Determine the coefficient of \(x^{2}\) in the expansion of \((a + 3x)^{6}\).

Express 75° in radians, leaving your answer in terms of \(\pi\).

If \(\log_{9} 3 + 2x = 1\), find x.

Evaluate \(\cos (\frac{\pi}{2} + \frac{\pi}{3})\)

Simplify \(\sqrt[3]{\frac{8}{27}} - (\frac{4}{9})^{-\frac{1}{2}}\)

A function is defined by \(f(x) = \frac{3x + 1}{x^{2} - 1}, x \neq \pm 1\). Find f(-3).

Find the remainder when \(5x^{3} + 2x^{2} - 7x - 5\) is divided by (x - 2).

A binary operation * is defined on the set of real numbers R, by a* b = -1. Find the identity element under the operation *.

Solve \(3x^{2} + 4x + 1 > 0\)