The second term of a geometric series is \( -\frac{2}{3} \) and its sum to infinity is \( \frac{3}{2} \). Find its common ratio.

How many different 8 letter words are possible using the letters of the word SYLLABUS?

Let '*' and '^' be two binary operations such that \(a * b = a^2b\) and \(a ^ b = 2a + b\). Find \((-4 * 2) ^ (7 * -1)\).

The population of a village decreased from 1,230 to 1,040 due to breakout of an epidemic. What is the percentage decrease in the population?

Evaluate: \(16^{0.16} \times 16^{0.04} \times 2^{0.2}\)

The area \(A\) of a circle is increasing at a constant rate of \(1.5\text{ cm}^2\text{s}^{-1}\). Find, to 3 significant figures, the rate at which the radius...

Make x the subject of the formula:

The interior angle of a regular polygon is five times the size of its exterior angle. Identify the polygon.

Evaluate: