Mathematics Past Questions and Answers

If \(2, (k+1), 8,...\) form an exponential sequence (GP), find the values of k.

If \(\frac{1}{5^{-y}} = 25(5^{4-2y})\), find the value of y.

Simplify: \((1 - \sin \theta)(1 + \sin \theta)\).

Given that \(3x + 4y + 6 = 0\) and \(4x - by + 3 = 0\) are perpendicular, find the value of b.

Given that \(x * y = \frac{x + y}{2}, x \circ y = \frac{x^{2}}{y}\) and \((3 * b) \circ 48 = \frac{1}{3}\), find b, where b > 0.