A box contains identical balls of which 12 are red, 16 white and 8 blue. Three balls are drawn from the box one after the other without replacement. Find th...

(a) Simplify \(\frac{3}{m + 2n} - \frac{2}{m - 3n}\) (b) A number is made up of two digits. The sum of the digits is 11. If the digits are interchanged, the ...

(a) What is the 25th term of 5, 9, 13,... ? (b) Find the 5th term of \(\frac{8}{9}, \frac{-4}{3}, 2, ...\). (c) The 3rd and 6th terms of a G.P are \(48\) and...

A simple measuring device is used at points X and Y on the same horizontal level to measure the angles of elevation of the peak P of a certain mountain. If X...

(a) In the diagram, BA is parallel to DE. Find the value of x. (b) Illustrate graphically and shade the region in which inequalities \(y - 2x < 5 ; 2y + x \g...

(a) Prove that the angle which an arc of a circle subtends at the centre is twice that which it subtends at any point on the remaining part of the circumfere...

The universal set \(\varepsilon\) is the set of all integers and the subset P, Q, R of \(\varepsilon\) are given by: \(P = {x : x < 0} ; Q = {... , -5, -3, -...

(a)(i) Given that \(\log_{10} 5 = 0.699\) and \(\log_{10} 3 = 0.477\), find \(\log_{10} 45\), without using Mathematical tables. (ii) Hence, solve \(x^{0.826...

(a) Simplify, without using Mathematical tables: \(\log_{10} (\frac{30}{16}) - 2 \log_{10} (\frac{5}{9}) + \log_{10} (\frac{400}{243})\) (b) Without using Ma...