The normal to the curve \(y = 2x^{2} + x - 3\) at the point (2, 7) meets the x- axis at the point P. Find the coordinates of P.

The second term of a geometric progression is 3. If its sum to infinity is \(\frac{25}{2}\), find the value of its common ratio.

Five digit numbers are formed from digits 4, 5, 6, 7 and 8. (a)How many such numbers can be formed if repitition of digits is (i) allowed (ii) not allowed? (...

(a) The roots of the equation \(x^{2} + mx + 11 = 0\) are \(\alpha\) and \(\beta\), where m is a constant. If \(\alpha^{2} + \beta^{2} = 27\), find the value...

(a) Write down the first four terms of the binomial expansion of \((2 - \frac{1}{2})^{5}\) in ascending powers of x. (b) Use your expansion in (a) above to f...

An object is projected vertically upwards. Its height, h m, at time t seconds is given by \(h = 20t - \frac{3}{2}t^{2} - \frac{2}{3}t^{3}\). Find (a) the tim...

Forces \(F_{1} = (10 N, 090°), F_{2} = (20 N, 210°)\) and \(F_{3} = (4 N, 330°)\) act on a body at rest on a smooth table. Find, correct to one decimal place...

Solve \(x^{\frac{2}{3}} - 5x^{\frac{1}{3}} + 6 = 0\).

Four boys participated in a competition in which their respective chances of winning prizes are \(\frac{1}{5}, \frac{1}{4}, \frac{1}{3}\) and \(\frac{1}{2}\)...