(a) If the coefficient of \(x^{2}\) and \(x^{3}\) in the expansion of \((p + qx)^{7}\) are equal, express q in terms of p.
(b) A man makes a weekly contribution into a fund. In the first week, he paid N180.00, second week N260.00, third week N340.00 and so on. How much would he have contributed in 16 weeks?
Calculate the gradient of the curve \(x^{3} + y^{3} - 2xy = 11\) at (2, -1).
A side of a rectangle is three times the other. If the perimeter increases by 2%, find the percentage increase in the area of the rectangle.
The line \(2y = x + 3\) meets the circle \(x^{2} + y^{2} - 2x + 6y - 15 = 0\) at points M and N, where N is in the first quadrant. Find the coordinates of M and N.
Three school prefects are to be chosen from four girls and five boys. What is the probability that :
(a) only boys will be chosen ;
(b) more girls than boys will be chosen ?
