biology tests are 0.9, 0.75 and 0.8 respectively. Calculate the probability of getting the highest marks in at least two of the subjects.

A student representative council consists of 8 girls and 6 boys. If an editorial board consisting of 5 persons is to be formed, what is the probability that the board consists of

(a) 3 girls and 2 boys ;

(b) either all girls or all boys.